^ LIBRARY OF THE University of California. Class r QUADRATIC PARTITIONS. BY Lt.-Col. ALLAN CUNNINGHAM, R.E., FELLOW OF KINOES COLLEGE, LONDON ; MEMBER OF THE LONDON MATHEMATICAL SOCIETY, &C. LONDON : FRANCIS HODGSON, 89 Farringdon Street, E.C. 1904. CONTENTS. PAGES Table of Primes (p), and Factors of (p— 1), up to p ~J$> 100,000 ... 1—240 „ p = (a 2 + b 2 ), (c 2 + 2d 2 ), (A 2 +3B 2 ), i(L 2 +27M2), up to i?> 100,000 1—240 „ p = e 2 -2f2, up to ^25,000 1—69 „ i? = (x 2 -5y 2 ), i(X 2 -5Y 2 ), (t 2 + 7u 2 ), i^+llw 2 ), up to j»> 10,000 1—31 ,, i> = A /2 -3B /2 , up to i?>10,000 241,242 „ p=x' 2 + 5y /2 , upto p> 10,000 243,244 „ p = G* + 6H?, up to /?> 10,000 245,246 „ i? = G ,2 -6H' 2 , up to p > 10,000 247,248 „ j3 = t' 2 -7u /2 , up to j?> 10,000 249,250 „ i? = | 2 + io^ up to p > 10,000 251,252 „ p = ^-iOt,' 2 , up to p^> 10,000 253,254 „ ^^v^-llw' 2 , up to i?>10,000 255,256 „ p or 2p = t 2 ±Du 2 , D = 13, 14, up to p> 1000 257 ,, p or 9p - t 2 ±Du 2 , D = 15, 17, up to j»> 1000 258 „ p or ip = t 2 ±Du 2 , D = 19, uptoj3>1000 259 Least Solutions (t, v) of t 2 -D.u 2 = ±1 [D ^ S 2 ], up to D > 100 ... 260 Multiple Solutions (t, u) of t 2 — D.u 2 = Tl, up to D>20 261 Least (oddj Solutions (t, v) of t 2 -D.u 2 = ±2, up to D j> 500 ... 262 Least (odd) Solutions (t, v) of t 2 -D.u- = ^4, up to D> 1000, and Values of D, [ > 1 500] , giving no solutions 263 Least (odd) Solutions (t, v) of t-'-Du 2 -= ±8 and ±16, up to D>500, and Values of D, [ > 1500], giving no solutions of t 2 -Du 2 = ± 16 264 APPENDIX. CORRIGENDA IN WORKS CONSULTED CORRIGENDA IN PRESENT WORK 265, 266 On back of Table of Contents. 217227 CORRIGENDA. i. Corrections in (p—1) column, pages 1-240, [Argument;/] : Argt. : p = 28621 ; 92189 ; 92569 ; 95569. Corrn. : p-\ = 4-27-5-53 5 4-19-1213; 8.3.7.19.29; 16.3.11.181. ii. Corrections in 2-ic parts, pages 1-240, [Argument p~] : Argt. : p = 311 Corrn. : x = 34 9679 ; 62563 ; 92569. x, y = 218, 87 ; L = 320 ; c, d = 119, 198. Minor Corrigenda. i. Insert dashes ( — ) missing in column named : Page 31, p = 10007, Col. of t, u ; Page 216, p = 88853, Col. of A, B. ii. Insert commas ( , ) missing in column named : Page: 4 ; 7 ; 9 ; 22 ; 23 ; 63 ; 84 ) 120. p - 881 ; 1549 ; 2243 ; 6581 ; 7027 ; 22157 ; 31177 ; 46411. Col. of v, w ; t, u ; c, d ; t, u ; v, w ; a, b ; A, B ; c, d. iii. Change commas (,) to dots (.) in column of (p — 1), [Argument p"]: Page 34, p - 10903 ; Page 46, p = 15527. iv. Insert dots (.) missing in column of {p — i), pages 1-240. as below [this is merely imperfect inking"] : Argument p. 463 5333 11173 15629 26681 48221 59H9 78241 88867 941 6029 11321 15727 26713 48661 633 1 1 78721 96517 1021 6673 "353 16103 28151 48679 63337 80077 97127 1723 6857 1 344i 16493 29137 48767 63367 83641 2207 7177 13963 22153 33i9i 491 17 66161 84163 3i87 7723 14011 22717 37039 556o3 66683 84827 3257 901 1 14083 24001 42061 56179 69239 85889 35ii 9433 14407 25453 43283 56453 70061 86851 3631 10391 1 5401 25819 45779 56767 71947 88237 3967 10459 155" 25951 46301 57731 72661 88741 N.B.— The Author would gladly receive a Note of any further Errata. They may be sent to care of the Publisher. p^Jc, y 100,000 detailed below, for all values of D < 20 and j=. k 2 . 8 ; and also (at the end) solutions of the Pellian equations t 2 — DV = ±1, ±2, ±4, ±8, ±16. la. Main Table (pages 1-240) . — This contains columns headed P 5 P— 1 5 a,b ; c,d ; e,f ; A,B ; L,M ; x,y ; X,Y ; t,u ; v,w. The first (p) column contains a complete list of all the primes (p) < 100,000 ; the second (p — 1) column contains the factorisation of (p— 1) into its prime factors ; the remaining nine columns contain the quadratic parts of the following quadratic partitions of each prime (p) — when capable thereof — as below, up to the limits (of p) stated: — 2-ic Parts : a, b Partition : p — a 2 + b- Limit : p > 100,000 2-ic Parts : Partition : p 7 •5y 2 c, d c 2 +2d 2 100,000 X, Y e, f e 2 -2f 2 25,000 A, B ; A 2 + 3B 2 ; 100,000 ; t, u £(X 2 -5Y 2 ); t 2 + 7u 2 ; i(v 2 + w 2 )j p> 10,000 L, M 100,000 Limit lb. Short Tables (pages 241-256). — These contain the quad- ratic parts of the following partitions of all primes (p) — when capable thereof — under 10,000 ; each kind in a separate table :— 2-ic Parts : A', B' *', y G, H G', H' Partition : p - A' 2 -3B' 2 x +5y G 2 + 6H 3 G /2 -6H' 2 Pages : 241, 242 243, 244 245, 246 247, 248 2-ic Parts : t', u' I, V t, n' v', w'. Partition : p = t' 2 -7u' 2 | 2 +10rj 2 |' 2 -10rj' 2 v ,2 -llw ,s Pages : 249, 250 251, 252 253, 254 255, 256. INTRODUCTION. lc. Short Tables (pages 257-259). — These contain the quad- ratic parts (t, u) of the following partitions of all primes (p) — when capable thereof — under 1000; each kind in a separate table : — p = t 2 + 13u 2 ; p or 2p = t 2 + 14u 2 ; p = t 2 +15u 2 ; ^ = t2-13u 2 ; p = t 2 -14u 2 ; p = t 2 -15u 2 ; 257 ; 257 ; 258 ; p or 9p — t 2 + 17u 2 ; p or 4p = t 2 +19u 2 . p =t ,2 -17u' 3 ; p = t' 2 -19u' a . Page : 258 ; 259. Id. Pellian Tables (pages 260-264). — These contain solutions of some of the fundamental Pellian equations. Page 260 ; t 2 — D. v 2 = ± 1 ; Least solutions (t, v) up to D i> 100. ,, 261 ; t 2 — D.u 2 = Tl ; Multiple solutions (t, u), for all values of D > 20 and ^ 5 s , up to t, v of 6 or 7 figures. „ 262 ; t 2 -D.u 2 = ±2 ; Least (odd) solutions (t, u) up to D>500. „ 263 ; t 2 -D.u 2 = =F4 ; Least (odd) solutions (t, v) up to D> 1000 ; Values of D ^ 1500 giving no (odd) solutions (t, v). ,, 264 ; t 2 -D.u 2 = ±8 and ±16 ; Least (odd) solutions (t, v) up to D > 500 ; Values of D > 1500 giving no (odd) solutions (t, v). le. Corrigenda (pages 265-266) in the various works con- sulted. 2a. Arrangement of Primes. — The odd primes are printed forty on each page (pages 1-240), or forty in each ^-column (pages 241-258) ; except that the last j>colunin of each Table contains only so many as required to reach the limits stated (100,000, 25,000, 10,000, or 1000, respectively). This arrangement facilitates the counting the number of (odd) primes within a given interval, and decreases the risk of omission. INTRODUCTION. Ill 2b. Factors of (p—1). — The (jp— I) -column (pages 1-240) contains the prime factors of (p — 1) arranged in order of magnitude (of the primes) ; but the (easily recognisable) powers of the small factors 2, 3, 5, 7, 11 are printed thus (to save space) : 2, 4, 8, 16, 32, &c. ; 3, 9, 27, 81, 729, &c. ; 5, 25, 125, 625 ; 7, 49, 343; 11, 121. The (less easily recognisable) powers of other primes (> 11) are printed by repeating the primes, thus: — 13.13, 17.17, &c. ; so that no exponents are printed. 3. Quadratic Forms. — Here follows a short sketch of the properties of Quadratic Forms (t 8 ±D.u 2 ) so far as needed to make ihese Tables readily useful. 4. Signs of the 2-ic parts. — The quadratic parts (t, u) of any partition (t 2 ± D.u 2 ), being determined only from their squares, (t 2 , u 2 ) may be of either (±) sign. In many cases this does not affect the result; but, in all cases involving (t±u), (t m =fcu M ), [m, n odd], some rule is required as to the (±) sign of each " part." One such rule is : — Even numbers are considered + . Odd numbers of form (4i + 1) are reckoned + , of form (4* — 1) are reckoned — . 5. Monomorphs. — If a number (N) be expressible in only one way in the form (t 2 + Du 2 ), or only in equivalent (i.e. auto- morphic*) ways in the form (t 2 ~Du 2 ), then N is said to be Monomorph (in that form). If expressible in more than one way (automorphs being reckoned as equivalent) in any one 2-ic form, it is styled Polymorph; such a number must be composite. * For explanation of this term, see Art. 12. iv INTRODUCTION. 6. Idoneals. — There is a certain class of numbers (D) such that, if any number (N) be monomorph in a 2-ic form (t 2 3? Du 2 ), then N is either a prime or a power of a prime. Such numbers (D) are termed Idoneals*; all others are termed Non- Tdoneals. Only 65 positive Idoneals are known : these are [D in t 2 +Du ! ] : D = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 15, 16, 18, 21, 22, 24, 25, 28, 30, 33, 37, 40, 42, 45, 48, 57, 58, 60, 70, 72, 78, 85, 88, 93 ; 102, 105, 112, 120, 130, 133, 165, 168, 177, 190 ; 210, 232, 240, 253, 273, 280, 312, 330, 345, 357, 385, 408, 462, 520, 760, 840 ; 1320, 1365 ; 1848; and there are no moref < 100,000. These numbers are useful in the determination of primes of form (t 2 4-Du 2 ). Most negative numbers (D) are Idoneal ; all squares > 144, and most numbers of form D = 8 2 + l, are negative Non- Idoneals. There are only 220 negative Non-Idoneals < 1000 : those < 250 are [D in t 2 — Du 2 ], see Note t below : D - 25, 34, 37, 49, 64, 79, 81, 82, 99 ; 100, 101, 121, 136, 141, 142, 145, 146, 148, 156, 169, 178, 189, 194, 196, 197 ; 205, 219, 220, 221, 223, 224, 225, 226, 229, 235. 7. Quadratic Forms of Primes. — An odd prime (p), in order that it may be expressible in one of the forms (t 2 ± Du 2 ) — with D ~jf> 19 J and =£ &S 2 — must be of the linear form shown in the following Table. This condition suffices when ±D respectively is an Idoneal (shown by the letter I in the Table) ; but, when ±D respectively is a Non-Idoneal (marked N in the Table), p may require to be multiplied by some suitable factor (2, 4,§ &c, as shown in Table) in order to be so expressible. * This is Euler's term. t See Abstract of a Paper " On Idoneal Numbers," by the Rev. J. Cullen and the present writer jointly, in British Association Report for 1901, page 552 ; it is hoped to publish this Paper in extenso shortly. % The limit of D in these Tables being 19 (page 259). § The multiplier 9, used in the Tables (page 258) with D = 17, is unnecessarily large, INTRODUCTION. V [Note. — Whenever (=FD/p) 2 = + 1, some factor /* may always be found such that jxp = t 2 ±Du 2 ; but the only (quadratic) forms of p admitted in these Tables are those of the principal genus of the determinant (fD) of the 2 -ic form (t 2 ±Du 2 ).] N.B.— The upper half of this Table relates to D in p = t 2 + Du 2 ; the lower half relates to D in p — t 3 — Du 2 . D 1 I 2-ic Form of p. Linear Form of p. I p - a 2 + b 2 iw+l 2 I p = c 2 + 2d 2 8w+l,3 3 I p - A 2 + 3B 2 6w + l 5 I ^ = x' 2 + 5y' 2 20w+l,9 6 I p = G 2 + 6H 2 24nr+l, 7 7 I p = t 2 +7u 2 14 = A' 2 -3B' 2 12w+l 5 p = x 2 -5y 2 10-aril 6 p - G' 2 -6H' 2 24nr+l, 19 7 ^ - t' 2 -7u' 2 28nr+l,9, 25 10 ^ = |' 2 _10t7' 2 40w±l, 9 11 /> = y 2 -iiw /2 44w+l, 5,9, 25, 37 13 jy - t /2 -13u' 2 26 = t' 2 -17u' 2 34nr±l,9, 13, 15 19 p = t' 2 -19u' 2 76w + l, 5, 9, 17,25,45,49,61 ,73 VI INTRODUCTION. 7a. Quadratic Forms of Odd Composites. — An odd composite number (-ZV), in order that it may be expressible in one of the forms (t 2 ±Du 2 ) — with D > 19, and ^ k& — must be of the linear form laid down in Art. 7 for a prime ; and it is further necessary that =FD respectively should be a 2-ic Residue* of every odd prime factor of N. When ±D respect- ively is an Idoneal (marked I in Table), these conditions suffice ; otherwise — when ±D respectively is a Non-Idoneal (marked N in Table) — N may require to be multiplied by some suitable factor (2, 4, &c, as shown in Table). Ex.— Is N = 3231 1 = G- 2 + 6H 2 ? Here D = 6, JT- 24rc + 7 = 79.409. Also 79 = 8i + 7 = 12/+ 7; 409 = 8i + l = 12/+7. V409 j = V409/ * V409/ * V409/ = -i)( + i)(-i) = +n + i)( + i)( + i)= + ij As D m + 6 is an Idoneal, and all the conditions are satisfied, therefore ^=G 2 + 6H 2 . 8. 2-ic Forms of Even Numbers. — It is beyond the scope of this Introduction to give the conditions for expressibility of even numbers (N) in general in given 2-ic forms. The general conditions that t 2 — Du 2 = N (an even number) will be given below only for those even numbers N = ±2, ±4, ±8, ±16 dealt with in these Tables (pages 262-264). 8a. Case of t 2 — Du 8 = N — ±4, ± 16. — Solutions (t, u) in even numbers are obvious. Thus — If (t , u ) be solutions of t 2 — Du 2 = + 1 or — 1, then (2t , 2u ) are solutions of t 2 -Du 2 = +4 or -4 ; and (4t , 4u ) are solutions of t 2 — Du 2 = + 16 or — 16. * If the factors of N be unknown, this condition is difficult to test ; in fact, it requires the establishment of a congruence of form t' 8 ±D . u' 2 = (mod N). INTRODUCTION* Vll By far the more important solutions, however (and the only- kind dealt with below), are t, u both odd when D is odd ; t even, u odd when D is even (2). Such solutions are possible, with few exceptions, in the following cases (see Tables, pages 263, 264) ; the exceptions occur only* when — D is Non-Idoneal. The symbols D', 8' are here used : thus D = D', 5=5' when t 2 -Du 2 = - 1, [t, v both odd] Then the forms of D required are N=+i; when (1) D = 85 + 5; (2) D = 4(45 + 3) ; (3) D = 325 ^ q (1a). iV=-4; when (1) D = 85 + 5 = D' ; (2) D = 45 = 45' ^ D (1b). N= + 16; when (1) D =85 + 1^ Q; (2) D = 165 = 16(8i + 3), T 2 -5y 2 = -2 (1c). i\ r =-16; when (1) D = 85 f 1 = D' ^ Q ; (2) D = 165 - 165' ^ q... (Id). 8b. Case of t 2 -Du 2 = N = ±2, ±8. — As in Art. 8a, the solutions sought are t, u both odd when D is odd ; t even, u odd when D is even (2). Now, let q x , q 2 , q s be the types of the primes (of the three kinds below) entering into D, viz. : ^ = 8k +1, ? 2 = 8k + 3, 2 8 = 8k + 7; and let II (q) denote a product of primes of type q. Also let the five kinds of D be denoted thus — T>[ = 85 + 1 = n (ft), T>" = 85 + 1 = n (q 2 ) or n {q 2 and q x ), D[" = 85 + 1 = n (q s ) or n {q 3 and q x ), D 2 = 85 + 3 = n (q 2 ) or n (? 2 and q x ), D 3 = 85 + 7 = n (q 3 ) or IT {q 3 and q x ) ; so that D is denned by its linear form 88 + 1, 3, 7, and by the sort of primes (q v q 2 , q s ) composing it. Then solutions of the kinds stated in (2) are possible, with few exceptions, for the forms of D stated below ; the exceptions occur only* when — D is Non-Idoneal. * And are in fact a proof of the Non-Idoneality of — D. Vlll INTRODUCTION. N= +2; when D - D 3 ; 2D[, 2T>'" ; 2D 3 (2a). N = -2 ; when D = D 2 ; 2Dj, 2D" ; 2D 2 (2b N = +8 ; when D = D(, D(" ; 4D 3 : 8D(, 8D;" ; 8D 3 ... (2c). N 8 ; when D = T>[, D("; 4D 2 ; 8D(, 8Di' ; 8D 2 ... (2d). Note that t 2 — Du s = ±2 are not possible together ; t 2 — Du 2 = ±8 are possible together only when r-Du : = —1. t 2 — Du 2 = ±2 and = ±8 are not possible together. t 2 — Du 2 = ±2 is not possible when D = 43. t 2 — Du 2 = ±8 is not possible when D = 168. 9. 2-ic Forms of ^.N. — Given a number (N) expressible in a 2-ic form (t 2 ±Du 2 ), it is sometimes useful* to know the lowest multiple (say /x .N), similarly expressible. The lowest factor fi required for each value of D > 19 (and ^ k . 8 2 ) is shown below : D m 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19 ; (t 2 + Du 2 ); fio - 2, 3, 4, 6, 7, 8, 11, 12, 14, 15, 16, 18, 20 ; =1 2 + D.l 2 . (t 2 -Du 2 ); fiQ= ., 2, 6, 4, 3, 2, 6, 5, 3, 2,10, 8, 5; = t 2 -D.v 2 , 0=1,2]. Given the 2-ic form of N, that of p .N can always be found by the process of Art. 10 ; given the 2-ic form of /* . iV, that of N can be found — always when ± D respectively is Idoneal, and sometimes when ±D is Non-Idoneal — by the process of Art. 15. 10. Gonformalf Multiplication. — When N = N X .N 2 , and each of N lt N 2 is given expressed in the same 2-ic form as A^-^DnJ, n 9 = %+Du\ (3), then N can be directly expressed (in two ways) in the same 2-ic form, say JV=T 2 + DU 2 (3a), * The 2-ic form of /u .JV is sometimes quite as useful as that of N: e.g., the form ip = L 3 + 3(3M) 2 was used by Jacobi for determining when (a/p) 3 = 1, and the form 4p = X 2 — 5Y 2 was used by Lloyd Tanner for work with complex 5-ic numbers. f A term introduced by the Author to express multiplication with preserv- ation of 2-ic form. The process is of more general application than here shown: see the Author's Paper on "Connexion of Quadratic Forms," in London Mathematical Society's Proceedings, Vol. xxviii., 1896, Arts. 6-9. INTRODUCTION. IX where T = t t t 2 ^ D^o,, U = i^n a ?b u^ \_opp. signs in T, U] ... (3b). Similarly, if JV^ = t 2 — Du^, N t = tj— BnJ (4), then AT = T 2 -DU 2 (4a), where T = t^ ^ D 1 u 1 u 2 , U = t^ q* u^ [same signs in T, U] ... (4b). These formulae give in each case two forms for N, on account of the double (±) sign in T, U. Similarly, if N = ^.N^.N^... N„ and each of N lt N Si . . . , N r be given expressed in the same form, say .A 7 ,. = t; - . ±Du,., then N t . JV 2 can be compounded as above into iV 12 in two ways ; N u . JV 3 can be compounded as above to form N m in four ways ; and so on. Finally, the product- form of N as T 2 ± D . U 2 will be produced in 2 r_1 ways; and the same 2 rl forms will result in whatever order the factors are combined. The above process — styled Gonformal* Multiplication — is of great use for finding the quadratic partitions of large composite numbers (JV), when the similar partitions of the factors of N are known. ^.—Express N - 32311 in the form (G- 2 + 6H 2 ). [Shown to be possible in Art. 7a.] Here i\ r = 79 . 409 = (5* + 6. 3 2 ) (5 2 + 6 . 8 2 ). [See page 245.] .-. 2V- (5. 5^6. 3. 8) 2 +6. (5. 8^3. 5) 2 = 119 2 + 6.55 2 = 169 2 + 6.25 2 . 11. Unit-Forms. — The equation t 2 — D.t/ 2 = 4-1 always admits of solution (where D -=f=. S 2 ) ; and in some cases r" — D . v = — 1 also admits of solution (see Art. 13). These are called Unit- forms. Now, by conformal multiplication (Art. 10), (t 2 -D. v 2 ) 2 = (r* + D. v*y-T>. (2tv) 2 = (±1) 2 = +1 ... (5a), ( T 2 _ D , v >y - ( t 3 + 3 d .rJy-B . (3t 2 v+ 2 v 8 ) = (±1) 3 = dbl (5b). Similarly, any power of a unit-form may be reduced to the same form : (T 2 -D.v 2 r = <-D.^ = (±ir = ±i (5c). * See footnote f on page viii. C T„ T„ T„ T, X INTRODUCTION. Thus the equation t 2 — D.v 2 =+1 always admits of an infinite number of solutions, as does also r" — D.v' = — 1 (if soluble at all). If the successive solutions, obtained as above, be denoted by 0o> v o)> ( T l> V l)> ( T 2> v 2 )> &c -> of t 2 — D.v 2 =+1: (tJ, v{), (T2, v 2 ), &c, of t' — D.v' =—1, they are connected by the following relations, which enable (t m , v n ), (t'„ v' H ) to be calculated in succession, either upwards or downwards, from any given adjacent pair : — T )i+1 = 2r x .T n — T n _!, v rt+1 = 2T 1 .v n —v n _ l (6a) ; i = 2T t . < — <_!, i4 + i = 2t 1 .u, , 1 — V,',.! (6b) ; -t„,_! = 2t 1 / .t, , ) , v n — v n _j = 2r[.v n (6c) ; r«-i = 2tJ.t m _„ v,'— l>i_, = 2t[.w m .! (6d). The solutions (tj, v x ), (tJ, vQ may be looked on as fundamental ; as from these — along with t = 1, v = (in all cases) — all the rest may be derived. Table of Least Solutions (page 260). — This Table gives the least solutions of t 2 -D. u 2 = + 1 and of t /2 -D. u' 2 = -1 (when possible), up to D > 100. Table of Multiple Solutions (page 261).— This Table gives a number of the successive solutions of T 2 -D.tr = ±l, for all values of D^>20, and =£ 8 2 , up to values of r, v of 6 or 7 figures. 12. Automorphs. — Any number (N) expressible in the form N ■= t 2 — D.u 2 can be expressed in an infinite number of ways in that form by conformal multiplication (Art. 10) by any power of the unit-form t 2 — D.v 2 = 1. Thus — N = t 2 -D . u 2 = (t 2 -D . u 2 ) (t 2 -D . v 2 )" m (t 2 -D . u 2 )(t 2 - D . v 2 ) = (tr, ( ^D.Uv„) 2 -D.(tv n ^UT, ( ) 2 [same sign in each bracket] ... (7). Denoting the successive values of (t, u) thus obtained by (t , u ), (t„ u,), (t 2 , u 2 ), &c, they are connected l>y the relatione : t M+ i = 2T 1 .t n ^t M .„ u H+1 = 2T 1 .u n ~u rt _ 1 (8), where (r a , v x ) is the least solution (t x > 1, Vj > 0) of t 2 — Dv a = + 1 ; these enable the quantities t M + 1 , u n+J to be calculated in sue- INTRODUCTION. XI cession from each pair of preceding values (t M , u H ), (t M _ b u„_,). Any particular values (t r , u,.) can be obtained from the preceding values (t r _ 1 , u,._,), or from the succeeding values (t r + 1 , u,.^) by the formulae : t r = t r _ j . T , + D . U r _! . Wj, u,. = t r _! . v x + u,..! . t, ... (9a) ; t r = t r + 1 .T 1 ^D.Tl r + 1 . V,, U,. = t,. + 1 . V 1 r^Vi,. JrX .r l ... (9b). Such forms, so obtainable from one another, are thereby equivalent (not independent) forms : they are styled Automorphs. 13. Antimorphs.— The two forms (t 2 — D.u 2 ), (D.u' 2 — t' 2 ), having the same D, are styled Antimorphs. A number A T , expressible in either form, is also expressible in the other forms when (and only when) a solution of r' — D . v~ = — 1 is possible. And, if a number N be given expressed in either form, it can (under the above condition) be directly expressed in the other form in an infinity of ways by conformal multiplication by odd powers of the negative unit-form. Thus — (rf-D.vf)" = (rf-D.v; 2 ) = (-1)" = -1, [n odd]. K= t 2 -Du 2 =-(t 2 -D.u 2 )(T^-D../';) = D.(tvn^nr n ) 2 -(trn^D.uv n )\ [nodd] (10a), N' = D.u ,2 -t' 2 - -(Du' 2 -t /2 )( T ,?-D.u;0 = (tT^D.u^^-D.^^UT;,) 2 , \\n odd'] (10b). [the same signs to be used in each bracket]. Hereby N is expressed in two series of forms ; the forms in either series are Automorphs of each other, and each series is the Antimorph of the other. And it is evident that such Antimorphs are equivalent (not independent) forms. The values of D which yield solutions of t /2 — Di/ 2 = — 1 are 1° D = 45+1 = prime; 2°*D = 5 2 +1 (11a); 3° when £D = 45 + 1 = prime, and — D is Idoneal (11b) ; 4° when D or |D = D^DgD^... ~=f=- D, (where each factor is of the kinds 1°, 2° above), and — D is Idoneal (lie) ; 5° when the continued fraction expression of VD contains a double middle term ( 1 1 d) . [Note that Case 5° includes all the preceding, but is troublesome to apply unless suitable Tables be available.] * This kind is omitted in Degen's Tables. Xli INTRODUCTION. 14. Base-forms. — Among the infinity of ways (Automorphs) in which a number (A T ) may be expressed in the form (t 2 — D.u 2 ), the most important is that in which t, u are the least possible : this is called the Base-form, and the values t , u therein are Tiase-vahtes of t, u. The following formulae, adapted from (9b) :-- t ( ._, = t v .T x ^D.u,.^, u,._! = t,..v l ^ u,..^ (12) (wherein v v v x is the least solution of t 2 — D.v 2 = +1), express the values t,._ 1? u,._! in terms of the succeeding t,., u,., and supply an easy test whether a given pair (t n u r ) are the lowest or not. For, if t r , u r be the lowest, then t r .j < t r and u r _! < u,.. These, when reduced, will be found to give as the condition* that t,., u,. should define the Base-form : t r > r -^.u, (13). v i If this condition is not satisfied, then a lower pair (t,._!, u^) will be given by (12), and the test again applied ; if it still fails, then t,._ 2 , u,._ 2 may be found, and so on. For facility of application, the reduced value of the ratio (t 1 + 1)-t-v 1 required in (13) is given below for all values of D > 20 and zfz 8 2 . D = 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20. (t 1+ 1) + W! = 2, 3, |, 3, 3, 4, V, V-, 4, f|, 4, 5, ±f , §, fg, 5. [All the Tables of p = t 2 — D.u 2 of the present work have been tested by this rule, and the Base -forms only are given.] Ex.— Given N - 6737 = 194 2 - 1 1 . 53 2 . Here t r = 194 < y . 53 ; so that lower values exist. Now r\ = 10, v x = 3 ; .•. tr-i- 194.10^11.63.3 - 191, u,._i = 194. 3 ~ 53. 10 = 52. Also ir-\ = 191 > V- . 52. Therefore N = 191 2 - 11 . 52 2 is the Base-form. * This very simple condition does not seem to have been published before. INTRODUCTION. Xlll 15. Conformal Division* — When a number (JV) is the quotient of F-z-f, and each of F, /is expressible in the same 2-ic form, Say F=T 2 ±T).U\ /=t 2 ±D.u 2 (15). This will in many cases involve — always when ±D is Idoneal, and also in many other cases — that N also is expressible in the same form, say J J N=x 2 ±D.y 2 (15a). When the forms (15) of F f f are both given, the actual ex- pression of N in that form — when such is possible — may be effected as follows, provided that / be monomorph, i.e. expres- sible in only one way (Art. 5) in the given form. Case i. — FsrTH-D.U*, /=t 2 + D.u 2 , tf = aj* + D.y s ... (16). Take X = tT^DuU, Y - tU^buT [opp. signs in X, Y] ... (16a). Case ii. — F = T 2 -D.U 2 , /=t 2 -D.u 2 , N=x>-V.y 2 ... (17). Take X = tT^D.uU, Y=tU^uT [same signs in X, Y] ... (17a). In both Cases i., ii. each of X, Y has two values (due to the double signs in X, Y) : one pair of these will always give X-r-/, Y-irf fractional, (these are of no further use) : one pair will give X-irf, Y+f both integral (whenever the process is possible) . Then, for use in N : x = X-i-f, y = Y-r-f (the integer values) ... (18). When /is not monomorph, i.e. when / is expressible in more than one way in the given form, it can always be resolved into factors (prime or composite), say / =s f u f 9 ./».../„ each of which separately is monomorph in the form. The above process may * Conformal Division. — A term introduced by the Author to denote division with preservation of form. For a full explanation of the process, see the Author' 8 Paper on " Connexion of Quadratic Forms" in Proceedings of the London Mathematical Society, Vol. xxviii., 1896, Arts. 15-23. XIV INTRODUCTION. then be applied, first, to F-r-f x , yielding as result F x ; and may next be applied to F x -r-f 2 , yielding as result F % \ and so on, ending with operating on F r _i-—f„ yielding finally N in the form required. [Note that the process way succeed (i.e. one value of X+f, Y-r-f may turn out integers), even when / is not monomorph, provided that the given form of F is the particular one out of all its polymorphs (Art. 5) suited to the given form of/; but this cannot be detected a priori. ~] If .F = T 2 -D.U 2 , /=t 2 -D.u 2 , they may— if they are not Base-forms — be reduced to Base-forms (Art. 14), so as to reduce the magnitude of the numbers (T, U, t, u) to be operated on before applying the process of this Article. This process is very useful for effecting the 2-ic partition of a large number i\T, when the similar partitions of some multiple of it, say F =f.N, is known (provided that of / also can be found) . t? rr Ar , fl ,A n 30024 2 -10.805 2 F £ , XT „ , A - Ex. - Given N = 78409 = ^^^ - j \ And *-*-!** (known to be possible, because — 10 is Idoneal). Applying the test (13), J^is seen to be a Base- form. Also / = 11414 = 2.13.439 = (6 2 -10.1 2 ). (23 2 -10. 3 2 )=/ 1 ./ 2 . Thus /is not monomorph (being a product of like forms, Art. 10) ; but its factors f x = 26, / 2 = 439 are both monomorph (for /, = 2x prime, and / 2 = prime, Art. 5), and are both Base-forms (Art. 14). Theu M = /, ; take j, - * - 3002 4*- !0 ■ 805* /,/»' /, 6=-10.1- -p "XV To reduce F x — — , take x x = — - , y x = (the integer values). /i /i /i 6.300024-10.1.805 --.<, 6.805-1.30024 ofto * 1 = 26 = 6619; ft = = 969. Therefore F x = 6619 2 - 10 . 969 2 (which is a Base-form), a N= F ^= 6619 2 -10. 9 69- an / 2 232-10. 3* * X Y Now take a* 2 = --, y< i = —2 (the integer values). Then /a A X x 23.6619 + 10.3.969 ... Y x 23.969 + 3.6619 Q . Xc — -J = — = 413 : y 2 = . = zz = 96. - / 2 439 • 2 / 2 439 Therefore N = 413 2 - 10. 96 2 (the Base-form of N, see Art. 14). INTRODUCTION. XV 16. Composition of Forma. — When a number N is given ex- pressed in two different forms (i.e. with different values of D), N = r 2 + mt 2 = s 2 + mu 2 [w, n may be i.ra^ »] ... (19). st) 2 — rt(ru) 2 _ (mst) 2 — mn (ru) 2 _ .F mt 2 — nv? (mt) 2 — mwu 2 f m, AT m(st) 2 — w(ru) 2 (mst) 2 — ww(ru) 2 F Then JV = - \ J 3 = ' , ^ V, = — , suppose (19a). i?Mfe of Signs. — The sign (T) attached to mn in F, f will be according as the signs of the given m, n are #£« or unlike. Here .F, / are of the same form. Some reduction may usually be made of the fraction F-i-.f by cancelling out common factors of mt, u, but without destroying the similarity of form. Writing the reduced result : *=5=^?=f urn, t — mnn J then, if N be actually expressible in the same form, N = x^—mny 1 (as will always be the case if — mn be Idoneal, and in many other cases), the actual expression of N in that form can be effected by conformal division (see Art. 15). Ex.— Given N= 78409 - 161 2 + 2.162 2 = 278 2 + 5.15 2 , find N=x' i -\(iy 2 (a possible form because —10 is Idoneal). Bv (1&0 N = (2-162.278) 2 -10(161.15) 2 = F ' v ; ' (2. 162) 2 -10. 15 2 / 30024 2 -10.805 2 F' „ ir ... ^, .. = ~To8 2 -10 5 2 = ~f ^ 7 cancelhn ^ out the factor 3 3- The reduction of this last result by conformal division has been given in the Example of Art. 15, giving N~ = 413 2 - 10 .96 2 . This process is very useful for finding directly the partition [x 2 — (±ra)(d=w)y 2 j of a large number N from two (given) partitions above. E.g. — The partition N = # 2 — D.y" of a large number (iV) by any tentative process is a distinctly difficult matter. The easiest way is in many cases to form, first, two partitions iV=r 2 + wt 2 = s 2 + wu 2 (m, n both +), such that mn = D, by some tentative process (as these are much easier to form than the required partition); and then find JV=# 2 — D.y 2 by the above direct process. XVI INTRODUCTION. Ex.— Given ^=5. 2^+1, find N = x 2 -5y 2 . Here it was found convenient first to determine N = a 2 + b 2 = *12455 2 + 3556 2 , and N = x /2 + 5y' 2 = *2766 2 + 5 . 5659 2 . The above process (26) gives, on reduction, N= x 2 -5y 2 = 417791 2 — 5. 186752 2 , wherein 2x < 5y ; and this, not being the Base-form (Art. 14), is reduced to the Base-form, wherein 2x > 5y, by (12), giving If- x 2 -5y 2 = 25079 2 -9604 2 . 17. Cubic Forms (x 3 =Fy 3 )-r-(x=Fy). — These cubic forms are interchangeable with the 2-ic form (A 2 +3B 2 ) ; for let N = (x 3 -y 8 )-Kx-y) = x 2 +xy + y 2 = A 2 + 3B 2 , [N odd] . (20). Both cubic forms are included in (20), since each of x, y may be either + or — . Then x, y and A, B may be interchanged by the following formulas : — i. x = 2B, y = A— B ; A = §x + y, B = |x ; [x even, y odd]. ii. x = A-B, y = 2B ; A = x + |y, B = |y ; [x odd, y even]. iii. x = B + A, y = B-A; A - |(x-y), B = |(x + y) ; [x, y both odd]. 18. Binomial Congruences. — The following binomial con- gruences : — x* = -l, x A = ±l, x* = -l, x« = -l, x u = -l, (mo&p), can be directly solved from the simpler 2-ic partitions [the (a, b), (c, d), (e, f), (A, B), (A', B')] of this work. Let x,, x„ a? 4 , x 6 , x n respectively be a root of the above (the suffix showing the congruence to which x belongs). The solutions (x) below are given in the form of fractions, x = X-f- Y (modp), which are to be used by determining m so that either of (Xzkmp) + Y or (Y±mp)-t-X = x, an integer ... (21). The value of x so found is a root of the congruence. Thus the solution of binomial congruences of the 2nd, 3rd, 4th, 6th, 12th * These two partitions were found by the Rev. J. Cullen, S.J. f INTRODUCTION. XV11 order is reduced — with the help of 2-ic partitions — to the solution of a linear congruence, so that they can be all solved* for all primes > 100000 (the limit of these Tables, pages 1-240). i. Let p = a 2 + b 2 . Then the two roots x 2 are either pair of #2 = ±a/b or = ±b/a (22). ii. Let p = A 2 + 3B 2 . Then A-B ^B_. B + A B-A * 3 ~ 2B ' A-B' B-A' BTA (23) ' The + pair are the roots of x* = + 1, and the — pair are the roots of x' A = — 1. iii. Let p = a 2 + b 2 = c 2 + 2d 2 = e 2 -2f 2 . The four roots are any sett of x = ± — a=fc b ± — a ±b ± A 5l±^ . A a±t> c ' a or b ' 2d ' a or b ' e * a or b ' 2f ' a or b ' *^*^ < 2 *>- iv. Let j3 = a 2 + b 2 = A 2 + 3B 2 - A' 2 - 3B' a . The four roots x 6 are given by x = x 2 .x 3 (25). They are also given as any set of *-*(***fi."»(*^).tf(*M;-* ■)• v. Let p = a 2 + b 2 - c 2 + 2d 2 = e 2 - 2f2 = A 2 + 3B 2 = A' 2 - 3B /2 . The eight roots x 12 are given by ^ m ^ ^ vi. Let # H be a root of x n =\,n odd and prime to 6. Then each root (x n ) may be combined J with the above roots to give roots of higher congruences. Thus Xin = X t .X ni X Zn 3 X 3 .X n , X± n = X 4 .X n , X 6n S #6-^, #12n 3 iP 12 . a? n ... (27) give roots of x*» = -l, **» si, **3-L z 6M = -l, a; 12 " = -l. * The Author has prepared Tables of solutions of the congruences x n =fl = 0, (mod p and p K ), for all values of n^p 15, complete up to j9 and p K "jf 10,000, and also for very many 5-figure primes in the case of n "jf> 8. It is hoped to publish these in due course. f The sets formed with (a, b) , (c, d) were communicated to the Author by Mr. A. E. Western. X This rule makes it easy to extend the Tables mentioned in the footnote * to much higher powers. d XV111 INTRODUCTION. Ex.— Let p = 1009 = 15 2 + 28 2 = 19 2 + 2.18 2 = 31 2 + 3.4 2 . . 28 . 28 + 8072 . ,, n L H S± „ S± _ T __ =±5 40. u. x 3 31-4 27 + 6046 =+63 aroot of *»= +1. 2.4 8 19 15-28 _ , 247 = =F 247 ±3 027 _. ±139 m. ^4-± 2>18 . 15 ==F 4>2 7.5- 4.27.5 27 = ±139±6045 = , 92 27 iv. x 6 = ±540.634 = ±342360 = ±309. v. x l2 s 634. (±192) s ±121728 = ±648. 19. Residuacity of Small Bases. — One of the most important applications of quadratic partitions is the ease with which they enable the possibility of dividing the small factors n = 3, 4, 8, out of the exponent (p — 1) in Fermat's congruence [a^^^+l (mod^))] to be tested, whereby the latter may be reduced to the simpler form : a<*-» + * == sfcl (mod 2>) (28). Rules for doing this in the case of all the small bases d=a = 2, 3, 5, 6, 7, 10, 11, 12, and also for the factor 16* when a = ±2, have been collected together in a simple form in the late Mr. C. E. Bickmore's two Papers f "On the Numerical Factors of (a n — 1)." Also rules as to casting out the small factors 3, 4, reduced to a simple form in the case of all the small prime bases q j>31, 29, respectively, are given in Pere Th. Pepin's " Memoire sur les lois de reciprocity relatives aux residus des puissances." J The above rules require the use of the (a, b), (c, d), (A, B), (L, M) partitions only, and these are given in the present Tables (pages 1-240) for all primes > 100,000. Further simple rules as to casting out the factor 4 applicable to any base (q) whatever, for which one of the partitions p = t 2 ±^ii 2 is known, are given in the present Author's Paper § " On 4-ic Residuacity and Reciprocity." * This rule was discovered by the present Author. t Messenger of Math., Vol. xxv., 1895, pages 1-44; Vol. xxvi., 1896, pages 1-38. J Atti delV Accad. Pont, de Nuovi Lincei, Rome, 1878. § Proc. Lond. Math. Soc, Ser. 2, Vol. i., pages 132-150. OFTHE UNIVERSITY OF INTRODUCTION. xix 20. Congruential Uses. — Quadratic partitions may be treated as Congruences (to modulus p), and are often of great use (along with other data) in solving congruences of form a* = zkb y , a*\ ^ = ±1, where x, y, x\ y' are the sought exponents of the (given) bases a, b. When no conditions are given as to x, y, x', y f , the number of solutions is infinite ; it is often desirable that one of the exponents — say y, y' — should be a minimum; this makes the solutions definite. An example will make this clear. Ex.— Let p = 2521. Find 2* ■ ±b y , 2* '. b y ' a ±1, when b = 3, 5, 7 ; y, y' to be minimum. The Tables (pages 10, 247, 249) give p = 2 3 .3 2 .5.7+l (1); - 3 6 + 7.2 8 (2); - 2 12 -7.3 2 .5 2 (3); - 3 2 .l7 2 -5.2 4 (4) ; - 5 2 .17 2 -6.2M 2 (5). Here (1) and (3) give 2 15 = -5 (6); (1) and (2) give 2 10 . 3 8 = — 1 (wherein y' is not a minimum) (7) ; (4) and (5) give 2 . 3 3 . V = 5 3 , and (3) gives 2 24 = 7 2 . 3 4 . 5 4 . These last give 2 25 = 3 . 5? s 3 . ( -2 105 ), by (6), whence 2 80 . 3 = - 1 . . . (8). Again, (3) gives 2 12 = 7. 3 2 . 5 2 = 7.3 2 . 2 30 , by (6) ; [Now multiply by 2 130 .] Hence 2 142 = 7. (3 2 . 2 160 ) a 7, by (8) (9). Here (6), (8), (9) are the required results with y, y' a minimum. Note that equation (2) leads to result (7), wherein y' is not minimum ; it does not seem easy to determine a priori what partitions (or other data) will lead to minimum values of y, y'. 21. Calculation of Haupt- Exponents (£). — The Haupt- Exponent (£) of a base a to a given prime modulus (p) is the least power (£) yielding a^ = + 1 (mod p) . The 2-ic partitions of p often yield great help — along with other data — in determining Haupt-exponents, and sometimes suffice of themselves without other data, as will be seen by some examples. Ex.— Let p - 2521. Find the £ of the bases 2, 3. In the Example of Art. 20, the results were found : 2 10 . 3 8 = -1 (7); 2 80 .3 = -1 (8). XX INTRODUCTION. Here, from (8), 2« 40 .3 8 = + 1, whence, by (7), 2 630 = -1 and 2 1260 = + 1 , and, from (7), 2 80 . 3 M = + 1, whence, by (8),- 3 s3 = -1 and 3 126 = + 1. Here it has been possible to obtain the Haupt- exponent (|) of the bases 2, 3 by the use of 2-ic partitions only, without other data. It is clear that for this purpose a sufficient number of suitable 2-ic partitions (or other data) must be available to yield two (independent) congruences connecting the bases in question. 21a. If the Haupt-exponent (£) of one base (a) be given, then, to obtain the Haupt-exponent (rj) of any other base (6), it will suffice to obtain one * congruence of form a x = ± b y or a x .b y = ±1, connecting a, b. Ex.—Qixea. 2 1260 = + 1 (mod p) = 2521, find the Haupt-exponent of 5. In the Example of Art. 20, it was found that 2 15 = — 5. Here 2 630 = -l, whence (2 15 ) 42 =-1, giving (-5) 42 = -1, whence 2^= +1. Caution. — In finding Haupt -exponents as in Arts. 21, 21a by the use of congruences of form a x = ±b y , a x . b y = ± 1 , it is necessary that the exponent (y } y') of the base (b) whose Haupt-exponent (77) is sought should be a minimum ; otherwise the value of 77 in the final congruence b 7 * = + 1 is liable not to be a minimum (as is required). 22. Number of Primes. — Here follows an Abstract showing the total number of (odd) primes of various forms which are < 1000, 10000, 100000 respectively. Limit. Total. + 7 + 7 CO + 22- + + + so + CM + < 1000 < 10,000 < 100,000 167 1228 9591 80 609 4783 87 619 4808 81 612 4784 86 616 4807 37 295 2384 40 306 2387 36 300 2373 19 144 1188 14 143 1180 18 152 1189 * This process has been largely used by the Author in the compilation of a Table of Haupt- exponents of all the bbses 2, 3, 5, 6, 7, 10, 11, 12 (mod p) up to jt?3f> 10,000 ; this work — undertaken in conjunction with Mr. H. J. Woodall, A.R.C.Sc— is now far advanced, and should shortly be published. ^ INTRODUCTION. XXI 23. Earlier Tables. — The only important published Tables of 2-ic partitions (known to the Author) are the two following, briefly alluded to as i. Jacobi's, (a, b), (c, d), (A, B) ; ii. Reuschle's, (a, b), (c, d), (A, B), & (p-l). i. C. G. J. JacobVs Tables, published in CrelWs Journal, t. xxx., 1846, pages 174-180 ; and again in Jacobi's Opuscula Mathematical Bd. i., Berlin, 1846, pages 326-332. These give (a, b), (c, d), (A, B) as follows :— Crelle, pp. Jacobi, pp. Tab. I. gives (a, b) up to p^ 12,000 ; 174-176; 326-328. Tab. II. gives (A, B) up to p > 12,010 ; 177-179; 329-331. Tab. III. gives (c, d) up to jo>>6000; 180; 332. Tables I., II. were computed by Herr Zornow, Table III. by Dr. Struve. For List of Errata, see Appendix, page 265. ii. C. G. Reuschle's Neue zahlentheoretische Tabellen, &c.,* Stuttgart, 1856. These give (a, b), (c, d), (A, B), (p—l) as follows : — Tab. Ill.a, pages 23-25, gives (A, B), (L, M) up to p = 5743. Tab. Ill.b, pages 26-28, continues (A, B) up to p$> 13670. Tab. III.c, pages 29-32, continues (A, B), where (10/js») 3 = 1, up to p > 50000. Tab. IV.a, pages 32-38, gives (a, b) up to p^> 12400 ; and (c, d), when p = 8w+ 1, up to p'jp 12400. Tab. IV.b, pages 38-41, continues (a, b), when (l0/p) 2 = +1, up to p$> 25000. Tab. IV. c, page 41, continues (c, d), when (10/p) 4 =+l, up to p-fr 25000. Tab. V.a, b, c, pages 42-61, gives {p—l) resolved into its prime factors up to p^> 15000. The restrictions on the form of p in Tab. III.c, IV.a, b, c causes these to be very incomplete Tables of (A, B) when p > 13670, of (a, b) when p > 12400, and of (c, d) throughout. These Tables are unfortunately badly printed, and contain many Errata. For List of Errata, see Appendix, page 266. * Published originally in a "Program" of the Konigl. Gymnasium at Stuttgart, 1856 ; and again, separately, by Schliessing, of Stuttgart. xxii INTRODUCTION. 24. Present Work. — Here follows a short account of the preparation, mode of checking, and history of the present work : — (1) Primes (p).—The list of primes up to p$> 100000 (pages 1-240) was copied off Barlow's* Tables, and checked off Lambert's*. Tables. (2) Factors of (p— 1). — Up to p '$> 15000 these were copied off Reuschle's Tables V.a-c, and then checked {oft Barlow's* and also off Sehaller's* Tables. From p > 15000 the factors were taken, as far as possible, off Barlow's Table, and checked off Sehaller's Table ; when beyond the limits of Barlow's Table, they were taken off Goldberg's* Table. (3) 2-ic Partitions (a, b), (c, d), (A, B), (L, M). — These were copied off Reuschle's Tables (Ill.a, b, c ; IV.a, b, c ; see Art. 22) up to the limits of his work, and checked off Jacobi's Tables (see Art. 22) up to the limits given by him. Beyond Reuschle's limits the greater part were specially com- puted t+ for this work. (4) Partition (X, Y).— This was copied off Prof. Lloyd Tanner's Table.* (5) All other 2-ic Partitions (pages 1-259) . — These were specially computed t for this work. (6) Least Solutions of t 2 — Du 2 = ±1 (page 260).— These were copied off Degen's Table, H and checked off Legendre's Table. H (7) Least [odd) Solutions of t 2 -Du 2 - ±2, ±8, ±16 (pages 262, 264).— Computed specially by the Author himself || from the data in Degen's Table. I (8) Least (odd) Solutions of t 2 -Du 2 = ±4.— Copied from Cayley's Table. * (9) Checking. — The whole of the Tables have been checked § at least once throughout (by recomputing), and in some parts twice. This checking was in addition to that obtained by the collation of the printed Tables, [paras. (2), (3) above]. * For full titles of these Tables, see the Appendix, pages 265, 266. t Partly by the Author himself, partly by two Assistants (Miss G. Stockton -Smith and Miss A. Woodward) under his superintendence. t Whilst this was in progress some assistance was derived from some MS. Tables prepared by the late Mr. C. E. Bickmore, completing Reuschle's Tables of (a, b), (c, d), (A, B), (L, M) up to j9> 30,000 ; these were kindly lent to help in this work. || With some help kindly given by the Rev. J. Cullen. U C. F. Degen's Canon Pellianus, Hafniae, 1817 ; and A. M. Legendre's Theorie des Nombres, 3* Ed., Paris, 1830, Tab. X. § Mostly by the Author's Assistants (Miss B. B. Haselden, Miss B. E. Haselden, Miss G. Stockton- Smith, Miss C. Woodward) under the Author's superintendence . INTRODUCTION. XX111 25. Corrigenda (on other Tables). — Errata were discovered in all the printed Tables used in the preparation of this work. The Corrigenda necessary, or in some cases (Tab. 5, 6) a reference only to the actual Errata, are given in the Appendix (pages 265, 266). 26. History of the Tables. — These Tables were begun by the Author in 1897 ; the original computations were carried out by himself with the aid of Assistants as stated above, under his superintendence and at his own expense. The work was laid before the Mathematical Tables Committee of the British Association in 1899, and continued under its auspices from 1899 to 1901 ; it was recommended for publication to the Association by this Committee and by the full Committee of the Mathematical and Physical Section of the Association in 1901 : but the Association was unfortunately unable to grant the necessary funds at the time, and the Mathematical Tables Committee was not reappointed. A grant of £30 was made in 1900 from the Government Grant Fund administered by the Royal Society towards the expense of checking the Tables ; and a grant of £80 was made in 1902 from the Royal Society's Publication Fund towards the cost of printing and publication. 27. Acknowledgments. — The Author is indebted to the Rev. J. Cullen, S.J., for some help in preparing the Tables of t 3 — Dv z = ±2, 8, and for advice in preparing this Introduction. QUADRATIC PARTITIONS. p P -\ a b c d e f A B L M x y X Y t u v w 2 i i, 1 0, 1 2, 1 3 2 — h 1 — 0, 1 °, 2 — — — 1, 1 5 4 1, 2 — — — — 5, 2 5, 1 — 3, 1 7 2-3 — — 3, 1 2, 1 1, 1 — — 0, 1 — 11 2 -5 — 3^ 1 — — — 4, 1 7, 1 2, 1 0, 2 13 4-3 3, 2 — — 1, 2 5i 1 — — — — 17 16 1, 4 3, 2 5, 2 19 2.9 — i, 3 — 4, 1 7, 1 8, 3 9, 1 - — — 23 2. II — — '■ 5> 1 — — — — 4, 1 9, 1 29 4-7 5, 2 — — — — 7, 2 11, 1 1, 2 — 31 2-3-5 — — 7* 3 2, 3 4, 2 6, 1 12, 2 — 5, 3 37 4-9 1, 6 — — 5, 2 ii, 1 — — 3, 2 7, 3 41 8-5 5, 4 3, 4 7, 2 — — 11, 4 13, 1 — — 43 2-3-7 — 5, 3 — 4, 3 8, 2 — — 6, 1 — 47 2.23 — — 7, 1 — — — — — 12, 2 53 4.13 7, 2 5, 2 6, 4 59 2.29 — 3, 5 — — — 8, 1 16, 2 — 15, 1 61 4-3-5 5, 6 — — 7, 2 i, 3 9, 2 i7, 3 — — 67 2.3.11 — 7, 3 — 8, 1 5, 3 — — 2, 3 13- 3 71 2-5-7 — — ", 5 — — 14, 5 17, 1 8, 1 3, 5 73 8.9 3, 8 1, 6 9, 2 .5, 4 7, 3 — — — — 79 2.3-I3 — — 9, 1 2, 5 i7, 1 18, 7 19, 3 4, 3 — 83 2.41 — 9, 1 89 8.11 5, 8 9, 2 11, 4 — — 13, 4 19, 1 — 9, 5 97 3 2 -3 9, 4 5, 6 13, 6 7, 4 19, 1 — — — i7, 3 101 4-25 1,10 — — — — 11, 2 22, 4 — — 103 2.3.17 — — n, 3 10, 1 13, 3 — — — 4, 6 107 2-53 — 3, 7 10, 1 — 109 4-27 3,i° — — 1, 6 2, 4 17, 6 21, 1 9, 2 — 113 16.7 7, 8 9, 4 11, 2 — — — — 1, 4 21, I 127 2.9.7 ~ — i5, 7 io, 3 20, 2 — — 8, 3 131 2-5-13 — 9, 5 — — — 16, 5 23, 1 — 137 8.17 11, 4 3, 8 13, 4 — — — — 5, 4 3, 7 139 2.3.23 — n, 3 — 8, 5 23, 1 12, 1 24, 2 — — 149 4-37 7,10 — — — — 13, 2 26, 4 11, 2 — 151 2.3.25 — — 13, 3 2, 7 19, 3 14, 3 27, 5 12, 1 — 157 4.3-I3 11, 6 — — 7, 6 14, 4 — — — 23, 3 163 2.81 — h 9 — 4, 7 25, i — — 10, 3 16, 6 167 2.83 — — 13, 1 — — — — — — 173 4-43 i3. 2 179 2.89 — 9, 7 — — — 28,11 29, 5 2, 5 21, 5 I s-\ 4 O i*n U QUADRATIC PARTITIONS. p *-l a b c d e f A B L M x y X Y t u V w 181 4-9-5 9,10 — — 13, 2 7, 5 19, 6 27, 1 — 25, 3 191 2.5.19 — — 17, 7 — — 14, 1 28, 2 4, 5 15, 7 193 64-3 7,12 11, 6 15, 4 1, 8 23, 3 — — 9, 4 — 197 4-49 1,14 13, 2 — 199 2.9.11 — — 19, 9 14, 1 Hi 5 18, 5 29, 3 — 20, 6 211 2-3-5-7 — 7, 9 — 8, 7 13, 5 16, 3 32, 6 6, 5 — 223 2-3-37 — — *5i iL 28, 2 — — 1, 9 227 2. 113 15, 1 229 4-3-19 i5> 2 — — n, 6 22, 4 27,10 3ii 3 5, 9 233 8.29 13, 8 i5, 2 19, 8 — — — — 11, 4 — 239 2.7.17 — — 17, 5 — 22, 7 31. 1 8, 5 — 241 16.3-5 15, 4 l 3, 6 21, 10; 7, 8 17, 5 3 1 , 12 33, 5 — — 251 2.125 — 3, 11 — — — 16, 1 3 2 , 2 — 27, 5 257 256 1,16 15, 4 17, 41 — — 18, 8 263 2.131 — — 19, 7 - — — — 16, 1 269 4.67 i&io — — 1 — — 17, 2 34, 4 — 30, 4 271 2.27.5 — — 17, 3 14, 5 29, 3 26, 9 33, T | ' — "277 4-3- 2 3 9> J 4 — — *3i 6 26, 4 — — : 5, 6 — 281 8-5-7 5> l6 9,10 17, 2! — 19, 4 37, 7|i3i 4 — 283 2-3-47 — 11, 9 — |i6, 3 32, 2 — — — — 293 4-73 17, 2 307 2.9.17 — 17, 3 — 8, 9 16, 6 — — — — 311 2-5-31 — — 19, 5 — — 24,13 37, 5 — 12,10 313 8-3-13 13,12 5,i2 21, an, 8 35, 1 — — — 19, 9 317 4-79 11,14 17, 2 27, 7 331 2-3-5-u — 13, 9 — 16, 5 1, 7 24, 7 37, 3 18, 1 35, 3 337 16.3.7 9,16: 7,12 25, I2JI' 5, 7 — — 15, 4 347 2.173 — 3>i3 2, 7 — 349 4.3.29 5,i8 — — 7,10 37, 1 23, 6 39, 5 — — 353 32.11 17, 815, 8 19, 2 9,11 359 2.179 — — J 9, I — — 22, 5 4i, 7 4, 7 — 367 ! 2.3.61 — — 23, 9 2,11 35, 3 — — — 37, 3 373 j 4-3-3 1 7,18 - — 19, 2 13, 7 — — n, 6 379 2.27.7 — 19, 3 — 4,11 29, 5 28, 9 39, 1 6, 7 25, 9 383 2. 191 — — 25, 1 1 — — — — 39, 1 389 4-97 17,10 — — — 37,M 4i, 5 *9i 2 15,11 397 4-9- 1 1 19, 6, — — 17, 6 34, 4 — — — 2,12 401 16.25 1,20 3,14 23, 8 — — 41,16 43, 7 17, 4 30, 8 409 8.3.17 3,2011,12 21, 4 19, 4 3i, 5 27, 8 4i, 3 " — 419 2. 11. 19 - 9,i3 — — 3 2 , 11 4ii 1 24,10 3<\ •b* Y7 *$ QUADRATIC PARTITIONS. p p-l a b c d e f A B L M x y X Y t u v w 421 I 4-3-5-7 15^4 — — 11,10 19, 7 21, 2 42, 413, 6 10,12 431 2.5.43 — — 23, 7 — — 26, 7 43, 5i6, 5 — 433 16.27 17,12 19, 6 21, 2 1,12 2, 8 — — — 29, 9 439 2.3.73 — — 21, 1 14, 9 28, 6 22, 3 44, 6 — 443 ! 2. 1 3. 1 7 — 21, 1 ^— — — — — 10, 7 21,11 449 64.7 7,2021, 2 29,14 ■ — 23, 4 46, 8 1, 8 39, 5 457 8.3.19 21, 413^2 23, 6 5." 10, 8 — — 3, 8 — 461 4-5- 2 3 19,10 - — — 3MO 43, 1 — — 463 2 3.7. 1 1 — — 25, 9 IO,II 23, 7 — — 20, 3 3*i 9 467 2.233 — 15, Ir 3, J 3 479 ! 2.239 — — 23, 5 . — 22, 1 44, 2 — — 487 2.243 — — 27,11 22, I 25, 7 — — 12, 7 43, 3 491 2.5.49 — 21, 5 — | — 44,i7 47, 7 22, 1 — 499 2.3.83 — 7,i5 — 16, 9 3 2 , 6 48,19 49, 9 18, 5 40, 6 503 \ 2.251 — — 29,13 — — — — — 509 4.127 5>22 — — — 23, 2 46, 4 — 45, 1 521 8-5-13 II,20 3>!6 23, 2 — 29, 8 47, 5 — ^^ 523 2.9.29 19, 9 — 4,13 43, 3 — — — — 541 4-27-5 21,10 — — 23, 2 29, 7 39,H 47, 3 17, 6 — 547 2.3.7- *3 23, 3 — 20, 7 1, 9 — 22, 3 — 557 4-139 19,14 - 23, 2 — 563 2.281 I 5 > 1 3 569 8.71 13,20 21, 8 3M4 — 43, l6 49, 5 11, 8 — 571 2-3-5- I 9 11,15 — 8,13 31, 7 24, 1 48, 2 2, 9 — 577 64.9 1,24 17,12 33,i6 23, 4 11, 9 — — — 47. 3 587 2.293 3, J 7 48, 2 593 16.37 23, 8 9,16 25, 4 599 2.13.23 — — 29,11 — — 38,13 49, 1 16, 7 36,10 601 8-3-25 5,24 23, 6 27, 8 I3, 12 26, 8 51,20 53, 9 — — 607 2.3. 101 — — 25, 3 10,13 49, J — — — 613 4.9.17 17,18 — — 5, T 4 47, 3 — 19, 6 — 617 8.7. 11 19,16 15^4 25, 2 — — 13, 8 42, 8 619 2.3.103 — i3,i5 16,11 17, 9 32, 9 5i, 5 — i,i5 631 2-9-5-7 — — 27, 7 22, 7 43, 5 26, 3 52, 6 8, 9 7,i5 641 128.5 25, 4 21,10 29,10 - 31, 8 53, 7 23, 4 45, 7 643 2.3.107 — 25, 3 — 20, 9 40, 6 — — 4i, 9 647 2. 17. 19 — — • 35,i7 — — — — — 27,13 653 4.163 13,22 25, 2 5i, 1 659 2.7.47 9,!7 — — — 28, 5 56, 10 22, 5 — 661 4.3-5-n 25, 6 6 7 10 s 7 19,10 49, 3 51 29, 6 57, 11 I3,i5 QUADRATIC PARTITIONS. p p-l a b c d e f A B L M x y X Y t u V w 673 32.3.7 23,12 5,i8 3M2 25, 4 37, 7 — — 15, 8 — 677 U-I3-I3 1,26 — — 683 2.11.31 — 21,11 — 26, 1 24,14 691 2.3.5.23 — 23, 9 — 4,i5 8,10 36,11 53, 3 ! — 17,15 701 4-25.7 5,26 — — 41,14 53, 1 1,10 — 709 4-3-59 15,22 — — 11,14 53, 1 27, 2 54, 4 3,io i9>*5 719 2-359 — — 3M* — — 58,23 59,11 Sh 5 727- 2. 3. 121 — — 27, 1 22, 9 44, 6 — 53, 3 733 4.3.61 27, 2 — 25, 6 5°, 4 — — 739 2.9.41 — I7,i5 — 8,15 16,10 28, 3 56, 626, 3 — 743 2.7.53 — — 29, 7 — — — — 20, 7 — 751 2.3.125 — — 33,i3 26, 5 41, 7 34, 9 57, 7 2 4, 5 23,15 757 4.27.7 9,26 - — i3,H 29, 9 — — 27, 2 38,12 761 8.5.19 19,2027, 4 31,10 — — 29, 4 58, 8 — — 769 256.3 25,1211,18 29, 6 1,16 49, 5 33, 8 59, 9 — 773 4.193 17,22 — — — — — [■ 54< 4 787 2-3-I3 1 — 25, 9 — 28, 1 3 1 , 9 — — — . — 797 4.199 11,26 — — — — — — , — 3,i7 809 8.101 5,28 3,20 29, 4 - — 53,2o 59, 7 19, 8 — 811 2.81.5 — |!9,i5 - 28, 3 56, 2 44,i5 57, 1 ~ — 821 4-5-41 25,i4 ! — — — — 29, 2 58, 411,10 — 823 2.3-I37 — i — 29, 326, 7 5,ii - 16, 9 49, 9 827 2.7.59 — 27, 7 1 — — 22, 7 — 829 4.9.23 27,10 — — ! 2 3, 10 7,n 57,22 61, 9 — 29,15 839 2.419 — : - — 29, 1 — — 38,11 59, 5 — 45, " 853 4.3.71 23,l8 — — 29, 2 35, 9 — i — ^ — 857 8.107 29, 427, 8 37,!6 — 859 2.3.11.13 — 29, 3 — 28, 5 i3,n 48,17 59, 3 — 3],i5 863 2.431 — — 31, 7 — — — 1 4,ii 36,14 877 4.3.73 29, 6 — — 17,14 59, 1 — 25, 6 881 16.5. n 25,16 9,20 41,20 — — 31, 4 62, 8 — 57 5 883 2.9.49 1,21 — i 4,i7 47, 7 - | 6,11 56, 6 887 2-443 — 35,i3 — — — — — 907 2.3.151 — 5,21 — 120,13 19,11 — — 30, I 8,18 911 2.5.7-13 — — 31, 5 — — 34, 7 67,13 8,11 60, 2 919 2.27.17 — — 37,1526, 9 52, 6 42,13 61, 324, 7 — 929 32.29 23,20 27,10 31, 4 — — 47,16 61, ij — 30,16 937 8.9.13 19,2417,18 35, I2 i3, I 6 61, 1 — — — — 941 4-5 47 29,10 - — — — 31, 2 62, 4 — 947 2.11.43 ~~ i5,!9 — 10,11 57, 7 QUADRATIC PARTITIONS. p H abed e f A B L M x 7 X Y t u v w 953 8.7.17 13,2821,16 3 1 , 2 — — — 29, 4 — 967 2.3.7.23 — — 43,2i 10,17 4i, 9 — — 20, 9 — 971 2.5-97 — 27,11 — — — 64,25 67,111 45,*3 9771 16.61 3*i 4 3^2 37,M — — — — 23. 8 27,17 983 2.491 — — 35, 11 "~" — — — — 5 1 , 11 991 2.9.5.1 1 33, 7 22,13 61, 3 46,15 63, 112,11 20,18 997| 4-3-83 3Ji 6 — — 5,i8 10,12 — . — ! — — 1009 16.9.7 15,2819,18 39,i6 3 T , 4 43, 9 33, 4 66, 8 1,13 — 1013 4.11.23 23,22 — 9.19 1019 2.509 — 21,17 — — 32, 1 64, 2 26, 7 — 102l' 4-3-5 J 7 ™*3° — — 7,18 14,12 39,1° 67, 9 — 50,12 1031 2.5.103 — — 37,i3 ■ — — 34, 5 68,10 32, 1 — 1 033 8.3.43 *3»|3*» 6 41,18 29, 8 53, 7 — — 5, 12 : — 1039 ! 2.3.173 — — 33, 5 26,1 1 59, 5 38, 9 69.11 41,15 1049 8.131 5.32 9,22 43,2o — 37, 8 7i,i3 — ^^9 1 051 2325.7 — 13,21 — 32, 3 64, 2 36, 7 72,14 22, 9 1061 4-5-53 31,10 — — — — 59,22 67, 7 i9, IQ 63, 5 1 063 2.9.59 — — 35, 9 14,17 65, 1 — — — — 1 069 4-3-89 13,30 — — 3 1 , 6 62, 4 33, 2 66, 4 — — 1087 2.3.181 — — 33, 1 2,19 55< 7 — — 32, 3 28,18 1091 2.5.109 — 133, 1 — — — 44,i3 67, 5 1093: 4- 3- 7- 1 3 33, 2 — 11,18 22,12 — — 29. 6 59, 9 1097 8.137 29,16 33, 2 35^ 8 1103 2.19.29 — — 41,17 — — — — 16,11 21,19 1109 4.277 25,22 — — — 67,26 71,11 — • 6,20 1117 4-9-3 1 21,26 — 23,1-4 65, 3 — — 33, 2 — 1123 2.3.11.17 — 3 1 , 9 — 16,17 35,ii — — 64, 6 1129 8-3-47 27,20 29,12 39,M 19,16 67, 1 43. J 2 69, 7 11,12 — 1151 2.25.23 — — 47,23 - — 34, 1 68, 2 — 1153 128.9 33, 8 1,24 35, 6 3i, 8 7,i3 — — 61, 9 1163 2.7.83 — 21,19 — 34, 1 — 1171 2.9-5-13 — 17,21 — 32, 7 11,13 36, 5 72,10 18,11 47,i5 1181 4-5-59 5,34 — — — — 41,10 73,ii — 18,20 1187 2-593 — 33, 7 ,, 2,13 — 1193 8.149 *3,3 2 15,22 35, 4 69, 1 1201 16.3.25 25.24 7,24 43, 1 8 1,20 59, 7 39, 8 77,i5 33, 4 — 1213 4.3.101 27,22 — — 25,14 17,13 — — 3 1 , 6 1,31 1217 64.19 3 J ,i6 33, 8 35, 2 1223 2.13.47 — — , 35, 1 — — — — — — - 1229 4.307 35, 2 — — — — 47,U 7i, 5 23,10 QUADRATIC PARTITIONS. V p-1 a b c d f A B L M X Y t u 1231 1237 1249 1259 1277 1279 1283 1 289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 2.3.5.41 4-3- io 3 32.3- J 3 2.17.37 4.11.29 2.9.71 2.641 8.7.23 2-3-5-43 16.81 4-25-13 2-3-7-31 2.653 2.659 8.3.5.H 2.3.13.17 16.5-17 2.683 4-343 4.3.5-23 2.3.233 128.11 .423 ( 2.9.79 1 427 2.23.31 I4294.3.7.17 1433 1439 8.179 2.719 1 447| 2.3.241 1 451; 2.25.29 1 453: 4.3. 121 1459 1471 1481 1483 9,34 — 3,25 15,32 n,34 4i,i534, 5 — 35, 2 49,24 7,20 39,u 15,23 33, 10 29,!5 35, 6 27,17 13,24 3,26 35, 8 1,36 25,26 5,36 31,20 37, 2 i5,34 25,28 21,22 — '33,i3 41,14 — 28,13 37, 623,16 4,i9 45,!9 37, 5 39,io 47,21 37, 2 37, 1 34, 7 2.729 2.3.5-49 8-5-37 2.3.13.19 43,i5 47,2o 39, 7 23,3° 37, 8 3,38 9,26 27,19 1,27 1487 2.743 1489 16.3.31 1493 1499 1511 4-373 2.7.107 2-5- I 5 I 1523 2.761 35,1633,14 — j 5,27 33,2029,18 7,38 - — 21,23 — 39, * 49,22 41,11 45,!7 39, 5 41,10 47,i9 39, 43, 1 3 11,20 2,21 19,13 41,11 53, 9 66,25 57,2o 5217 43,n 78,31 — 37, 4 67, 5 36, 1 25, J 3 — — I 61,22 55, 9 — 73, 9 - 7i, 3 — 7i, 1 - 7i, 3 4,i4 37, 2 34, 9 10,21 29,!4; 38, 5 4f. 8 79,i5 — 10,13 91,2529, 8 72, 2 — — 17,12 73* 5 36, 1 76,10 73, 3 82,16 3i,i3 68, 6 20, i< 7*i 5 38, 1 1,22! 28,15! 38, 3 20,19 17,20 35, J 3 67, 7 56,10 76, 2 37,i3 77, 1 69,26 38, 3 73,28 12,13! 32, 7 1,14 3,H 77, 9 76, 6 79, II 3 I > 8| 24,11 58,12 69, 5 57,i3 65, 9 40,18 45, J 7 19,21 72, 2 53,i5 12,22 39, 1 9 75, 1 29,21 77,3o 38, 1 64,23 48,13 54,i7 59,2o 47,12 68,25 46,11 81,1327,10 76, 2 16,13 77, 5 38, 1 — 9, T 4 79, 9 — ! 77, 3 36, 5 77, 137, 4 54,i6 60,14 3 1 , 2 81,11 79, 7 83,13 — 7i, 9 11,14 34, 7: 26,11; 59,i5 45,!9 15,23 69,11 QUADRATIC PARTITIONS. V P -l a b c d e f A B L M x 7 X Y t u V w 1531 2.9.5.17 — 37, 9 32,13 7,i5 44, 9 87,i7 — . — 1543 2.3.257 — 5M3 26,17 77, 3 — — — 76, 6 1549 4-9-43 35.i8 " 31.14 11,15 63,22 79, 3 3 l . 61,15 1553 16.97 23.32 39. 4 41, 8 1559 2. 19.41 — — 53.25 — — 58,19 79, 1 — — 1567 2.27.29 — — 55.27 22,19 79, 1 — — — 52,18 1571 2.5-I57 — 39. 5 — — 76,29 83," — 72,10 1 579| 2.3.263 — 11,27 16,21 32,14 52,15 81, 7 2.15 — 1583 2.7.113 — — 41, 7 . T— — — — 20,13 — 1597 1 4-3-7-19 21,34 — — 25,18 5°, 1 2 — — 15.14 — 1601 64.25 1,40 33.i6 49.20 — — 4i, 4 82, 8 — — 1607| 2.11.73 — — 43. « — — — 40, 1 57,i7 1 609| 8.3.67 3.4o 31.18 41, 6 29,l6 i9,i5 67,24 81, 5 — 10,24 1613 '4.13-31 13.38 1 619 2.809 39. 7 — 88,35 89,17 38, 5 — 1621 1 4.81.5 39.io — 13,22 79, 3 Si»i4 ^3, 9 37, 6 70,12 1627 2.3.271 . — 13.27 — 40, 3 80, 2 — — — — 1 637 4.409 31,26 — 27.23 1657 8.9.23 19.36 37. 12 53.24 35.J2 7o, 8 — — 1663 2.3.277 — 4i, 3 34,i3 73. 7 — 40, 3 — 1667 2.49.17 — 33.17 22,13 — 1669 4-3-139 15.38 — — 37,io 67, 9 43. 6 86,12 — — 1 693 4-9-47 37,i8 — — 41, 2 47,13 — — — — 1697 32.53 4i, 4 27,22 47,16 - 78, 8 1699 2.3.283 — 4i, 3 — 32,15 64,10 48,11 89.15 — 80, 6 1709.4-7-6i 35.22 — — 47,10 9i>i7 41, 2 81, 5 1 721 8.5.43 11,40 39.!° 43. 8 — 61,20 83. 1 — 3,25 1 723 2.3.7 41 — 29,21 — 20,21 40,14 — — 34, 9 — 1 733 4-433 17,38 - 19.14 — 1 741 4-3-5- 2 9 29,30 — 17,22 49.13 79.3o 87,11 — 67,15 1 747 2.9.97 17,27 — 40, 7 61,11 — — 3°. JI ^3, 3 1 753 8.3.73 27.32 41, 6 49,18 5.24 10,16 — — — 26,24 1 759 2.3.293 — — 47.15 26,19 3i.i5 42, 1 84, 2 24,13 — 1 777 16.3.37 39.!6 25.24 43. 6 7,24 14,16 — — — — 1783 2.81. 11 — — 45.li 14,23 83, 3 79, 9 1 787 2.19.47 — 27.23 — — - - — 38, 7 63.17 1789 4.3.149 5.42 — — 41, 6 82, 4 87.34 9i.i5 33.io — 1801 8.9.25 35.24 i,3° 51,20 37,i2 74, 8 91.36 93.17 3.!6 — 1811 2.5.181 1 — • 33.19 — — — 44, 5 88,10 — — 1823 2.911 — 49.17 — — — — ~~ ~~ QUADRATIC PARTITIONS. p p-\ a b c d e f A B L M x J X Y t n v w 1831 2.3.5.61 — — 43, 3^34,15 68,10 74,27 87, 7 16,15 85, 3 1847 2.13.71 — — 43, 1 — — — i — — , — 1861 4-3-5-3I 3^30 — — 43, 2 37,i5 59,i8 87, 5 — 1 — 1867 2.3.311 — 43, 3 — 28,19 85, 3 — — — i — 1871 2.5.11.17 — — 47,i3 — — 46, 7 92,14 32,n 75,13 1873 16.9.13 33,28 35>i8 55,24 41, 8 65,11 — — 9,16 34,24 1877 4.7.67 41,14 43, 2 — 1879 2-3-3 r 3 — — 5M9 2,25 73, 9 78,29 89, 9 — 7i,i5 1889 32.59 17,40 33,20 49,i6 — — 47, 8 94,16 — — 1901 4.25.19 35,26 — — — — 49,10 97,19 23,14 27,25 1907 2-953 — 15,29 — 48,22 1913 8.239 43, 8 39,i4 59,28 — — — — 11,16 — 1931 2.5.193 — 3,3 X — — — 44, 1 88, 2 1 1933 4.3-7-23 13,42 — — 31,18 62,12 — ! — 4i, 6 — 1949 4.487 43,io — — — — 73,26: 89, 5 1 1951 2.3-25. J 3 — 49,i5 38,13 M7 86,33 93,i3 — 73,i5 1973 4.17.29 23,38 — ! — 81,11 1979 2.23.43 — 27,25 — — — 68,23 89, 1 — — 1987 2-3-33 1 — 23,27 — 20,23 89, 1 — — — — 1993 8.3.83 43,12 29,24 45, 4 35,J6 13,17 — — — — 1997 4.499 29,34 25,14 — 1999 2.27.37 — — 57,25 26,- 2 1 52,14 98,39 99,i9 44, 3 — 2 003 2.7. 11. 13 — 9,3i 34,u 24,26 2 011 2-3-5-67 — 43, 9 — 44, 5 59,i3 56,15 93, JI 38, 9 5,27 2 017 32.9-7 9,44 37,i8 45, 2 17,24 34,i6 — — 15,16 7,27 2 027 2.1013 — 45, 1 2,17 87, 7 2 029 4.3.13-13 45, 2 — — 1,26 77, 9 47, 6 94,12 — 85, 9 2 039 2.1019 — — 61,29 — — 62,19 91, 5 4,i7 84,10 2 053 4.27.19 17,42 — — 5,26 83, 7 — — 45, 2 — 2 063 2.1031 — — 49,i3 — — — — — — 2 069 4.11.47 25,38 — — — — 67,22 91, 1 37,io 9°, 4 2 081 32.5.13 41,20 27,26 47, 8 — — 49, 8 98,16 17,16 — 2 083 2-3-347 — 25, 2 7 — 44, 7 23,17 — — 3°, 1 3 59,2i 2 087 2.7.149 — — 53,19 — — — — 8,17 — 2 089 8.9.29 45, 8 i7,3o 5M6 19,24 38,16 53,i2 99,i7 — — 2 099 2.1049 — 39,17 — — — 52,11 101,19 • 39,25 2 111 2.5.211 — — 47, 7 — — 46, 1 92, 244, 5 — 2113 64.3. 1 1 33,32 3!,24 49,12 41,12 82, 8 — — — 46,24 2 129 16.7.19 23,40 9,32 59,26 — — 47, 4 94, 841, 8 — 2131 2-3-5-7I — 41,15 — 16,25 9i, 3 76,27 93, 5 — — QUADRATIC PARTITIONS. p p-l a b c d e f A B L M x 7 X Yj t a V w 2 137 8.3.89 29,3643^2 47, 6 37,i6 85, 7 — — 45, 4 23,27 2141 4.5.107 5,46 — — — — 89,34 97,i3 — — 2143 2.9.7.17 — 55,2i 46, 3 92, 2 — — 36,n 61,21 2 153 8.269 37,28 45, 8 61,28 — — — 19,16 — 2 161 16.27.5 15,44 !9,30 53,i8 31,20 29,17 71,24 93, 1, 25,27 2179 2.9.121 — !,33 — 44, 9 88, 6 48, 5 96,1046, 3 79,15 2 203 2.3.367 — 5*33 — 4,27 8,18 — — — 89, 9 2 207 2 1103 — — 47, 1 — — — — 32,13 — 2213 4-7-79 47, 2 29,14 — 2 221 4.3-5-37 45»M — 47, 2 53,i5 49, 6 98,12 39,io 2 237 4.I3.43 11,46 47, 2 18,28 2 239 2.3.373 — — 49, 9 34,i9 9i. 5 58,15 99,i3 — : — 2 243 2.19.59 — 39i9 ■ — — — — — — ; — 2 251 2.9.125 — 37,2i — 8,27 16,18 84, 3 r 97, 9 2( — 2 267 2. 11. 103 — 45, IT : 57,23 2 269 4.81.7 37,3o — — 41,14 83, 9 57,i4 101,15 J , 18 65,21 2 273 32.71 47, 8 15,32 49, 8 — — — ! 2 281 8.3.5.19 45, 16 47, 6 57,22 43,!2 86, 8 51, 8 I02,l6 — 95, 3 2 287 2.9.127 ■ — ■ — 63,29 10,27 20,l8j — i — - 2 293 4-3- J 9i 23,42 — — 29,22 37,i7 5,18 91, 9 2 297 8.7.41 19,44 27,28 53,16 — — — — 43, 8 93, 7 2 309 4-577 47,10 — — — — 53,io 106,20 — 2 311 2.3.5. 7.11 — — 67,33 38,17 89, 7 54,n 107,2148, 1 35,27 2 333 4-II-53 43,2 2 — — — — — — 3i,i4 9,29 2 339 2.7.167 — 33,25 — — — 92,35 101,1334,13 — ■ 2 341 ! 4.9.5-I3 15,46 — — 37,18 74,12 69,22 97, 3 — 83,15 2 347 2.3.17.23 — 13,33 — 32,21 64,14 — 18,17 37,27 2 351 2.25.47 — — 49, 5 — — 74,2 5 97, 1 — — 2 357| 4.19-31 41,26 — — 87,13 2 371 2.3.5.79 — 47, 9 — 28,23 4i,i7 96,37 103,15 — — 2377 J8.27.11 21,44 35,24 55,i8 5,28 79, 11 — 37,i2 97, 3 2 381; 4-5.7.17 35,34 — — — — 49, 2 98, 4 41,10 30,28 2 383 2.3.397 — — 49, 3 14,27 28,18 — — • — — 2 389 4.3. i99 25,42 — — 19,26 59,i5 83,30 99, 7 11,18 — 2 393 8.13.23 37,32 9,34 49, 2 — — — — — • — 2 399 2. 11. 109 — — 49, 1 — — 62,17 101,11 — 75,19 2 411 2.5.241 — 27,29 — — — 104,41 107,19 — • — - 2 417 16.151 49, 4 45, J 4 53,H — — — — 25,16 — 2 423 2.7.173 — — 59,23 — — — — 20,17 21,29 2 437 4.3.7.29 49, 6 43, 1 4 c 1,19 13,18 10 QUADRATIC PARTITIONS. V P -l a b c d e f A B L M x y X Y t u v w 2 441 8.5.61 29,40 33.26 67,32 - — 61,16 103,13 — — 2 447 2.1223 — — 55,i7 — — — 40,11 63,23 2 459 2.1229 — 3.35 — — 52, 7 104,14 46, 7 — 2 467 2.9.137 — 17.33 40,17 11,19 — — — 43,27 2 473 8.3.103 13^8 49, 6 51, 8 11,28 73,i3 — — 45, 8 71,21 2 477 4.619 19,46 - 2 503 2.9.139 — — 5i. 7 5°, 1 47,i7 — — 44, 9 2 521 8.9-5-7 35 5 36 37.24 53. 1 2 13,28 97, 5 51, 4 102, 8 27,16 2 531 2.5-11-23 — 9,35 — — — 56,11 112,22 2,19 57,25 2 539 2.27.47 — i9,33 — 4,29 83,11 72,23 101, 3 — 16,30 2 543 2. 31. 41 — — 65.29 — — — — 4,i9 — 2 549 4.49.13 7,5° — — — — 77,2.6 IOI, I 43.1° — 2 551 2.3.25.17 — — 5i, 5 26,25 49,i7 66,19 103, 9 — 1 — 2 557 4-9-7 1 21,46 — — 23,26 101, 1 — — 17.18 47.27 2 579 2.1289 39,23 — — — 52, 5 104,10 — 96,10 2 591 2.5-7-37 — 7i,35 — — 86,31 103. 7 8,19 — 2 593 32.81 17,48 1,36 5i, 2 49, 8 25,19 — — | — 2 609 16.163 47,20 51, 2 53,1° — 1 1 103,40 109,17 — 2 617 8.3.109 5 1 * 4 5,36 63,26 43,i6 91, 9, — — • — — 2 621 4-5 131 ii,5° — — — — 71,22 103. 5 — 78,20 -2 633 8.7.47 43,28 5 1 , 4 55,H — — — — 29,16 81,19 2 647 2.27.49 — — 53, 9 5°. 7 29,19 — — 48, 7 — 2 657 32.83 49,16 33,28 65,28 — 1 i — 47, 8 — 2 659 2-3-443 — 47,i5 — 28,25 i°3, 1 52, 3^04, 6 — — 2 663 2.121.1 1 — — 61,23 — _ — — — 9,3i 2 671 2.3.5.89 — — 57.17 22,27 44,i8 54, 7108,14 12,19 28,30 2 677 4.3.223 39.34 — — 35,22 31,19 — — — i°3, 3 2 683 2.9.149 — 35,27 — 40,19 97, 7 — — 46, 9 — 2 687 2.17.79 — — 55,i3 — — — — — 87,17 2 689 128.3.7 33.4° 49,12 67,30 31,24 62,16 63,16109,15 41,12 9i,i5 2 693 4.673 47,22 — 39,29 2 699 2. 19.71 — 5i, 7 — — — 52, 1 i5!,49 26,17 i5.3i 2 707 2.3.11.41 — 23.33 — 52, 1 55,i7 — — — 53,27 2 711 2.5.271 — — 53, 7 — — 94,35107,11 52, 1 63,25 2 713 8.3.113 3.5 2 11,36 69,32 19,28103, 3 — 5*. 4 — 2 719 2.9.151 — — 63,25 14,29101, 5 62,15111,17 — — 2 729 8.11.31 5.52 5i„ 8 7i,34 — 1 — 53, 4106, 8 — 90,16 2 731 2.3-5-7-I3 — 43,2i — 52, 3 IQ 4, 2 56, 9112,18 34,i5 32,30 2 741 4.5.I37 25,46 — — — 1 — 61,14113,19 37,H — 2 749 4.3.229 43.3o — — 7,3o 14,20 57.io 114,20 — — QUADRATIC PARTITIONS. 11 p p-l able d e f A B L M x y X Y t u v w 2 753 64-43 7,52,21,34 61,22 — ; , 31,16! 21,31 2 767 2.3.461 65,27 38,21 76,14 — — 52, 3| 2 777 8.347 29,4427,32 53, 4 102, 8 2 789 4.17-41 i7,5o " — — 53, 2 106, 4 — — 2 791 2-9-5-3 1 — — 53, 3 46,15 92,IO 54, 5108,10 ■ — — 2 797 4-3- 2 33 3M4 — — 47, J 4 89,11 — — 23,18 98,12 2 801 16.25.7 49,20 5 1 , 10 53, 2 — 89,32 107, 7 1,20 — 2 803 2.3.467 — 25,33 — 44,i7 95, 9 — — — 104, 6 2 819 2.1409 — 9,37 — — — 68,19 109,11 — 45,29 2 833 l6 -3-59 23,48 41,24 59,i8 49,12 98, 8 — — — — 2 837 4.709 4i,34 — — — — — — 53, 2 — 2 843 2.49.29 — 5 1 , 11 50, 7 96,14 2 851 2.3.25.19 — 49, 1 5 — 52, 7 73,i5 84,29 107, 3 18,19 — 2 857 8.3.7.17 51,1647,18 57,U 53, 4 41,19 — — 43, 1 2 — 2 861 4.5. n. 13 i&59 — — — — 79,26 107, 1 — 75,23 2 879 2.1439 — — 73,35 — — 118,47 119,23 52, 5 — 2 887 2 -3- I 3-37 — — 75,37 2,3! 91,11 — — — 107, 3 2 897! 16.181 3 J ,44 3,38 55, 8 18,32 2 903! 2. 145 1 • — — 59,i7 2 909 4.727 53,io — — — 73,22 109, 7 47,10 69,25 2 917 4.729 i,54 — — 53, 6 106, 4 — — — — 2927! 2.7.11.19 — — 55, 7 — — — — 20,19 108, 2 2939:2.13.113 — 5M3 — ~- 88,31 io 9, 5 _.._ — 2 953 8.9.41 53,i2 !9,3 6 55, 6 35,24 70,16 — 74,24 2 957 4-739 29,46 — — — — — — . — 93,i7 2 963 2.1481 — 15,37 46,11 5!, 2 9 2 969 8.7-53 37,4o 9,38 59,!6 — — 83,28 109, 1 13,20 — 2 971 2. 27. 5. 11 — 53, 9 — 28,27 56,18 64,15 117,19 — 97,15 2 999 2.1499 — — 61,19 — 62,13 121,23 — — 3 001 8.3.125 51,20 43, 2 4 63,22 53, 8 77,i5 61,12 122,24 — 5,33 3 011 2.5-7-43 — 33,3i — — — 56, 5 112,10 22,19 — 3 019 2.3-5°3 — 29,33 — 44,i9 13,21 92,33 in, 7 38,15 85,21 3 023 2.1511 — — 55, 1 — — — — — 39,3i 3 037 4.3.11.23 n,54 — — 55, 2 49,!9 — — — i3,33 3 041 32.5.19 55, 427,34 77,38 — — 71,20 113,11 — 30,32 3 049 8.3.127 45,3249,18 57,io 43,20 17,21 77,24 in, 55 1 , 8 — 3 061 4.9.5-17 55, 6 • — — 19,30 38,20 109,42 H7,i753, 6 65,27 3 067 2.3.7.73 5,39 — 52,11 19,21 ■ — — !5°, 9 i7,33 3 079l2.8i.ig — — 69,29 i4,3 J 79,i5 82,27 111, 1 — — 3 083 2.23.67 — 45,23 — — ' — — — — in, 1 12 QUADRATIC PARTITIONS. p p-l a b c d e f A B | L M x y X Y t u i V w 3 089 16.193 55, 8 39,28 59,M — ii3,44|H9,i9 J 7,2o 105,11 3 109 43-7.37 47,3° — 53,io 23,21 117,46121,21 29,18 3119 2.1559 — — ! 7i,3i — — 58, 7 116,1444,13 3 121 16.3.5.13 39,4o 23,36 57, 8 7,32 89,13121,48 123,23 " 3 137 64.49 1,56 33,32 67,26 — — ; — — 55, 4 — 3163 2. 3.17. 31 — u,39 56, 3 112, 2 — — — — 3 167 2.1583 — — 65,23 — — — — 1 3 169 32.9. 1 1 55,i2 37,3o 63,20 49,16 97,ii 57, 4 114, 8 — 101,15 3181 4.3.5-53 45,34 — 47,18 94,12 81,26 113, 3 3 187 2.27 59 — 55, 9 — 40,23 29,21 — — 10,21 — 3 191 2. 5. 11. 29 — — 77,37 — — 86,29 113, 1 — 108,10 3 203 2.1601 — 39,29 — 26,19 3 209 .8.401 53,2o 3,4o 61,16 — — 67,16 121,19 — — 3 217 16.3.67 9,56 25,36 57, 4 55, 8 3 J ,2I — — 47,12113, 3 3 221 4.57.23 55,M — — — 61,10 122,2043,14105,13 3 229 4.3-269 27,50 — — 23,30 46,20 57, 2 161,5131,18 — 3 251 2. 125. 13 — ■ 57, 1 — — 64,13 127,25 — . — 3 253 4.3-271 57, 2 — — 35,26 «3> 3 ! 3 257 8. 1 1 37 11,56 57, 2 65,22 — ' ! — i53, 8 42,32 3 259 2.9.181 — 53,i5 — 44,2i 88,14 108,41 119,1554, 7 56,30 3 271 2.3.5.109 — — 61,15 2,33 4,22 74,21 117,1152, 9103,15 3 299 2.17.97 — 57, 5 — — — 112,431121,1746,13 • — 3 301 4.3.25-11 49,3o — — 43,22 109, 7 59, 6118,12 51,10 35,33 3 3071 2.3.19.29 — 43,27 — 28,29 59**9 — — — — 3 313 16.9.23 57, 8 55,i2 75,34 31,28 "5, * — — 39,i6 — 3 3191 2.3.7.79 — — 59, 9 38,25 37,2i 58, 3 116, 6 36,17 — 3 323 2. 1 1. 15 1 — 5i,i9 — — — — 24,34 3 329 256.13 25,52 21,38 61,14 — 73,20119,13 23,20 — 3 331J 2.9.5.37 — J 7,39 — 8,33 16,22 n6,45 123,19 — 115, 3 3 343 2.3.557 — — 65,21 34,2 7 68,18 — — 16,21 — 3 347 2.7.239 — 57, 7 — 5o,n 87,23 3 359 2.23.73 — 71,29 — 58, 1 116, 2 — 81,25 3 361 32.3.5-7 15,56 47,24 81,40 17,32 113, 5 79,24 117, 7 57, 4 — 3 371 2.5-337 — 3,4i — — 124,49 127,23 58, 1 3,35 3 373 4.3.281 3,58 — — 49,18 98,12 — — — — 3389:4.7.121 5,58 — — — — 103,38 119,11 1,22 9,35 3 391 2.3.5. 1 13 — ' — 63,1758, 3 I][ 6, 2 94,33 117, 5 — 100,18 3 407 2.13.131 — | — 73,3i — . 3 413 4.853 7,58 — — — — --- — 5,22 111,11 3 433 8.3.11.13 | 27,52 29,36 61,12 19,32 77,i7 — ~~ — 86,24 QUADRATIC PARTITIONS. 13 p p-\ a b c d e f A B L M x y X Y t u v w 3 449 8.431 43,4057,1° 59, 4 - j — 107,40 121,13 — — 3 457 128.27 39,4453,18 63,i655, I2 no, 8 — — — 43,33 3 461 4-5-173 3!,5° — — — — 59, 2 118, 4 - — 3 463 2-3-577 — j — 59, 3M,33 28,22 — — — 116, 6 3 467 2.1733 J27,37 — — — — 38,17 — 3 469 4.3.17.17 45,38 — — i,34 103,11 63,10 126,20 9,22 95,2i 3 491 2-5-349 — |57i" — — — 64,11 128,22 — 117, 5 3 499 2.3-II-53 — 159, 3 — 5 6 ,ii| 89,15 68,15 129,23 - 64,30 3 511 2 27.5.13 — 1 — 69,2558, 7! 79,!7 66,13 132,26 44,15 — 3 517 4.3-293 59, 6 - — 7,34109, 9 — — — — 3 527 2.41.43 — — 83,41 — — — — — — 3 529 8.9.49 35,48 1,42 73,3059, 4 47,21 93,32 119, 3 27,20 "Sj 9 3 533 4.883 13,58 - — — 3 539 2.29.61 — 33,35 — — — 88,29 119, 1 58, 5 — 3 541 4.3-5-59 25,54 — -»- 29,30 58,20 61, 6 122,12 — — 3 547 2.9.197 — 37,33 — 32,29 119, 1 — — — 47,33 3 557 4.7.127 49,34 — 13,22 117, 7 3 559 2.3.593 — i — 61, 9 26,31 67,19 102,37 121, 9 — — 3 571 2.3-5.7-17 23,39 — 52,17 T,23 76,21 123,13 22,21 — 3 581 4-5-179 59,io — — — 119,46 127,19 47,H — 3 583 2.9.199 — 71,27 50^9 7,23 — — — — 3 593 8.449 53,2845,28 61, 8 — — — — 59, 4 3 607 2.3.601 — — 67,21 58, 9, Il6 » 6 — — 60, 1 3 613 4.3-7-43 43,42 — — 55,14 13,23 — — 15*22 14,36 3 617 32.113 41,4427,38 77,34 93,23 3 623 2.1811 — — 61, 7 — — — 40,17 84,26 3 631 2.7, 5.I2I — — 63,13 38,27 76,18 106,39 123,11 — 68,30 3 637 4.9.IOI 39,46 — — 13,34 115, 7 — — 37,i8 — 3 643 2.3.607 — 59, 9 — 56,13 17,23 — — — — 3 659 2.3I.59 — 51,23 — — — 92,31 121, 1 — — 3 671 2.5-367 — — 61, 5 — — 74,i9 127,17 — — 3 673 8.27.I7 37,48 55,i8 81,38 59, 8 83,i7 — — — , — 3 677 4.919 59,M — — — — — — 17,22 78,28 3 691 2.9.5.4I — 53,2i — 4,35 101,13 64, 9 128,18 46,15 — 3 697 16.3.7. 11 49,36 13,42 85,42 25,32 7M9 — — 57, 8 53,33 3 701 4-25-37 55,26 — — — — 61, 2 122, 4 — 102,20 3 709 4.9.IO3 53,3o — — 41,26119, 5 73,18129,19 — — 3 719 2.II.I3.I3 — — 61, 1 — — 62, 5^24,10 4,23 75,29 3 727 2.81.23 — — 63,11 58,n 25,23 — — — 83,27 3 733 4.3.3II 57,22 — — 61, 2 55,2i — — 59, 6 26,36 14 QUADRATIC PARTITIONS. p p-1 a b c d e f A B L M 1 x yjX Y, t uj 1 J 1 v w 3 739 2.3.7.89 — 61, 3 — 8,35 113, 9 72,17131,21 6,23 — 3 761 16.5.47 25,56 57,i6 73,28 — — 71,16133,2331,20 — 3 767 2.7.269 — — 67,19 — — — — 8,23 3,37 3 769 8.3.157 13,60 59,i2 63,10 61, 4 73,19 67,12; 134,24 — 1 — 3 779 2.1889 — 9,43 — — — 68,13' 136,26 - ! — 3 793 16.3.79 33,5 2 61, 6 69,22 55, 16 103,13 — — — 94,24 3 797 4-13-73 41,46 3 803 2.1901 — 21,41 — — — — — 10,23 s — 3 821 4.5.191 61,10 — — — — 79,22 127,13 — 15,37 3 823 23-49-I3 — — 8i,37 50,21 100,14 — — 36,19 — 3 833 8.479 53,32 39,34 65,14 — — — 61, 4 69,31 3 847 2.3.641 — — 83,39 62, 1 59,2i — 12,23 — 3 851 2. 25.7. 11 — 51,25 — — — 64, 7 128,14 62, 1 123, 5 3 853 4.9.107 3,62 — — 49,22 115, 9 — — 34,36 3 863 2.1931 — — 85,41 — 3 877 4.3.17. 19 31,54 — — 43,26 35,23 — — 1 1 8, 1 2 3 881 8.5-97 59,2o 3,44 77,32 — • — 109,40 127,11 — 93,25 3 889 16.243 17,60 19,42 71,24 1,36 2,24 63, 4 126, 8 33,2o — 3 907 2.9.7.31 — 55,2i — 32,31 61,21 — 62, 3 — 3 911 2.5.17.23 — — 67,17 — — 134,53 137,25 — — 3 917 4.11.89 61,14 23,22 123, 7 3 919 2-3-653 — — 63, 5 62, 5 77,i9 138,55 i39, 2 7 — 76,30 3 923 2.37.53 — i5,43 — — — — — — — 3 929 8.491 35,52 27,40 79,34 — — 77,20 131,17 59, 8 — 3 931 2.3-5- I 3i — 59,i5 — i6,35 89,i7 84,25 127, 9 58, 9 125, 3 3 943 2.27.73 — — 75, 2 9 26,33 52,22 — — 60, 7 124, 6 3 947 j 2.1973 — 45,3i — — — — — — 27,37 3 967 2 3.661 — — 63, 1 38,29 125, 3 — — — — 3 989 4.997 25,58 — — 1 - 1 67,10 134,20 — — 4 001 32.125 49,40 63, 4 83,38 — 89,28 127, 5 47,16 — 4 003 2.3.23.29 — 3i,39 — 56,17 107,13 — — — — 4 007 2.2003 — — 77,3 r — — — — — 12,38 4 013 : 4.17-59 13,62 — 25,22 126, 4 4 019 , 2.49.41 — 63, 5 — — — 68,11 136,22 62, 5 5i,35 4 021 j 4.3.5.67 39,5° — 61, IC 9i,i7 99,34 127, 3 — — 4 027 2.3.H.61 — 43,33 — 52,21 104,14 — 18,23 112,18 4 048 1 16.11.23 55,32 57,20 89,44 1 — 73, J 6 139,25 — 75,3i 4 051 1 2.81.25 — i,45 — 28,33 56,22 i 64, 3 128, 6 65,33 4 057 4 073 18.3.13.13 59,24 23,42 75,28i3,3^ j 26,24 I — — 5,24 127, 3 8.509 37,5 2 45,32 71,22 1 " 1 " 1 — — — 111,19 QUADRATIC PARTITIONS. 15 p p— 1 a b c d e f A B L M x 7 X Y It u v w 4 079| 2.2039 — — 73,25 — -~ 82,23131,13 — 60,34 4 091' 2.5.409 — 27,41 — 1 — — 64, 1 128, 2 — — 4 093 4.3.11.31 27,58 — — 25,34 127, 3 — — — 46,36 4 099 2.3.683 — 7,45 ,64, 1 67,21 88,27 129, 7 54,13 — 4111 2.3.5-!37 — — 8i,35 ; 2,37 109,13 66, 7 132,14 32,21 — 4 127 2.2063 — — 65, 7 — — — 40,19, — 4 129 32.3.43 23,60 59,!8 77,3049,24 98,16 103,36 129, 5 — j I2 5, 9 4133 4.1033 17,62 — — 4 139 2.2069 — 21,43 — ■ — 112,41 169,49 46,17120,14 4153 ; 8.3.173 43,48 25,42 65, 6 6l,I2 122, 8 — — 11,24 — 4 157 4.1039 59,26 _ __ 4 159 2. 27. 7. 11 — ■ 71,21 22,35 83,19 98,33 129, 1 64, 3 "SMS 4177 16.9.29 9,64 55,24 73,24 !7,36 34,24 — 4 201 8.3.25.7 5MQ 49,3° 67,12 43,28 127, 5 i4i,5 6 |i43,27 T 3, 2 4! 4211 2.5.421 — 63,11 — — — 116,43133,13 58,n 105,23 4 217 8.17.31 11,64 57,22 65, 2 — 117,17 4 219 2. 3-19-37 — 13,45 — 56,19 !,25 68, 9 136,181 — — 4 229 4-7-I5 1 65, 2 — — — ■ 107,38 131, 729,22129, 5 4 231 2.9.5.47 — — 9i,45 58,17 7,25 66, 5 132,10 — — • 4 241 16.5.53 65, 4 3,46 71,20 — 79,20 i37,i9 — — 4 243 2.3.7. 101 — 65, 3 — 64, 7 85,19 — — 34,2i — 4 253 4.1063 53,38 65, 2 — 4 259 2.2129 — 39,37 — — — 92,29 131, 5 - — — 4 261 4.3-5.7I 65, 6 — — 53,22 13,25 69,10 138,20 — 95,27 4 271 2.5.7.61 — ■ — 73,23 — 86,25 i33,n 64, 5 45,37 4 273 16.3.89 57,32 41,36 75,26 65, 4 53,23 — — — 19,39 4 283 2.2141 — 51,29 — 81,31 4 289 64.67 65, 8 33,4o 67,10 — 97,32 131, 1 — — 4 297 8.3.179 61,24 65, 6 83,36 35,32 131, I — — — — 4 327 2.3.7.103 — — 67, 9 38,31 55,23 — — 48,17 73,33 4 337 16.271 49,44 45,34 85,38 — — .— 65, 4 78,32 4 339 2.9.241 17,45 — 64, 9 128, 6 72,13 144,26; — 25,39 4 349 4.1087 43,5° — — — — 73,H 146,28 31,22 114,20 4 357 4.9.121 1,66 — — 5,38 119,11 — - — 97,27 4 363 2.3.727 — 59,2i — !6,37 127, 7 — 66, 1 — 4 373 4.1093 23,62 — 4 391 2 -5439 — 67, 7 — — 106,37 i33, 5; 4,25 — ■ 4 397 4-7-157 61,26 — 55,i4 — 4 409 8.19.29 53,4039,38 9i,44 — — 67, 4 134, 8; — 6,40 4 421 4-513-17 65,14 — — — — 101,34 133, I, 5i,io — 16 QUADRATIC PARTITIONS. p p-1 a b c d e f A B L M x y X Y t u v w 4 423 2.3.11.67 — — 69,13 34,33 68,22 — 3i,39 4 441 8 3-5-37 29,60 43,36 79,3o 37,32 59,23 69, 8 138,16 — 4 447 2.9.13.19 — — 73,2i 58,19 115,^3 — — 60,11 !33, 3 4 451 2.25.89 — 33,4i — — — 136,53 143,23 — — 4 457 8-557 19,64 15,46 67, 4 4 463 2.23.97 — — 7i,i7 — — — — 44,i9 — 4 481 128.5.7 65,16 63,16 •67, 2 — — H9,44i37,i3 41,20 18,40 4 483 2.27.83 — 55,27 : — 40,31 i33, 3 — — — 4 493 4-1123 67, 2 — — — — — — 129,11 4 507 2-3-75 1 — 67, 3 20,37 91,19 — — — — 4 513 3 2 '3.47 47.48 65,12 8l,32 25,36 50,24 — — — *$h 9 4517 4.1129 49,46 — — — — — 67, 2 — 4 519 2.9.251 — 69,11 62,15 124,10 82,21 141,19 12,25 115,21 4 523 2.7. 17.19 5 J ,3i 50,17 4 547 2.2273 — 63,17 58,i3 48,38 4 549 4-3-379 65,18 — — 43,3o 86,20 123,46.139,15 — 4 561 16.35.19 31,60 67, 6 69,10 47,28 37,25 81,20143,2123,24 — 4 567 2.3.761 — — 75,23 2,39 4,26 — — — — 4 583 2.29.79 — — 91,43 — — — — — — 4 591 2.27.5.17 — — 71,15 22,37 i33, 5 114,41 137, 9 — 92,30 4 597 4-3-383 41,54 — 67, 6 134, 4 — — — — 4 603 2-3-!3-59 — 61,21 — 64,13 103,17 — — 30,23 4i,39 4 621 4-3-5-7.ii 61,30 — 17,38 I3 1 , 7 79,18 147,25 57,M 130,12 4 637 4.19. 61 59,34 — — — 4 639 2.3.773 — — 8l,3I 46,29 41,25 78,17 149,27 — — 4643 2. 11. 211 — 15,47 46,19 9,4i 4 649 8.7.83 5,68 5!,32 7M4 — — 77,16 151,29 43,2o — 4 651 2.3-25.31 — 67, 9 — 68, 3136, 2 76,15 152,30 — 127,15 4 657 16.3.97 39,56 7,48 75,22 65,12130, 8 — — 25,24 103,27 4 663 2.9.7.37 — — 69, 7 10,39 20,26 — — 64, 9 — 4 673 64.73 7,68 21,46 79,28 — — — — 65, 8 126,16 4 679 2.2339 — — 77,25 — — n8,43 i39>" — i5,4i 4 691 2.5.7.67 — 63,19 — — — 104,35 137, 162,11 i35, 7 4 703 2.2351 — — 7i,i3 - — — — — — 4 721 16.5.59 25,64 39,4o 89,40 — — 71, 8 142,16 — — 4 723 2.3.787 — 4i,39 — 56,23 125,11 — — — 136, 6 4 729 8.3.197 45,52 11,48 69, 429,36 58,24 93,28 i39, 9 61,12 — 4 733 4-7- I 3- I 3 37,58 — — — — — — 1,26 21,41 4 751 2. 125.19 — — 73,i7 — — 86,23 i43, 1 7 — — 4 759 2.3.13.61 — — 69, 1 M,39 28,26 122,45 141,13 — — QUADRATIC PARTITIONS. 17 p p-1 a b c d e f A B L M x y X Y t u V w 4 783 2.3.797 — — 79,27 26,37 85,21 — — 60,13 49,39 4 787 2.2393 — 33-43 — — — — 4 789 1 4-9-7.19 55,42 • — 67,10 97,i9 147,58 151,27 69, 2 7o,36 4 793 8.599 13,6869, 4 95,46 4 799 2.2399 — — 71,11 — — 98,31 T 39, 5 68, 5 111,25 4 801 64.3.25 65>2447, 3 6 97,48 1,40 121,13 151,60 !53, 2 9 — 85-33 4 813 4-3-4 01 67,18 — — 65,14 107,17 — — 9,26 — 4 817 16.7.43 41,5657,28 73,i6 — — — 55,!6 — 4 831 2.3.5.7.23 — — 87,37 34^35 71,23 126,47 143,15 48,19 — 4 861 4-243-5 69,10 — — 23,38 J37, 5 71, 6 142,12 — — 4 871 2.5.487 — — 77,23 — 74,ii 148,22 — 60,38 4 877 4-23-53 6i,34 — 117,23 4 889 8.13.47 67.20 69, 8 79,26 — — 83,20 149,23 — i35,n 4 903 2.3.19.43 — — 75,*9 70, 1 73,23 — — — — 4 909 4.3.409 3,7o — — 47,3° 94,20 97,3° 141, 7 39,22 131,15 4 919 2.2459 — — 91,41 — — 82,19 151,25 — 4 931 2.5.17.29 — 57,29 — — — 76,13 152,26 120,22 4 9334-9- I 37 33,62 — 59,22 7,27 — — — 74,36 4 937 8.617 29,64 63,22 73,H — — — — 67, 8 138, 8 4 943 2.7.353 ~~ — 7i, 7 — — — — 64,11 84,34 4 951 2. 9.25. 11 — 93,43 58,23 11,27 i34,5 J 147,19 24,25 20,42 4 957 4-3-7-59 69,14 — — 25,38 89,21 — — 15,26 — 4 967 2. 13. 191 — — 83,31 — — — — 68, 7 — 4 969 8.27.23 37,6o 19,48 71, 6 13,40 133, 9 107,36 141, 1 — — 4973 .4.11. 113 67,22 141, 1 4 987 s 2.9.277 53,33 — 68,11 101,19 — — 128,18 4 993 128.3.13 63,32 49,36 81,28 65,16 17,27 — — 31,24 — 4 999i 2.3.49.17 — — 99,49 46,31 i39, 5 138,53 149,21 36,23 140, 6 5 003 2.41. 61 — 69,11 39,4i 5 009' 16.313 65,28 3, 5o 7i, 4 — — 73, 8 146,16 47,20 8i,35 5 011 2.3.5.167 — 3i,45 — 56,25 19,27 96,29 143, 9 — 5 021 4-5-251 11,70 — — — — 71, 2 142, 4 17,26 135,13 5 023 2.81.31 — — 7i, 3 50,29 i37, 7 — — 44,2i — 5 039 2. 11. 229 — — 7 1 , 1 — — 142,55 151,23 — 141, 5 5 051 2.25. 101 — 5i,35 — — — 116,41 i43, 7 26,25 — 5 059 2.9.281 — 7i, 3 — 4,4i 119^5 72, 5 144,10 — — 5 0771 4-27.47 71, 6 — — 67,14 25,27 — — 53,i8 — 5 081 8.5.127 59,4o 9,5° 91,40 — — 101,32 H3, 5 — — 5 087 2.2543 — — 73,n — — — — ■ — 3,43 5 099 , 2.2549 — 69,13 — — — 88,23 149,19 — — 18 QUADRATIC PARTITIONS. p p-1 a b c d e f A B L M x y X Y t u v w 5 101 4-3-25-*7 5i,5o — — 49,3o 98,20 111,38 H3, 3 - 5 107 2-3- 2 3-37 — 65,21 — 8,41 13 1 , 11 — — 2,27 32,42 5 113 8.9.71 53,48 7i, 6 75,!6 35,36 70,24 — — 6i,39 5119 2.3-853 — — 87,35 38,35 i43, 1 158,63 "5*3" 4,27 125,21 5147 2.31.83 — 27,47 38,23 5153 32.7-23 23,68 69,14 95,44 — — — — 7i, 4 129,19 5 167 2.9.7.41 — — 73, 9 62,21 124,14 — — 8,27 — 5 171 2.5. 11.47 — 57,3i — — — 76,11 152,22 — 75,37 5 179 2.3.863 — 61,27 — 64,19 121,15 72, 1 144, 2 — 1104,30 5189 4.1297 17,70 — — — — 133,50 149,17 67,10 5 197 4-3-433 29,66 — ■ — 65,18 130,12 — — 113,27 5 209 8.3-7-3* 5,72 41,42 81,26 59,24 118,16 77,12 154,24 69, 8 — 5 227 2.3.13.67 — 5,5i — - 52,29 35,27 ! — — — — 5 231 2-5-523 — — 73, 7 — — I 74, 7 148,14 5 2 , x 9 — 5 233 16.3. 109 7,72^5,48 75, J 4 71, 8 95,2i — 65,12 5 237 4.7. 11. 17 7i,i4 43,22 123,23 5 261 4.5.263 19,70 — — — — 79,14 158,28 23,26 87,35 5 273 8.659 67,28 69,16 79,22 — — — — 59,!6 51,41 5 279 2.7.13.29 — - — 73, 5 — — 82,17 161,31 64,13 5 281 32-3-5- 11 41,60 59,3o 77,i8 47,32 143, 5 81,16162,32 — M5, 3 5 297 16.33 1 71,16 57,32 73, 4 — — — — — 5 303 2.1 1. 241 — — 85,3i — — — — 40,23 141,11 5 309 4.1327 535o — — — — 73, 2 146, 4 — — 5 323 2.3.887 — Ii,5i — 56.27 112,18 — — — — 5 333:4 31-43 73. 2 6,44 5 347 2. 243. 1 1 — 73, 3 28,39 56,26 — — 97,33 5 35ll 2.25.107 — 77,i7 — — 74, 5 148,10 — i35,i7 5 381 4.5.269 65^34 — — — — 149,58 157,25 — — 5 387 2.2693 — 45,4i 58,17 5 393 i6-337 73, 8 39,44 9i,38 111,29 5 399 2.2699 — — 101.49 — — 98,29 149,11 32,25 !05,3! 5 407 2.3-I7.53 — — io3,5! 70,13109,19 — — — — 5 413 4.3.11.41 63,38 — — 11,42 22,28 — — 45,22 86,36 5 417 8.677 59,44 3,52 77,16 — — — |l02,32 5 419 2.9.7.43 — 37,45 — 64,21 128,14132,49151,15 62,15 — 5 431 2.3.5.181 — — 83,27 62,23131,13 74, 3H8, 6 — 5 437 4.9.151 69,26 — — 73, 6146, 4 — — 142,12 5 441 64.5.17 71,20 21,50 79,2o - 161,64163,31 73, 4 5 443 2.3.907 — 49,39 — 20,41 143, 7 — 54,19 7i,39 5 449 8.3.227 43,6o 29,48 93,4o 61,24 122,16 123,44 149, 9 139,15 QUADRATIC PARTITIONS. 19 p p-1 a b c d e f A B L M x y X Y t u v w 5 471 2-5-547 — — 89,35 — . — 74, 1 148, 2 68,11147, 5 5 477 4-37-37 i,74 __ i 5 479 2.3.11.83 — 77,i5 74, 1 71,25 78,11 156,22 — 145, 9 5 483 2.2741 — 69,19 — — • — — — 74, 1 96,34 5 501 4.125. 11 5,74 — — — — 89,22 157,23 — [123,25 5 503 2.3.7.131 — — 81,23 74, 3 148, 2 — - — 20,27 131,21 5 507 2-2753 — 33,47 5 519 2.31.89 — — 79,i9 — ■ — 118,41 i49, 5 - — 5 521 16.3-5-23 65,36 61,30 87,32 73, 8 49,27 79,12158,24 — — 5 527 2.9.307 — — 75, 7 22,41 101,21 — — 72, 7 52,42 5 531: 2.5.7.79 — 27,49 — — — 76, 7 152,14 34,25 93,35 5 557! 4-3-463 9,74 — — 35.38 149, 1 — — — — 5 563! 2.27.103 — !9,5! — 4,43 i33,i3 — — — — 5 569 64.3.29 63,40 3!,48 99,46 41,36 82,24 87,20 161,27 9,28 i,45 5 573 4.7.199 47,58 29,26 — 5 581| 4-9-5-31 35,66 — — 17,42 34,28 81,14 162,28 73, 6 7,45 5 591 2.5-I3.43 — — 77,i3 — -— 86,19 163,29 — 45,43 5 623 2.3.937 — — 75, 1 74, 7 53,27 — — 60,17 — 5 639 2.2819 — — 83,25 — — 122,43 151, 744,23 — 5 641 8.3.5.47 75, 4 67,24 77,12 29,40 9!, 2 3 131,48 i53,i3 — 17,45 5 647 2.3.941 — — 87,3i 10,43 139,11 — — — 10 3,33 5 651i 2.25. 113 — 63529 — — — 76, 5 152,1074, 5 — 5 653' 4.9.IS7 73,i8 — — 19,42 38,28 — — 75, 2 — 5 657. 8.7.101 61,44 75, 4 85,28 — — — — 13,28 87,37 5 659 2.3.23.41 — 59,33 — 56,29 143, 9 148,57 159,23 — J 9,45 5 669 4. 1 3. 1 09 65,38 — — — — 107,34 151, 5 — 150, 4 5 683 2.3.947 — 65,27 — 64,23 5,29 — — 5 689 8.9.79 75, 8 71,18 91,366; 7,29 117,40 l 5h 3| — — 5 693 4.1423 43,62 — 31,26 — 5 701 4.3-25.19 i5,74 — — 37,38 77,25 101,30 i53, TI — 23,45 5 711 2.5-571 — — 97,43 — — 94,25 i57,i9 — — 5 717 4.1429 71,26 5 737 8.3.239 5i,56 47,42 83,2443,36 86,24 — — 75, 4 — 5 741 4.5.7.41 29,70 — — — — 79,10 158,2071,10 — 5 743 2.9.1 1.29 — — 89,33 14,43 "5i I 9 — — — 79,39 5 749 4-3-479 57,5o — — 61,26 17,29 77, 6 154,1259,18 — 5 779 2.27.107 — 73,i5 — 76, 1 79,25 168,67 169,33126,27 29,45 5 783 2.49.59 — — 101,47 — — — — 76, 1 — 5 791 2.3-5-193 — — 79,15 46,35 59,27 106,33 i53, 7 52,21 140,18 5 801 8.25.29 5,76 5 X ,40 77, 8 — — 139,52 i57,i7 — 150, 8 20 QUADRATIC PARTITIONS. p p-1 a be d e f A B L M x y X Y t u v w 5 807 2.2903 — — 103,49 __ 1 _ — — 68,13 — 5 813 4-1453 73,22 69,41 5 821 4-3-5-97 75»i4 — — 23,42 46,28121,42 i53, 5 33,26 — 5 827 2.3.971 — 25,5i — 28,41 95,23 — — — — 5 839 2 -3-7-i39 — — 81,19 74,11 107,21 78, 7 156,14 76, 3 116,30 5 843 2.23.127 — 15,53 — — 5 849 8.17.43 35,68 21,52: 79,14 77, 4 154, 8 19,28 — 5 851 2.9.25.13 — 53,39 — 76, 5 61,27 n6,39 i53, 1 — — 5 857 32.3.61 9,76 5.54 77, 6 7,44125,17 — — — io7,33 5 861 4.5- 2 93 3i,7o — — — 91,22 163,25 67,14 138,20 5 867 2.7.419 — 75,n' — 62,17 147,13 5 869 4.9.163 45,62 49,34 151, 5i43,54 I59,i9 — — 5 879 2.2939 — — 77, 5 — - | 82,13 164,26 — 129,25 5 881 S-3-5-49 75>i6 7,54 97,42 53^32 149, 7 99,28 157,154; — 5 897 8.11.67 11,76 45,44 ! 77, 4 57,43 5 903 2.13.227 — — 79,i3 — — — — 4,29 — 5 923 2.9.7.47 — 71,21 — 76, 7 97,23 — 6,29 151, 9 5 927 2.2963 — — i 77, 1 — — — — — 93,37 5 939 2.2969 — 39,47 — — — 88,19 169,31 — — 5 953 64.3 .31 57, 5 2 n>54 79,i2 65,24 130,16 — — — — 5 98L 4.5.13.23 59,5° — — — — 151,58 163,23 — — 5 987 2.41.73 — 57,37; — 10,29 i53, 7 6007 2.3.7. 11. 13 — — | 83,21 38,39 76,26 — — 48,23 68,42 6 011! 2.5.601 — 69,25 — — 104,31 i57,n — 135,23 6 029 4 11. 137 77,io - — — — — 97,26 161,1973.10 75,4i 6 037 43.503 41,66 — — 77, 6 154. 4 _ _ 127,27 6 043 2 -3-i9-53 — 29,51 44,37 67,27 — — 74, 9 139,21 6 047 2.3023 — — 97,4i — — — — — — 6 053 4.17.89 47,62 54,44 6 067 2-9-337 — 55,39! 32,41 155, 3' — — — 6 073 8.3-11-23 77,12 59,36 85,2461,28 i45,n — — 75, 8 134,24 6 079 2.3-1013 — 1 — J 79. 9 2 ,45 4,3°, 78, 1 156, 2 — — 6 089 8.761 67,4033,50 83,20 — — 163,64 169,29 — — 6 091 2.3.5.7.29 — 77, 9 — 4,45 8,30 96,25 163,2178, 1 — 6101 4.25.61 25,74 — — 109.34 i57, 7 37,26 — 6 113 32.191 73,28 69,26 79, 8 — — — — 25,28 • — 6 121 8.9.5.17 45,64 17,54 89,30 77, 8 101,23 171,68 173,33 — 47,45 6 131 2-5-613 9,55 — — — 124,43 i57, 5 — 15,47 6 133 4.3-7-73 7,78 — — 29,42 58,28 — 69,14 — 6143 2-37-83 ~ 79, 7 — - 1 — — 16,29 36,46 QUADRATIC PARTITIONS. 21 p p-l abed e f A B L M x J X Y t u v w 6 15L 2.3.25.41 — — | ioi,4574 5 i5 148,10114,37 i57, 3 — — 6163 2.3- J 3-79 — 3i,5! — 4o,39 80,26 — — — 89,39 6 173 4.1543 53,58 6 197 4.1549 7!,34 - - 53,22 147,17 6 199 2.3-i°33 — — 93,3534,4* 89,25 102,29 161,15 68,15 — 6 203 2-7-443 — 75, J 7 - 50,23 — 6 211 2.27.5.23 — 73,2i — 68,231: 84,13 168,26 18,29 — 6 217 8.3.7-37 21,76 77,12 87,26 67,24 134,16 — — 27,28 — 6 221 4.5.311 61,50 — — — — 79, 2 158, 4 — — 6 229 4-9-I73 73,3o — — 77,10 47,29 93,22 169,27 — 155, 9 6 247 2-9-347 — — io7,5 r 58,3! 151, 9 — — — — 6 257 16.17.23 79, 4 45,46 85,22 • 27,47 6 263 2.31. 101 — — 109,53 — — — — — 81,41 6 269 4.1567 37,7o — — — — i37,5o 161,13 79, 2 — 6 271 2. 3.5. 11. 19 — iu,55 14,45 28,30 86,15 172,30 — 53,45 6 277 4-3.523 79, 6 — — 53,34 49,29 — — — — 6 287 2.7.449 — — 95,37 — — — — 20,29 — 6 299 2.47.67 — 5i,43 — — — 88,17 176,34 — — 6 301 4.9.25.7 75,26 — — 73,18146,12 89,18 177,35 i,3° n5,33 6 311 2.5.631 — — 83,17 154,59 167,23 44,2 5 — 6 317 4-1579 29,74 ~ — i53,i3 6 323 2.29.109 — 39,49 — ! — 74,n 159, 1 6 329 8.7.113 77,2069,28 101,44 — — 107,32 161,11 29,28 150,16 6 337 64.9. 1 1 71,36 53,42 93,34 23,44^55, 7 — — 73,i2 2,48 6 343 2.3.7.151 — — 85,21 74,i7 125,19 — — 76, 9 — _ 6 353 16.397 73,32 9,56 89,28 — — — — 79, 4 — 6 359 2. 11. 17. 17 — — 9i»3« — — 158,61 169,25 156,10 6 361 8.3.5.53 69,40 23,54 81,10^7,12154, 8 141,52163,15 — 10,48 6 367 2.3.1061 — — 97,3962,29149,11 — — 72,13148,18 6 373 4.27.59 17,78 - — 5,46 133^7 — — 106,36 6 379 2.3.1063 — 177,15 — 52,35 53,29 132,47 161, 966,17 — 6 389 4.1597 55,58| — — — — 83,10 166,20 — i59, 5 6 397 ^•^^i 59,54J — — 7,46|i45,i3 - — — — 6 421 4.3-5- io 7 39,7o — — 61,30 122,20 99,26 167,21 11,30 — 6 427 2.27.7.17 — 35,5! — 80, 3160, 2 - — 78, 7 133,27 6 449 16.13.31 7,8057,40107,50 — — 127,44 161, 531,28,111,35 6 451 2.3-25-43 — 49,45 — 76,15 152,10 84,11 168,22 58,21! 80,42 6 469 4.3.49.1 1 63,50, — — 11,46127,19 117,38161, 3 13,30.145,21 6 473 8.809 43,6851,44 109,52 - | - — — 129,29 6 481 16.81. 5 9,80 73,24 9i,3o 41,40 79,27 81, 4 162, 8 ~ — 22 QUADRATIC PARTITIONS. V abed e f A B L M x yiXYitu vw 6 491 6 521 6 529 6 547 6 551 6 553 6 563 6 569 6 571 6 577 6 581 6 599 6 607 6 619 6 637 6 653 6 659 6 661 6 673 6 679 2.5,11.59 8.5.163 1 28.3. 1 7 2.3.1091 2.25.131 8.9.7.13 2.17.193 8.821 2-9-5-73 16.3.137 4-5-7-47 2.3299 2.9.367 2.3.1103 4.3-7.79 4.1663 2.3329 4.9.5.37 16.3 139 2.9-7.53 6 689 32.11. 19 6 691 2.3.5.223 6 701 6 703 6 709 4.25.67 2.3.1117 4-3- I 3.43 6 719 2.3359 6 733 4.9. 1 1- 1 7 6 737 6 761 6 763 6 779 6 781 6 791 6 793 6 803 6 823 6 827 6 829 6 833 6 841 16.421 8.5.13-13 2.3.49.23 2.3389 4.3.5.ii3 2.5.7.97 8.3.283 2. 19. 179 2.9.379 2.3413 43.569 16.7. 61 8.9.5.19 — 21,55 11,8039,50 65,4879,12 — 7,57 37,72 55,42 — 81, 1 i3,8o|8i, 2 — [37,51 81, 4!77,i8 41,70 — 97,38 81, 473,20 13,31 — 80, 7 59,29 83,13 81, 259,32155, 9 89,26 6i,54 53,62 81,10 63*52 17,80 35,74 25,78 3,82 3i,76 19,80 75,34 67,48 77,30 47,68 21,80 85,18 91,29 105,47 32,43 65,28 n,57 81, 7 29,54 81, 8 79,i5 37,42 101,4279,12 5o,37 64,29 17,46 97,25 J 9,3i 61,29 23^3! 121,21 136,49163,1146,25 75,43 149,56167,1961,20105,37 97.24171.25 — { — 38,27 — 86.13172.26 — — — 69,16 — — 26,29 — 83, 8166,16 — — 96.23173.27 — 128,30 — 33,28 — [31,46163, 74326 45,47 82, 5 164,101 — J — 88,15176,3054,23 — — 57,22158,12 74,28 - 158, 8 109,5146,39 92,26 83,10 — i59,n 92,19181,3574,13 15,49 91,18182,3619,30 — — I — 81, 4 — 82, 3164, 648,25 — 103,28169,1979, 8141,25 ' — 67,45 8,47149,13144,53167,15 111,53 34,43 163, 3 — 19,46157, 9 83, 6166,12 3,58 81,10 6i,39 27,55 3i,54 81,11 45,49 5^46 7i,3° IJ 3,55 — — 82, 1 — 49,38 65,29 103,44 83, 8 73 83, 7 105,4661,32 91,2714,47 — 79,i4 85,14 — 161,621173,25 73,14! — — — 40,27 161, 9 80,11 113,23 \2 139 35,3! 167,13 . 169,17 7 169,66 177,29 86,11 172,22 109.32 148,55 164, 2 155," 37,3i 10,31 177,70181,3323,30 71,45 0^,14 — — |7 I , I 6 107,4867,28,151,13,181,72183,3553,24 6,3! 8,31 60,46 101,39 162, 8 149,21 120,34 !57,i5 H7,35 129,31 164, 6 QUADRATIC PARTITIONS. 23 p p-1 a b c a e f AB L M x y X Y t u v w 6 857 8857 61,5663,38 83, 4 — — — — 37,28 147,23 6 863 2-47-73 — — ! 89,23 — — — — — — 6 869 4.17.101 55,62 - — — — 83, 2 166, 459,22 135,29 6 871 2.3.5.229 — — ^3, 3 82, 7 103,25 114,35 167, 912,31 — 6 883 2-3-3!-37 — 41,5* — 16,47 125,21 — — 66,19 — 6 899 2.3449 — 81,13 — — 88,13 176,26 82, 5 — 6 907 2.3.1151 - ;83, 3! 80,13 41,31 — — — — 6 911 2.5.691 — : — 103,43 — — 134,47 167, 7 32,29 12,50 6 917 4.7. 13.19 79,26 — — — — — — 83, 2 138,28 6 947 223.151 — 157,43 6 949 4-9-193 15,82 — — 59,34 43,31 107,30 171,17 — — . 6 959 2.49.71 — — 97,35 — — 98,23 179,29 76,13 — 6 9611 16.3.5.29 81,2083, 6 H7,58 7,48 14,32 129,44 167, 3 — 50,48 6 967: 2.81.43 — — 93,29 82, 9 164, 6 — — 80, 9 92,42 6971 2. 5. 17.41 — 3,59 — — — 124,41 167, 1 — — 6 977 64.109 71,4475,26 95,32 87,43 6 983 2.3491 — — 85,11 — — — — 16,31 39,49 6 991 2-3-5-233 — — 87,17 38,43 91,27 86, 9 172,18 — — 6 997 4-3-H-53 39,74 — — 83, 6 166, 4 — 75,H 167, 3 7 001 8.125.7 35,76 27,56 101,40 — — 91,16 182,32 ^3, 4 102,40 7 013 4-1753 17,82 7 019 2. 121.29 — 5!,47 — — — 92,17 i84,34 - 24,50 7 027 2.3.1171 — 23,57 — 20,47 161, 9 — — — 12733 7 039 2.9.17.23 — — 89,21 58,35 47,3! 138,49 169, 944,27 — 7 043 2-7-5°3 — 9,59 34,29 144,26 7 057 16.9.49 1,84 35,54 87,16 73,24 146,16 — — 55,24 — 7 069 4.3.19.31 75,38 ■ — 71,26 149,15 87,10174,20 — — 7 079 2.3539 — — 109,49 — — 118,37169, 7 52,25 — 7103 2-53-67 — — 95,3i — — — — — — 7 109 4.1777 47,7o — — — 133,46 169, 5 61,22 45,49 7121 16.5.89 55,64 57,44 89,20 — — 1 5h 56^73,17 73> l6 147.25 7 127 2.7.509 — — 85, 7 — — — — 20,31 — 7 129 8.81. n 27,80 73,3o 91,2477,20 i37,i9 123,40169, 3 — 79,45 7 151 2.25. 11. 13 — — ii3,53; — — 86, 7172,14 68,19 123,35 7 159 2.3.1193 — — 101,3946,41 77,29 142,51 171,11 — 5,5i 7 177 8-3 13-23 11,84 83,12 87,1437,44 95,27 — — 3,32 58,48 7 187 2-3593 — i5,59 — — n7,37 7193 8.29.31 67,52 75,28 85, 4 — — — — 5,32 — 7 207 2.3.1201 — — 85, 3 2,49 i45, J 7 — — 72,17 — 7 211 2.5.7.103 — 69,35 — — — 184,73 187,35 22,31 — 24 QUADRATIC PARTITIONS. p *>-l a b c d e f A B L M x y x'y it u v w 7 213 4.3.601 83,18 — 79,18158,12 — — 7 219 2.9.401 — 7i,33 4,49 *5M5 188,75189,37 46,27 155,21 7 229 4-i3i39 85, 2 — — — 103,26179,25 7 237 4.27.67 81,26 — 85, 2 79,29 — — 7 243 2. 3.17. 71 — 85, 3 56,37 55,3i — — — !9,5i 7 247 2.3623 — — 103,41 — — — — 80,11 93,43 7 253 4-49-37 23,82 — 85, 2 51,49 7 283 2. 11. 331 — 81,19 — — 1141,29 7 297 128.3.19 39,76 85, 6 93,26 65,32 161,11 — — — 62,48 7 307 2. 13. 281 — 75,29 — 153,23 7 309 4.9.7.29 35,78 — 3^46 169, 5127,42171, 1 71,18 25,51 7 321 8.3.5.61 61,60 11,60 III,50 83,12 166, 8 101,24 183,29 — — 7 331 2-5-733 — 63,41 — — "^35»73r« 38,29 168,10 7 333 4-3-!3-47 63,58 — 85, 6 170, 4 — — 51,26 — 7 349 4.11.167 25,82 — — — 163,62^79,23 — 9o,44 7 351 2.3.25.49 — — 99,35 74,25 i,33 86, 3172, 6 76,15,100,42 7 369 8-3-3°7 85,12 13,60 87,10 59,36 118,24 93,16186,32 — — 7 393 32.3.7. 11 47,72 79,24 n5,54 71,28 i3,33 — — 15,32 3h5\ 7 411 2-3-5- I 3- I 9 — 47,5! 28,47 JI 3, 2 5 96,19 192,38 — — i 7 417 8.9.103 19,84 53,48 n7,56 85, 8 61,31 — — 75^6 133,33 7 433 8.929 53,68 45,52 119,58 7 451 2.25.149 3,6i — — — 136,47 173, 5 — 48,50 7 457 3 2 - 2 33 41,76 27,58 95,28 — — — — 17,32 — 7 459 2.3 ,11.113 — 3i,57 — 16,49 163,11 108,29 179,2186, 3 35,51 7 477 4.3.7.89 9,86 - — — 83,14 125,23 — - ,85, 6 — 7 481 8.5.11.17 85,16 57,46 91,20 — — i3 J ,44 173, ! — 75,47 7 487 2.19.197 — — 97,3! — — — -— 40,29 — 7 489 64.9.13 33,8o 17,60 99,34 4i,44 i73, 1 87, 4 174, 8 — n5,39 7 499 2.23.163 — 69,37 — — — 88, 7 176,1474,17! 7 507 2.27.139 — 73,33 — 68,31 25,33 — — i73, 3 7 517 4.1879 11,86 18,52 7 523 2.3761 — 9,61 7 529 8.941 77,40 81,22 89,14 — — 107,28 181,2319,32 129,35 7 537 16.3-157 79,36 83,18 87, 4 25,48 50,32 — — — 7 541 4-5- I 3-29 71,50 — — — 179,70 187,31:53,26 — 7 547 2.343. 1 1 — 75,3i — 62,23 123,37 7 549 4.3-!7-37 85,18 — — 7,5o 143^9 87, 2 174, 4 — 89,45 7 559 2.3779 — — 91,19 — — 158,59 179,19 — 7 561 8.27.5.7 75,44 19,60 87, 2 67,32 29,33 91,12 182,2469,20! 70,48 7 573 4-3- 6 3 T 87, 2 — — 35,46 103,27 — — 1 "" 4i, 5 1 QUADRATIC PARTITIONS. 25 abcde fABLMxyjXY t U V w 7 577 7 583 7 589 7 591 7 603 7 607 7 621 7 639 7 643 7 649 7 669 7 673 7 681 7 687 7 691 7 699 7 703 7 717 7 723 7 727 7 741 7 753 7 757; 7 759! 7 789] 7 793 7 817 7 823 7 829 ! 7 841; 7 853: 7 867| 7 873 7 877i 7 879! 7 883 ! 7 901 7 907 7 919 7 927 8-947 59*6487. 2.17.223 — 4.7.271 65,58 2.3.5.11.23 — 2.3.7. 181 — 2.3803 — ■ 4.3.5.127 15,86 2.3.19.67 2.3821 ! — 49.5 1 32.239 45*53 55,6869,38 87,10 83,28 25,84 i,34 75,32 43,54 27,59 79,27 35,57 9M7 97,29 4.27.71 8.7.137 5 I2 -3-5 2.9.7.61 2.5.769 2.3.1283 2.3851 4-3-643 2.27. 11 13 - 2.3863 4-9-5-43 75,46 8.3.17.19 3,8865,42 4.7.277 i 9 ,86| — 2.9.431 4-3-i i-59 83,30 - 16.487 I 7,88 ! 39,56 89, 8 8.977 61,6433,58115,52 2.3911 4-i9-io3 73,5° 32.5.49 79,40 67,58 107,44 89,13 93,23 IJ 5,53 H7,55 109,46 82,17 20,49 — 187,74 31,33106,27 127,23 — 11,50161,13149,54 86, 9 172, 6 162,61 — — jii3,32 i3,5 OI 37,2i: 93,M 95,26 93,2273,28157,15 119,36 23,61 22,49169, 9 — I — 1104,25 56,39112,26 88, 3 37,46i75, 3 80,21 160,14 ~~ I ~~ 71,30142,20 99,32^29,48 89, 986,11 i7,5o 58,32 - 119,25 102,23 4-13-151 2.9.19.23 64.3.41 4.11.179 2.3.13.101 2.7-563 4.25.79 2.59.67 2.37.107 2-3-1321 63,44 89, 7 97,2 37,57i 57,6885,18 95,2431,48 49,74 85,26 21,61 87,i3 8,51 [1,48 99,3126,49 93, I 95 8 ,39 E 167,11 16,34 62,32 121,25 Il6,26 97,18 157,58 89, 4 !9i,35 183,25 I77,i3 2i9,59 I79,i7 186,28 177,11 187,29 176, 6 — 138,32 80,13 84,46 83,10; — J 67,i5 50,27 — 170,12 4,33 9*,45 171,11 114,40 37,3o 85, 8 87, 4 !75, 3 8,33 137,33 JO,33 178,12 |6i,24 55,26 i9i,33 194,36 25,32 44,29 181,17 178, 871,20 178,69 189,29 67,22 16,33 34,3! , 2178, 4 — — |82,i 3 182,71:191,31:88, 5 111,41 n9,39 3,53 49,5i 169,15 130,36 69,49 105,43 42,52 i75, 9 i77, 5 27,53 26 QUADRATIC PARTITIONS. V abcde fABLMx y X Y t U V w 4.3.661 256.31 4.1987 7 951! 2.3.25.53 7 963 2.3.1327 7 933 7 937 7 949 7 993 8 009 8011 8 017 8 039 8 053 8 059 8 069 8 081 8 087 8 089 8 093 8101 8 111 8117 8 123 8147 8 161 8 167 8.27.37 8.7. n. 13 2.9.5.89 16.3.167 2.4019 4.3. 11. 61 2.3.17.79 4.2017 16.5. 101 2.13-311 8-3-337 4.7. 17.17 4.81.25 2.5.811 4.2029 2.31-131 2.4073 32.3.5-I7 2.3.1361 43,78 — J — 89, 4 75,34125,62 35,82 — — 97,27 5,63 — 53,7289, 6 91,12 85,2851,52109,44 — 53,51; — 31,8467,42103,36 — I — 9i,n 87,22 — — 11,63 — 65,62 — j — 41,8087,16! 91,10 107,41 67,6059,48111,46 37,82 1,90 IJ 9,55 89, 2 62,37 95,29 143,50179, 7 49,33186,73193,33 81,14 — 89, 2 — 148,30 8171 2.5.19.43 8 179 2.3.29.47 8 191! 2.9.5.7.13 8 209, 16.27.19 8 219 2.7.587 8 2214-3-5-137 8 231 2.5.823 8 233 8.3.343 8 237| 429.71 8243,2.13.317 8 263 2.243.17 8 269 4.3.I3.53 8 273, 16. 1 1.47 8 287| 2.3.1381 8 291 2.5.829 8 293 4.3.691 14 — 69,41 87,17 81,4031,60 27,61 4i,57 55,72 11,90 89,12 5i,53 |77,48 49,54 [29,86 81,29 13,90 23,88 47,78 9,64 87,19 113,48 123,59 127,63 91, 6 9i, 5 99,28 83,20143,21 147,52181, 9 86, 9 29,32 75,49 — 155,27 87, 8 82,48 — 159,25 — 134,36 66,23 — 76,27152,18 85, I 6i33, 2 3 133,44179, 1 44,45 ! 88,30116,33183,17 47,44179, 1 — — 1122,37 181,11 61,38 53,33 — 16,51 32,34 92, 9184,18 107,26 191,29 169,64187,23 88, 7 51,28125,39 1 i,34 — .2106,28 91, 6182,12! 3,34i73,i5 1106,25193,31 — |i8o, 2 5,34 — 96,46 9i, 3 91, 2 io5,37 7,52 7o,33 56,41 46,45 49,44 89,10 11,52 86,17 79,26 22,51 91, 2 163,15121,36183,13 140,22 — — 104,23197,3538,31 179, 5 ^2,43 181, 3 - 92,30114,31 i87,2i'48,29 83,31177,68191,27 — — 92, 7184,1462,25 59,33i5i,54i83,ii — 188,22' — 94,11 145,21 37,23 — I »35' II 3>3o 44,34 — — 164,6 85,3i - j85,i2 86,11 189,2387,10 187,19' — 157,27 72,50 65,5i 103,45 45,53 J 79, 9 93,47 81,49 174,16 172,18 QUADRATIC PARTITIONS. 27 p p-l a b c d e f & B L M x J X Y t u v w 8 297 8.17. 6i 91, 445,5 6 i°3,34 — — ] \ — ■ 53,28 177,13 8 311 2-3-5- 2 77 — — 93,!3 8 2,23 I 3,35 I 46,5 i ; 183, 7 88, 9 — 8 317 4.27.7.11 91, 6 — — 55,42 110,28 — 15,34 178,12 8 329 1 8-3-347 75,5261,48; 119,549!, A 103,29 93, 8 186,16 — — 8 353 32.9.29 87,2891, 6 109,42 89,12 178, 8 — 81,16 169,21 8 363 2. 37.113 — ! 75,37 — — — — — — 144,34 8 369 16.523 25,8887,20 121,56 — — 193,76 199,35 89, 8 126,40 8 377; 8-3-349 \Sh7* 85,24 95,i8 67,36 134,24' — — — • — 8 387' 2.7.599 — • 63,47 — 50,29 168,22 8 389 4-9- 2 33 i7,9° — — 91, 6 182, 4 197,78 201,37 — — 8 419 2.3.23.61 . 79,33 — 88,15 176,10 92, 3 184, 6 — 4o,54 8 423 2.4211 — — H5,49 — — — — 80,17 — 8 429 4-49-43 77,5°, — — — — 97, 14 194,28 71,22 2i,55 8 431 2.3.5.281 — — 103,33 2,53 161,17 94, 9 188,18 — 107,45 8 443 2.9.7.67 — 9*i 9 — 4,53 155^9 — — 9°, 7 — 8 447 2.41.103 — — 95,17 — — — — — — 8 461 4-9-5-47 19,90 — — 3*»5° 119,27 159,58 187,15 — — 8 467 2.3.17.83 — 23,63 — 92, 1 89,31 — — 58,27 — 8 501 4.125. 17 55,74 — — — — 109,26 197,3* — 27,55 8 513 64.7.19 7,9 2 75,38 95, 16 — — — — 55,28 — 8 521 8-3-5-7I 85,36 77,36 93, 8 61,40181, 7 99,t6 198,32 67,24 — 8 527 2.3.49.29 — 97,21 10,531149,21 — — 92, 3 — 8 537 8.11.97 91,16 87,22 113,46 — — — — 37,32 57,53 8 539 2.3.1423 67,45 92, 5 IQ 7,29 108,25 199,33 — 109,45 8 543 2.4271 — — H9,53 — — — — — — 8 563 2.3.1427 — 25,63 — 44,47 185, 1 — — 74,2i 184, 6 8 573 4.2143 43,82 114,44 8 581 43-5- II - I 3 65,66 — — 91,10 121,27 101,18 202,36 185, 3 8 597 4-7-3°7 89,26 — — — — — — 85,H — 8 599 2.3-I433 — — 93, 5 82,25 i57, J 9 102,19 204,38 — — 8 609 32.269 47,8o 81,32 97,2o — — 103,20 206,40 — — 8 623 2.9.479 — — ■ in,43 14,53 1731*3 — — — — 8 627 2.19.227 — 87,23 I77>i7 8 629 4-3-7I9 23,9° — — 77,3° 154,20 93, 2 186, 4 — i79,!5 8 641 64.27.5 71,60 53,54 93, 2 23,52 133,25 129,40 187, 9 8 647 2.3.11.131 — — 93, 1 38,49 109,29 — — 32,33 163,27 8 66S 2. 61. 71 — — 125,59 — — — — 44,3! — 8 66£ ► 4.11.197 85,38 — — 167,62 191,15 — 174,20 8 67^ 1 4.9.241 81,46 — — 85,22 151,21 — ,93, 2 182,12 8 681 -8.5.7.31 91,2c 93, A ^109,40 > — — |i49,5 2 187, "i |83,^ > — 28 QUADRATIC PARTITIONS. p p-1 a b c d e f A B 1 L M x y X Y t u V w 8 689 16.3.181 15, 9 2 83,3 117,5089,16 4i,35 97,12 194,24 39,32 — 8 693; 4.41.53 73,58 186, 4 8 699 2.4349 — 93, 5 — — — 188,73 i99,3i — 39,55 8 707 2.3.1451 — 47,57 — 92, 9 184, 6 — — — — 8 713 8.9.121 93, 8 i,66 105,3491,12 182, 8 — — — 79,5! 8 719 2.3.1453 — 113,4586,21 172,14 158,57 189,13 12,35 8 731 2.9.5.97 — 9M5 — 68,37 43,35 144,49 187, 3 66,25 8 737 3 2 -3-7-i3 41,84 5,66 95*1225,52 181, 9 — — 57,28 98,48 8 741 4-5- I 9- 2 3 79,5° — — — — 139,46 187, 1 — — 8 747 2.4373 — 93, 7 82,17 — 8 753 16.547 17,92 45,58 H9,52 ! 8 761 8.3.5.73 75,56 7,66 97,1843,48 86,32 171,64 193,21 93, 4H3,45 8 7792. 3.7. n. 19 — 29,63 ~ l5 2 ,45j I0 4,3o 128,39 189,11 34,33i85, 9 8 783 2.4391 — 95,ii — ™ — — — 129,41 8 803 2.27.163 — 89,21 — 40,49187, 3 — — 54,29 56,54 8 807 2.7.17.37 — — "5>47 — — — — 92, 7 — 8 819 2.4409 — 87,25 — — — 208,83 209,41 — . — 8 821 4-9-5.49 89,3° — — 67,38 47,35 99,14 198,28 27,34 8 831 2.5.883 — — 97,i7 — — 94, 1 188, 2 16,35 i°5,47 8 837 4-47-47 i,94 — — 183,13 8 839 2.9.491 — — io 9,39 94, 1 97,3i 162,59 191,15 — 8 849 16.7.79 65,68 93, r o 101,26 — 113,28 199,29 41,32 30,56 8 861 4-5-443 5,94 — — — 121,34 193,19 — — 8 863 2.3.7. 211 — — . 95, 9 94, 3 l8 8, 2 — — 76,21 8 867 2. 11. 13.31 — 57,53 — — — — — 123,43 8 887 2.3.1481 — U7,49 62,41 185, 7 — 72,23 — 8 893 4.9I3.I9 53,78 — — 89,18 178,12 — — — 146,36 8 923 2.3.1487 — 61,51 — 80,29167,17 — — — — 8 929 32.9.31 73,6o 91,18 127,60 71,36142,24143,48 189, i 89,12 8 933 4.7. 11. 29 47,82 -- _ ; _ 1 _ 29,34189, 1 8 941 4-3-5-I49 29,90 — -- 79,30158,20111,26 203,33 87,14 5,57 8 951 2.25.179 — — 101,25 ! 166,61 I93,i7 — i — 8 963 2.4481 — 39,6i , — i59,3i 8 969 8.19.59 35,88 63,5° 131,64 1 157,56 191,11 59,28 51,55 8 971 2.3-5- I 3- 2 3 — 77,39 — 92,13 53,35 96, 7 192,14 86, 15, 8 999 2. 11. 409 — — 107,35 — i — 98,11 196,22 68,25189, 5 9 001 8.9.125 51,80 17,66 99,20 77,32 i73, I 5 I °9,24 207,37 — 155,33 9 007 2.3.19.79 — — 95, 3 70,37 181,11 — — — i7,57 9 011 2-5.I7-53 — 8i,35 — — — 104,19 208,38 94, 5 — 9 013 4-3-75 1 1 87,38 — — 61,42 122,28 — — 75,22 139,39 QUADRATIC PARTITIONS. 29 p p-1 a b c d 1 e f ■A B L M x J X Y t u v w 9 029 4.37.61 95, 2 - - — — 107,22 211,41 — !7i,25 9 041 16.5. 113 95, 4 93, r 4io3,28 — - — H9,3 2 197,23 79,20 — ■ 9 043 2.3,11.137 — 95, 3 — 76,33 I 5 2 ,22 — — — 64,54 9 049 8.3.13.29 93,2o 43,60101,24 91,16139,25 187,72201,29 — — 9 059 2.7.647 — 9,67 , — — — I 52,53 I 9i, 7 22,35 — 9 067 2.3.1511 — ■ 83,33 — 88,21 176,14 — — 38,33 23,57 9 091 2.9.5. 101 — 7i,45 — 4,55 169,17 96, 5 192,10 — 25,57 9103 2-3-37-4I — — ■ IQ 5,3i 26,53 !85, 9 — — — ' — 9 109 4.9.11.23 55,78 — — i9,54 38,36 i47,5o J 9!, 3 53,30119,45 9 127 2. 27. 13.13 — — I2 5,57 5o,47 191, 1 — — — — 9 133 4.3.761 93,22 — — . 95, 6 190, 4 — — — 89,51 9 137 16.571 71,64 87,28 io7,34 — — — — 95, 4 — 9 151 2.3.25.61 — — 103,27 74,35 i79,i3 174,65 197,21 24,35 — 9 157 4.3.7.109 79,54 — — ■ 53,46 85,33 — — 83,18 !57,33 9161 8.5.229 85,44 93,i6 119,50 — — 131,40193,11 — 138,40 9 173 4.2293 73,62 9 181 4.27.5.17 91,30 — — 4i,5o I9 1 , 3 199,78207,35 33,34 — 9 187 2 -3- I 53 l — 95, 9 — - 68,39136,26 — ' — — — 9 199 2.9.7.73 — — 129,61 94,11 6i,35 98, 9196,1864,27164,30 9 203 2.43.107 — 15,67 _____ 9 209 8.1151 53,8o 39,62 97,10 — - — 203,80209,3761,28 — 9 221 4.5.461 95, 14 101,14202,2867,26153,35 9 227 2.7.659 — 93,i7 — — — — i — ■ 50,31192, 2 9 239 2.31-149 — — r 33, 6 5 — — 178,67199,23 — — 9 241 8.3.5. 7. 11 5,96 23,66 113,42 83,28 i,37 211,84213,41 13,36 35,57 9 257 8.13.89 59,76 3,68 103,26 — — — — — — 9 277 4-3-773 21,94 — — 23,54 46,36 — — 95, 6 37,57 9 281 64.5.29 95,i6 33,64 97, 8 — — 151,52193, 5 — — 9 283 2-3-7-I3-I7 — 79,39 — 80,31 !3,37 — i — 90,13 — 9 293 4.23.101 77,58 — — 89,14126,44 9 311 2.5.49.19 — — 97, 7 — — 146,49193, 1 92,11 63,55 9 319 2-3-1553 — — 101,21 46,49 i93, 1 182,69 201,25 88,15 — 9 323 2.59.79 75,43 — 9 337 8.3.389 11,96 25.66 97, 6 35,52 121,29 — — — 193, 3 9 3411 4.5.467 85,46 — — — — 169,62197,17 — — 9 343 2.27.173 — — 105,29 94,i3 !33, 2 7 — ! — — 191, 9 9 349 4.3.19.41 95,i8 — — 43,5° 107,3! 123,34199,21 93, IQ — 9 371? 2-5-937 — 93**9 — — — 104,17208,34 — — 9 377 32.293 79,56 63,52 97, 4 — — — 47,32 162,32 9 391 2-3-5-3I3 97, 3 62,43 67,35 186,71 203,27 96, 5 1 — 30 QUADRATIC PARTITIONS. p p-1 a b c d e f A B L M x j\ X Y t u V \v 9 397 4.81.29 71,66 — 1 77.34 25.37 — — : — 43,57 9 403 2.3.1567 — 85.33 — 40,51 80,34 — — 94. 9 181,21 9 413 4.13. 181 97. 2 — 9 419 2.17.277 — 21,67 — — — 112,25 211,3786,17 120,46 9 421 43-5- I 57 45.86 — — 97. 2 9i,33 129,38 197,15 — 190,12 9 431 2.5.23.41 — — 109,35 — 106,19 212,3852,31 180,22 9 433 89.131 93,2891,24 111,38 5.56 I73.I7 — — 19,36 — 9 437 4-7-337 9 J .34 — — 97, 2 — 9 439 2.3.121.13 — — 121,51 58,45 116,30 122,33 201,23 — 145.39 9 461 4-5- JI -43 25.94 — — — 109,22 217.43 37,34 90.52 9 463 2.3.19.83 — — 99.13 7o,39 140,26 — — 76,54 9 467 2-4733 — 45.6i — — 9 473! 256.37 97. 815,68 131,62 — — — - 95, 8 — 9 479 2.7.677 — — 101,19 — — 98, 5 196,1076,23 — 9 491 2.5.13.73 - ,87.31 — — — 164,59 I97.I3 — 192,10 9 497:8.ii87 61,7675.44 133.64 — — — — ;• — H7.47 9 511 2.3-5-3I7 — f — 123,53 94,i5 188,10 194,75 207,31 — — 9 521 16.5.7-17 89.4057.56 137.68 — — 121,32 203,2597, 4 — 9 533 4.2383 53.82 — 9 539 2.19.251 — 33.65 — — — 128,37 i99,!7 — — 9 547 2 3-37-43 — 5.69 92,19 35.37 — — — — 9 551 2.25. 191 — — 103,23 — — i34,4i 197,11 — 177.25 9 587 2-4793 — 63,53 2,37 — 9 601 128.3.25 95,2449,60 99,10 97. 8 73,35 159,56 197, 9 23,36 127,45 9 613 4.27.89 3.98 — — 95.U 137.27 — — 39,34 — 9 619 2.3.7.229 — 41,63 — 88,25 163,21 168,61 i99,i5 6,37 80,54 9 623 2.17.283 — — 101,17 — — — — 171,29 9 629 4.29.83 5.98 — — — — 103,14 206,28 79,22 15.59 9 631 2.9.5.107 — — 127,57 98, 3 196, 2 206,81 2i3,37 — — 9 643 2.3.1607 — 11,69 — 64.43 i93, 7 — — 54,3i — 9 649 16.9.67 57.8o 71,48 107,30 89,24 178,16 127,36 201,19 — — 9 661 4-3-5-7-23 69,70 — — 73.38 4i.37 119,30 207,29 97, 6 175.27 9 677 4.41.59 29,94 9 679 2.3.1613 — 129,59 98, 5 ,113.31 222,89 |2i9,43 — — 9 689 8-7-173 35.92 21,68 101,16 — — i33,4o |i99, 1 3 83,20 159.35 9 697 ' 3 2 -3- 101 81,56 97,12 115.42 17.56 185,13 — — 25.36 — 9 719 | 2.43.1 13 — — l^ 1 * 61 — 118,29 209,31 — — 9 721 8-243-5 '75.64 89.30 123.52 53,48 106,32 99, 4 198, 8 — — 9 733 4-3-8ii 97,18 — — 91,22 157.23 — — H9.39 9 739 2.9.541 91,27 — 44, 5 1 88,34 172,63 201,17 1 46,33 I9M5 QUADRATIC PARTITIONS. 31 p p — 1 a be d e f A B L M x J X Y t u v w 9 743 2.4871 ! — | — H9,47 — 9 749 4-2437 55, 82 — — — — 163,58 199,11 — 186.20 9 767 2.19.257 107,29 — — — 88,17! - 9 769 8.3.1 1.37 145,8879,42 99, 419,56 149-25 117,28 211, 335^32 185,21 9 781 4-3-5. l6 3 4i,9o — — • 67,42 134,28 99, 2 198, 4 59,3° 9 787 2.3.7.233 — 43,63 92,21 184,14 — — 78,23 — 9 791 2. 5. 11. 89 [ — — |i37 5 67 — — 106,17 212,34 — 108,50 9 803 2. 13.13.29 — 99, 1 — — — — — — — 9 811 2.9.5.109 — 17,69 — 8,57 16,38 116,27 2i3,35 82,21 — 9 817 8.3.409 99, 4 85,36117,4477,36 *54,24 — — — 118,48 9 829 4.27.7.13 J 5,98 _ 1 59*46 79,35 107,18 214,36 99, 2 — 9 833'8.i22 9 37,92 99, 4109,32 9 839- 2.4919 — . — 121,49 — — 158,55 i99, 7 J6,37 I95* 1 * 9 8511 2.25.197 — 99, 5 — — — 176,65 203,19 74,25 — 9 857 128.7. 11 89,44 75,46 127,56 — — — 97, 8 123,47 9 859 2.3.31.53 — 97,i5 — 28,551193, 9 108,19 216,38 — J 3!,45 9 8711 2.3.5.7.47 : — — *". 35 38,53 J 97, 5 114,25 217,39 36,35 172,30 9 883 2. 81. 61 — 19,69 — 176,37 187,13 — — — I 5 I ,39 9 887! 2.4943 — — 103,19; — — — — — 93,53 9 901 4-9-25- 11 99, IQ — — 49,5° IOI > 33 111,22 222,44 — 2,60 9 907 2.3.13.127' — 95,2i — 52,49199, 1 — — i8,37 — 9923 2. 121. 41 81,41 86,19 189,19 9 929 8.17.73 85,52 99, 8 119,46 — — 197,76211,31 — — 9 931 2.3.5.331 — 83,39 — 88,27 176,18 124,33207,25 — i93,i5 9 941 4.5-7.71 71,70 — — — — 131,38 203,17 43,34 — 9 949 4-3-829 ' 43,90 — — 89,26 167,21 137,42 201,11 81,22 14,60 9967 2.3.11.151 — — 105,23 98,11 131,29 — — — 167,33 9 973 4-9-277 57,82 — — 35,54 70,36 — — — — 10 007 2.5003 — — I2 5,53 — — — — — 10 009 | 8.9.139 3,100 53,6o 111,3491,24 182,16 — — 10 037^ 4-i3-i93 89,46 1 10 039 2.3.7:239 — — 101, 9 74,39 148,26 — 10 06l|4-5-5°3 35,94 — — — — — 10 067, 2.7.719 — 33,67 — 10 069 4-3-839 87,50 — — 61,46 i99, 5 — 10 079 2.5039 — — 127,55 — — — 10 091 2.5.1009 — 3,7i — — — 10 093 4-3-29.29 93,38 — — 1,58 175^9 — — — — 10099 2.27. 11. 17 — 89,33 — 32,55 133,29 — 10103 2-5051 — — 101, 7 — — — — 32 QUADRATIC PARTITIONS. p p-l a b c d e f A B j L M 10111 2.3-5-337 — — 119, 45 98, 13 59, 37 10 188 4.17. 149 ! 23, 98 — — — — 10 189 2.37-I37 — ■ 99, 13 — — — 10141 4-3-5- I 3- I 3 85 ? 54 — — 7, 58 181, 17 10151 2.25.7.29 — — 101, 5 — — 10159 2.3.1693 — — 103, 15 94, 21 188, 14 10 163 2.5081 — 9, 7i — — — 10169 8.31. 41 13,100 69, 52 101, 4 — — 10177 64.3.53 31, 96 95, 24113, 36 97, 16 i45, 27 10181 4-5-5°9 95, 34 — — — 10 193 16.49.13 97, 28 99, 14 IOI, 2 — — 10 211 2.5.1021 — 57, 59 — — J 223 2.19.269 — — 121, 47 — — 10 243 2.9.569 — 7i, 51 100, 9 200, 6 10 247 2.47.109 — !*33, 61 — — 10 253 4 11.233 83, 58 — • — 10 259 2.23.223 — 81, 43 — — — 10 267 2-3-29-59 — 85, 39; — 88, 29 J, 39 10 271 2.5*3-79 — — io 3, J 3 — — 10 273 32.3.107 87, 52 101, 6111, 32 89, 28 5, 39 10 289 16.643 17,100 51, 62 II 9 , 44 — 10 301 4.25.103 101, 10 — — — 10 303 2.3. 17.101 — — 105, T 9 50, 5 1 TOO, 34 10 313 8.1289 43, 92 99, 16 109, 28 — 10 321 16.3-5-43 95> 3^ 67, 54io3, 12 47, 5 2 !Q9, 33 10 331 2.5-i°33 — 93, 29 — 10 333 4.9.7.41 27, 98 — 71; 42 142, 28 10 337 32.17.19 79, 64 S3, 68 115, 38 — — 10 343 2.5171 — — 139, 67 — — 10 357 4.3.863 39, 94 — 83, 34 19, 39 10 369 128.81 63, 80 1, 72 129, 56 3i, 56 J 37, 29 10 391 2.5 1039 — — IO7, 23 — — 10 399 2.3-1733 — — in, 3 1 82, 35 23^ 39 10 427 2. 13.401 — 75, 49 — — — 10 429 4.3.11.79 5,102 — — 4i, 54 82, 36 10 433 64.163 97, 32 81, 44 131, 58 — — 10 453 4-3-I3-67 7,102 - — 19, 58 193, !3 10 457 8.1307 101, 16 87, 38 113, 34 — — 10 459 2.9 7 83 — 9i, 33 — 4, 59 173, 21 10 463 1 2.5231 — — 119, 43 — — QUADRATIC PARTITIONS. 33 p P -l a be d e f A B L M 10 477 4.27.97 99, 26 — — 95, 22 29, 39 10 487 2.49.107 — ■ — i*5. 37 — — 10 499 2.29. 181 — 39, 67 — — — 10 501 4-3- I2 5-7 49, 9° — — 101, 10 71, 37 10 513 16.9.73 73, 72 89, 3 6lo 5, l6 49, 52205, 1 10 529 32-7-47 23,100 27, 70109, 26 — — 10 531 2.81.5. 13 — 73, 5 1 — 28, 57 56, 3^ 10 559 2.5279 — — 103, 5 — — 10 567 2.9.587 — — 107, 21 58, 49205, 3 10 589 4.2647 85, 58 — — — — 10 597 4.3.883 79, 66 — 43, 54 86, 36 10 601 8.25.53 101, 20 99, 20 103, 2 — — 10 607 2.53 3 — — 103, 1 — — 10 613 4-7-379 103, 2 — — — — 10 627 2. 3.7. 11. 23 — 103, 3 — • 88, 31 181, 19 10 631 2.5.1063 — — 109, 25 — — 10 639 2.27.197 — — in, 29 14, 59/91, 15 10 651 2.3.25.71 — ioi, 15 — 92, 27184, 18 10 657 32.9.37 81, 64 17, 72 i45, 72 103, 4ii5, 33 10 663 2.3.1777 — — I3 1 , 57 86, 33172, 22 10 667 2-5333 — 3, 73 — — — 10 687 2-3- I 3-^37 — — 105, 13 98, 19 4i, 39 10 691 2.5.1069 — 57, 61 . — — 10 709 4.2677 103, 10 — — 10 711 2.9.5.7.17 — — 123, 47 94, 25 169, 23 10 723 2.3.1787 — 65, 57 — 64, 47 77, 37 10 729 8.9.149 27,100 19, 72 109, 24 77, 4o 43, 39 10 733 4.2683 8 3 , 62 — — — 10 739 2-7-13-59 9, 73 — — — 10 753 5J2-3-7 103, 12 85, 42 in, 28 95, 24 190, 16 10 771 2-3-5-359 — io 3, 9 — 32, 57 64, 3^ 10 781 4.5.49. 1 1 9i, 5 | — — — — 10 789 4.3-29-31 95, 42 — 101, 14 143, 29 10 799 2-5399 — — 119, 41 — — 10 831 2.3.5.19.19 — — i37, 63 82, 37 i93, J 5 10 837 4-9-7-43 89, 54 — 67, 46 205, 7 10 847 2. 11. 17. 29 — — 113, 3 1 — — 10 853 4-2713 97, 38 — — — 10 859 2.61.89 — 99, 23 — — — 10 861 4.3.5.181 45, 94 — 97, 22 163, 25 34 QUADRATIC PARTITIONS. -* p p-1 a b c d e f A B L M 10 867 2.3.1811 — 97, 27 — ;ioo, 17 49, 39 10 883 2.5441 — 15, 73 — — — 10 889 8.1361 67, 80 33, 7o *$h 56 — — 10 891 2. 9.5. 121 — 37, 69 — !io 4 , 5 119, 33 10 903 2.3- 2 3 ? 79 — — 141, 67 34, 571 68, 38 10 909 4.27. 101 53, 90 — — 103, 10133, 31 10 937 8.1367 11,104 57, 62 107, 16 — — 10 939 2.3.1823 — 83, 45 — 56, 5 1 II2 , 34 10 949 4.7.17.23 65, 82 — — — — 10 957 4.3.11.83 99, 34 — — 47, 54 94, 36 10 973 4.13.211 37, 98 — — 10 979 2. 11. 499 — 81, 47 — — — 10 987 2.3.1831 — 67, 57 — 92, 29179, 21 10 993 16.3.229 57, 88 25, 72 105, 4 89, 32 11003 2-55 01 — 45, 67 — — — 11027 2.37.149 — 105, 1 — — — 11047 2.3.7.263 — — 115, 33 62, 4 11057 16.691 89, 56 105, 4 107, 14 — — 11059 2.3.19.97 — 103, 15 — 104, 9208, 6 11069 4.2767 85, 62 — — — — 11071 2.27.5.41 — — in, 25 86, 351911 17 11 083 2.3.1847 — 101, 21 — 100, 19 157, 27 11087 2.23.241 — — 113, 29 — — 11093 4-47-59 103, 22 — — — — 11 113 8.3-463 77, 72 49, 66 121, 42 85, 36 170, 24 11117 4-7 397 61, 86 — — — — 11119 2.3.17-109 — — 119, 39 26, 59 203, 11 11 131 2.3-5-7-53 — 77, 5 1 — 52, 53 107, 35 11149 4.3.929 93, 5° — — 49, 54 98, 36 11159 2.7.797 — 109, 19 — — 11161 8.9.5.31 69, 80 73, 54 107, 12 19, 60 38, 40 11171 2.5.1117 — 33, 7 1 1 — — 11 173 4.3.49 19 97, 42 — — 101, 18 202, 12 11 177 8. 1 1. 1 27 19,104 15, 74 115, 32 — — 11197 4.9.311 9 1 , 54 — 103, 14 61, 39 11213 42803 67, 82 — — — 1123S ► 2.3.1873 — — 117, 35 106, 1 109, 35 1124S 2.7-II-73 — 75, 53 — — 11251 2.9.625 — 1, 75 1 68, 47 209, 7 11 253 8.3.7.67 21,104 103, i£ 1 123, 44 43, 56 125, 33 QUADRATIC PARTITIONS. 35 p p-i a b c d e f A B L M 11 261 4-5-563 5,106 — , — 11273 8.1409 53, 9 2 45, 68 "9j 3 8 — — 11279 2.5639 — — 121, 41 — 11287: 2. 27. 11. 19 — 1 — 107, 9 82, 39 164, 26 11299 2.3.7.269 — 7, 75 — 64, 49 2 n, 5 11 311| 2.3.5.13.29 — — 113, 2 7 106, 5 9i, 37 11317I4-3-23-4I 9,106 — — 35, 58 139, 3i 11 321| 8 5.283 85, 64 39, 7o 107, 8 — ~ 11 329; 64.3.59 95, 48 3 1 , 72 *$h 54 23, 60 46, 40 11351 2.25.227 — — 107, 7 — — 11353 8.3.11.43 93, 5 2 101, 24 in, 22 9i, 3 2 5, 4i 11369 8.49.29 37,100 99, 28 109, 16 — — 11383 2.3.7.271 — - — 139, 63106, I2 7, 33 11393 128.89 103, 28 21, 74 125, 46 — — 11399 2.41-139 — — 107, 5 — — 11411 2.5.7.163 — 63, 61 — — — 11423 2.5711 — — "9, 37 — — 11 437j 4-3-953 5 1 , 94 — — 97, 26 19, 41 11 443 2.3.1907 — 79, 5 1 — 80, 41 2 °3, I 3 11447 2.59.97 — — 107, 1 — — 11467 2.9.49.13 — 107, 3 — 3 2 , 59 209, 9 11471 2 -5-3!-37 — — 143, 67 — — 11483J 2.5741 — 99, 29 — — — 11489 32.359 55, 92 69, 58 109, 14 — — 11491 2.3.5.383 — 103, 21 — 104, 15 208, 10 11 497 8.3.479 101, 36 83, 48 r 35, 58 107, 4 95, 37 11503 2.81. 71 — — i45, 69 86, 37 25, 4i 11 519j 2.13.443 — — 113, 25 — — 11 527! 2. 3.17. 113 — — i47, 7i 7°, 47 7i, 39 11549 4.2887 107, 10 — — — — 11551 2.3.25. 7.11 — — 151, 75 74, 45 148, 30 11579 2.7.827 — Sh 67 — — — 11 587| 2.3.1931 — 97, 33 — 100, 23 3h 4i 11 593 8.9.7.23 107, 12 35, 72 109, 12 59, 5 2 97, 37 11 597,4.13.223 19,106 — — — 11 617| 32.3.121 49, 96 95, 36 113, 24 47, 56 215, 3 11 621 4-5-7-83 65, 86 — — — — 11633 16.727 103, 32 9, 76 139, 62 — — 11657 8.31.47 29,104 63, 62 115, 28 — — 11677 4-3-7-139 21,106 — — 73, 46 211, 9 36 QUADRATIC PARTITIONS. p p-l a b c d e f A B L M 11681 32.5-73 41,100 27, 74 109, 10 — 11689 8.3.487 5>i°8 67, 60 141, 64 83, 40 37, 4i 11699 2.5849 — 57, 65 — — — 11701 4.9.25.13 105, 26 — — 13, 62 173, 25 11 717 4.29. 101 79, 74 — — — — 11719 2.27.7.31 — — 109, 9 94, 3i 187, 21 11 731 2-3-5- I 7- 2 3 — 47, 69 — 92, 33 184, 22 11743 2.3.19.103 — — in, 17 106, 13 145, 3 1 11777 512.23 31,104 15, 76 145, 68 — — 11 779 1 9,3.1^152 — 23, 75 — 52, 55 217, 1 11783 2.43- J 37 — — 109, 7 — — 11789 4.7.421 83, 7o — — - — 11801 8.25.59 101, 40 87, 46 113, 22 — — 11807 2-59°3 — — , 137, 59 — — 11813 4.2953 47, 98: — — — — 11821 4-3-S-I97 61, 90 — 17, 62 203, 15 11827 2.81.73 — 73, 57 — 68, 49 79, 39 11831 2.5-7.i3- I 3 — — i°9, 5 - — 11 833 8.3.17.29 13,108 85, 48 149, 72 62, 52 217, 3 11839 2.3-!973 — — 129, 49 26, 61 i57, 29 11863 2.9.659 — — 109, 3 46, 57 92, 38 11867 2.17.349 — 3, 77 — — — 11 887 2.3.7.283 — — 113, 21 38, 59 215, 7 11897 8.1487 109, a\ 75, 5 6 127, 46 — — 11903 2. 11. 541 — — 222, 37 — — 11909 4.13.229 97, 5o — — — 11 923 2.3.1987 — 49, 6 9 — 4, 63 8, 42 11927 2.67.89 — — 125, 43 — -— 11933 4.29.257 107, 22 — — — — 11939 2.47.127 — 9, 77 — — — 11941 4.3-5- x 99 95, 54 — — 43, 58 217, 5 11 953 16.9.83 17,108 109, 6 135, 56 t 7i, 48 142, 32 11959 2.3-!993 — — 231. 5 1 1 86, 39 172, 26 11969 64. 1 1. 1 7 65, 88 81, 52 113, 20 — — 11971 2.9.5.7.19 — 89, 45 — 8, 63 16, 42 11981 4-5-599 109, 10 — — — — 11987 2.13461 — 87, 47 — — — 12 007 2.9.23.29 — — 117, 29 10, 63 20, 42 12 011 2.5. 1201 — 93, 4i — — — 12 037 4-3-17-59 81, 74 — — 107, 14 149, 3 1 QUADRATIC PARTITIONS. 37 V p-1 a b c a e f A B L M 12 041 8.5.7.43 35> IQ 4 ! 33, 74 ! i37, 58 — 12 043; 2.27.223 — ! io 9, 9 40, 59 137, 33 12 049 16.3.25 1 105, 32 41, 72 121, 36 79, 44 53, 4i 12 071 2.5.17.71 !33, 53 12 073 8-3-503 83> 72 79, 54 115, 24 109, 8 85, 39 12 097 64.27.7 71, 84107, 18 125, 42 95, 32 191, 21 12101 4-25.121 1,110 — — 12 107 2.6053 — ! 45, 7i — — 12109 4.3.1009 3, IIQ — — 97, 30 194, 20 12 113 16.757 97, 52 99, 34 119, 32 — — 12 119 2-73-83 — — 149, 7i — — 12 143 2.13.467 — — i$h 73 — — 12 149 4.3037 7,110 — — — — 12 157 4-3-1013 69, 86 — — 25, 62 161, 29 12161 128.5. 19 95, 56 ^3, 64 *$h 5° — — 12163 2.3.2027 — 65, 63 — 16, 63 32, 42 12 197 4.3049 31,106 — — — — 12 203 2.6101 — 69, 61 — — — 12 211 2-3-5- ri -37 — 31, 75 — 56, 55 109, 37 12 227 2.6113 — 57, 67 — 12 239 2. 29. 211 — — IT 9, 3i — — 12 241 16.9.5.17 55, 96 71, 60 123, 38 73, 48 146, 32 12 251 2.125.49 — 99, 35 — — — 12 253 4.3.1021 43,102 — — 89, 3^ 203, 17 12 263 2.6131 — — 125, 41 — — 12 269 4.3067 13,110 — — — — 12 277 4.9.11.31 89, 66 — — 77, 46 61, 41 12 281 8-5-307 109, 20 27, 76 133, 52 — — 12 289 4096.3 25,108 11, 78 in, 4 1, 64 193, 21 12 301 4.3.25.41 99, 5° — — 47, 58 127, 35 12 323 2.61. 101 — in, 1 — — — 12 329 8.23.67 77, 80 in, 2 121, 34 — — 12 343 2.3.121.17 — — 115, 21 no, 9 220, 6 12 347 2.6173 — 93, 43 — — — 12 373 4-3-1031 103, 42 — — . 29, 62 215, 11 12 377 8.7. 13.17 91, 64 105, 26 113, *4 — — 12 379 2.3.2063 — 101, 33 — 44, 59 221, 5 12 391 2.3-5-7.59 — — 123, 37 22, 63 44, 42 12 401 16.25.31 49,100 5i, 7o 149, 70 — — 12 409 8.3.11.47 85, 72 103, 30 129, 46 11, 64 181, 25 38 QUADRATIC PARTITIONS. p p-1 a b c d e £ A B L M 12 413 4.29.107 53, 98 — — — 12 421 4.27.5.23 in, 10 — — 107, 18214, I2 12 433 16.3.7-37 63, 92 61, 66 i5 J , 72 55, 56 113, 37 12 437 4.3109 71, 86 — — — — 12 451 2.3-25-83 — 97, 39 — 52, 57 104, 38 12 457 8.9.173 109, 24 17, 78 153, 74 13, 64205, 17 12 473 8i559 107, 32 39, 74 155, 76 — — 12 479 2.17.367 — 119, 29 — — 12 487 2.3.2081 — — 133, 5 1 98, 31 5, 43 12 491 2.5.1249 — 3, 79 — — — 12 497 16.11,71 41,104 57, 68 i37, 56 — — 12 503 2.7.19.47 — — 115, l 9 — — 12 511 2.9.5.139 — — 143, 63 94, 35 11, 43 12 517 4.3.7.149 in, 14 — — 85, 42 170, 28 12 527 2.6263 — — 113, " — — 12 539 2.6269 — 99, 37 — — — 12 541 4.3.5. 11. 19 21,110 — — 71, 50221, 7 12 547 2. 9.17. 41 — 55, 69 — 112, 1 115, 37 12 553 8.3-5 2 3 3,ii2 95, 42 131, 48 101, 28 17, 43 12 569 8.1571 5, 112 87, 5° 113, 10 — — 12 577 32.3-131 in, 16 47, 72 115, 18 17, 64 175, 27 12 583 2.27.233 — — I2 5, 39 26, 63 52, 42 12 589 4.3.1049 67, 90 — — 79, 46 217, 11 12 601 8.9.25.7 51,100 107, 24 127, 42 67, 52 223, 5 12 611 2.5-I3-97 — 81, 55 — — 12 613 4.3.1051 47,102 — — 9i, 38 2 3' 43 12 619 2.9.701 — 37, 75 — 112, 5 97, 39 12 637 4-243- J 3 91, 66 — — 103, 26 25, 43 12 641 32-5-79 79, 80 33, 76 113, 8 — — 12 647 2.6323 — 115, J 7 — — 12 653 4-3163 77, 82 — — — — 12 659 2.6329 — in, 13 — — — 12 671 2.5.7.181 — 113, 7 — — 12 689 16.13. 61 65, 92 99, 38 i33, 5° — — 12 697 8.3-23.23 59, 96 23, 78 113, 6 ^3, 44 215, 13 12 703 2.3.29.73 — • — 119, 27 7o, 5i 140, 34 12 713 8.7.227 13,112 in, 14 115, 16 — — 12 721 I6.3.5-53 in, 20 83, 54 117, 22 89, 40 3i, 43 12 739 2.3.11.193 — 79, 57 — 8, 65 203, 19 12 743 2.23.277 — — i$h 47 — — QUADRATIC PARTITIONS. 39 V p-1 a b c d e f A B L M 12 757 ! 4-3- Io6 3 39,106 — 35, 62221, 9 12 763 2.9.709 — 109, 21 — 40, 61 223, 7 12 781 4.9-5-7 1 109, 30 — — IJ 3, 2119, 37 12 791, 2.5.1279 — ■ — ■ i57, 77 — — 12 799 2.81.79 — T 59, 79 82, 45*64, 30 12 809 8.1601 53, IO ° 3, 80 119, 26 — — 32 821 4-5- 6 4i 89, 70 — — — — 12 823 2.3.2137 — — r 39, 57 Io6 , 23 37, 43 12 829 4.3.1069 27,110 — — 73, 5°i 77, 4i 12 841 8.3.5.107 45, io 4 113, 6 121, 30 77, 48 ( i54, 32 12 853 4-27-7-T7 57, 98 — 109, 18218, 12 12 889 8.9.179 35,^8 91, 48 117, 20 59, 56227, 1 12 893 4- 1 1.293 107, 38 — — — — 12 899 2.6449 in, 17 — — — 12 907 2.27.239 107, 27 — 112, 11 79, 4i 12 911 2.5.1291 — 119, 25 — — 12 917 4.3229 41,106 — — — — 12 919 2.3.2153 — — 141, 59 62, 55 103, 39 12 923 2. 7. 13.71 — 21, 79 — — — 12 941:4.5.647 29,110 — — — — 12 953 8.1619 67, 92 69, 64 149, 68 — — 12 959 2. 11. 19.31 — — 121, 29 — — 12 967 2.3.2161 — — 117, 19 no, 17 161, 31 12 973 4.3.23.47 83, 78 — — 65, 54 13°, 36 12 979 2.9.7.103 — 7i, 63 — 76, 49 223, 9 12 983 2.6491 — _ 115, Ir — — 13 001 8.1 25.13 85, 76 99, 40 I5 1 , 7o — — 13 003 2.3.1 1. 197 — 59, 69 — 104, 27 208, 18 13 007: 2.7.929 — — 143, 6l — - — 13 009 16.3.27 1 97, 60 29, 78 119, 24 47, 60 94, 40 13 033! 8.9. 181 37,io8 109, 24 125, 36 85, 44 47, 43 13 037j 43259 109, 34 — — — — 13 043' 2.652 1 — in, 19 — — — 13 049 8.7.233 107, 40 57, 7o J 39, 56 — — 13063:2.3.7.311 — — IJ 5, 9 34, 63 68, 42 13 093 4.3.1091 113, 18 — — 5, 66 10, 44 13 099 2.3.37.59 — 43, 75 — 44, 61 i39, 35 13 103 2.6551 — — 119, 23 — — 13 109 4.29-113 103, 5° — — — — 13 121 64.5.41 95> 6 4 in, 20 161, 80 — 40 QUADRATIC PARTITIONS. p "p-1 a b c die f 1 A B L M 13 127 2.6563 — — 115, 7 — — 13147 2-3-7-3 I 3 — 5, 81 — 52, 59 125, 37 13151 2.25.263 — — i37, 53 — — 13159 2.9.17.43 — — 147, 65 22, 65 173, 2 9 13163 2.6581 — 99, 4i — — — 13171 2-3-5-439 — 7, 81 — 64, 55 229, 3 13177 8.27.61 109, 36 53, 72 117, 16 107, 24 214, 16 13183 2.3- I 3- I 3- I 3 — — 121, 27 no, 19 53, 43 13 187 2.19.347 — 87, 53 — — — 13 217 32.7-59 49,104 63, 68 115, 2 — — 13 219 2.3.2203 — 113, 15 — 112, 15 224, 10 13 229 4-33°7 ii5, 2 — — — — 13 241 8-5-331 U5» 4 21, 80 127, 38 — — 13 249 64.9.23 57>!°° 107, 30 143, 60 31, 6 4 223, 11 13 259 2.7.947 — 51, 73 — — — 13 267 2.9.11.67 — 73, 63 — 100, 33 200, 22 13 291 2.3-5-443 — 13, 81 — 88, 43 217, 15 13 297 16.3.277 79, 84 115, 6 117, 14 97, 36 194, 24 13 309 4.3. 1 109 85, 78 — — 103, 3° 206, 20 13 313 1024.13 103, 52 75, 62 125, 34 — — 13 327 2.3.2221 — — 153, 7i 7°, 53 89, 4i 13 331 2-5-3I-43 — 57, 7i — — — 13 337 8.1667 101, 56 105, 34 145, 62 — — 13 339 2.27. 13.19 — 109, 27 — 104, 29 191, 25 13 367 2.41. 163 — — i55, 73 — — 13 381 4.3-5-223 95, 66 — — 43, 62 i43, 35 13 397 4.17.197 89, 74 — — — — 13 399 2. 3.7. 11. 29 — — i57, 75 94, 39 188, 26 13 411 2.9.5.149 — 17, 81 — 112, 17 61, 43 13 417 8.3-I3-43 5i»i°4 113, 18 147, 64 115, 8 91, 4i 13 421 4.5. 11. 61 115, J 4 — — — — 13 441 1283.5.7 65, 96 : 79, 60 129, 40 73, 52 229, 7 13 451 2.25.269 — 93, 49 — — 13 457 16.29.29 1,116 3, 82 i33, 46 — — 13 463 2.53.127 — — 131, 43 — — 13 469 4-7-13-37 37,no — — — — 13 477 4-3- " 23 in, 34 — 107, 26 185, 27 13 487 2. 11. 613 — — i43, 59 — 13 499 2.17.397 — 99, 43 — 13 513 8.3.563 43,108 115, 12 119, 18 35, 6 4 157, 33 QUADRATIC PARTITIONS. 41 p p-1 a b c d e f A B L M 13 523 2.6761 — 81, 59 — — 13 537 32.9-47 9,116 37, 78127, 36 113, 16 65, 43 13 553 16. 7. 121 113, 28 51, 74I5 1 , 68 — — 13 567 2. 3.7. 17.19 — — i37, 5 1 10, 67 211, 19 13 577 8.1697 11,116 45, 76125, 32 — — 13 591 2.9.5.151 — — 117, 7 62, 57 124, 38 13 597 4.3.11.103 69, 94 — — 23, 66 46, 44 13 613 4.41.83 83, 82 — — — — 13 619 2. 11. 619 — 87, 55 — — — 13 627 2-9-757 — 107, 33 — 112, 19 169, 3 1 13 633 64.3-71 33,112 95, 48 13 1 , 42 65, 56 233, 3 13 649 16.853 95, 68 93, 5° 119, 16 — — 13 669 4.3.17.67 113, 3° — — 101, 34 1, 45 13 679 2.7.977 — — <27, 35j — 13 681 16.9.5. 19 15,116 109, 30 117, 2103, 32 7, 45 13 687 2.3.2281 — — 117, 1 no, 23 179, 29 13 691 2.5.37.37 — 117, 1 — — — 13 693 4.3.7.163 117, 2 — — 25, 66 5°, 44 13 697 128.107 89, 76 117, 2 157, 74 — — 13 709 4.23.149 115, 22 — — — — 13 711 2.3.5.457 — — 119, 15 98, 37 13, 45 13 721 8.5.343 61,100 117, 4 143, 58 — — 13 723 2.3.2287 — 85, 57 — 16, 67 217, 17 13 729 32.3-n.13 105, 52 101, 42 159, 76 89, 44 221, 15 13 751 2. 625. 11 — 149, 65 — — 13 757 4.19.181 9.*i 74 — — — — 13 759 2.3.2293 — — 121, 21 106, 29 19, 45 13 763 2.7.983 — 105, 37 — — 13 781 4-5-J3-53 41,110 — -- — 13 789 4.9.383 117, 10 — 7i, 54 142, 36 13 799 2.6899 — — I3 1 , 41 — — 13 807 2.9.13.59 — — 135, 47 58, 59 119, 39 13 829 4-3457 65, 98 — — — — 13 831 2.3.5.461 — — 141, 55 34, 65 161, 33 13 841 16.5.173 55, IQ 4 87, 56 121, 20 — — 13 859 2. 13.13. 41 — 9, 83 — — — 13 873 16.3.17.17 47,108 115, 18 119, 12 1, 68 203, 23 13 877 4.3469 7*1 94 — — — — 13 879 2.27.257 — — 123, 25 94, 4i 29, 45 13 883 2. 11. 631 45, 77 G 42 QUADRATIC PARTITIONS. V V' f jA B L M 13 901! 4.25.139 13903:2.3.7.331 13 907 13 913 13 921 2.17.409 8-37-47 32.3.5.29 13 931 2.5.7.199 13 933 4-81.43 13 963 23.13.179 13 967 2.6983 13 997 4-3499 13 999 2.3.2333 14 009 8. 1 7. 103 14 01l| 2.3 5.467 140294.3.7-I67 14 033 16.877 14 051 2.25.281 14 057 8.7.251 14 071 2.3.5.7.67 14 081 256.5. 1 1 14 083 i 23.2347 14 087 2.7043 14107 2.3.2351 14143 2.3.2357 14 149 4.27. 131 14153 8.29.61 14 159i 2.7079 14173 4.3.1181 14177 14197 14 207 14 221 14 243 14 249 14 251 14 281 14 293 14 303 14 321 14 323 14 327 32-443 4.3-7. x 3 13 2.7103 4-9.5.79 2.7121 8.i3-!37 2.3.125.19 8.3.5-7.I7 4-9-397 2.7151 16.5.179 2. 3.7. 11. 31 2. 13.19.29 115, 26 37, 112 in, 40 3,n8 109, 46 115, 28 57, 105, 113, 117, 29, 69, 67, 129, 73 — 38,139, 241147, 11 — 81 — 37, 74, 53 7, 68 49, 62 116, 13 77, 90 — 97, 68 99, 63, 9i, 76 93, 25,116117, 11 115, 119, 68 149, 69 46.119, 71 52125, |i2 3 , 14127, 81 J63, 119, 49 9 Il8 > 5 64 - 92, 43 233, 7 i97, 25 i37, 37 77, 43 103, 41 37, 45 31, 66 62, 44 8 — 15,118 — 107, 52 51, 76 117, 22 ( - 119, 4 27, 119, 6 — 35,n4! — — in, 115, 32 81, — 101, 85, 8 4 | 13, 87, 82: 89, 80 39, — H9> 82 So 9 119, 119, 143, 127, 157, 121, 139, 28 — 23 118, 32 — |I04, 79 — J 1 00, 3 26, 107, 2 — 7 i39, 37 33208, 22 I _ 37211, 21 67 175, 3 1 30214, 20 56 3 1 14 72 13 5° i33, 4: 119, 2 125, 39 115, 18 230, 12 113, 22 47. 45 28, 59, 67 60 229, Il8, 13 40 35, 66 70, 44 116, 17 — 167, 33 QUADRATIC PARTITIONS. 43 p P -l a b c d e f A B L M 14 341 4-3-5- 2 39 79, 9° — . — 53, 62 239, 3 14 347' 2.9.797 — 35, 81 — 8, 69 16, 46 14 369 32-449 113. 4o in, 32 161, 76 — — 14 387 2.7193 — 105, 4i — — — 14 389 i 4.3- II - I °9 105, 58 — — 83, 5° 233, 11 14 401' 64.9.25 1,120 17, 84 163, 78 23, 68 227, 15 14 407! 2.3 49.49 — 123, 19 5°, 63 100, 42 14411 2. 5. 11. 131 H7, 19! — — — 14 419; 2.81.89 89, 57j - 112, 25 187, 29 14 423 2.721 1 — — I3 1 * 37 — — 14431 2.3.5.13.37 — 153, 67 118, 13 i57, 35 14 437 4.9.401 Ill, 46 — — 37, 66 74, 44 14 447J 2.31.233 — 127, 29 — — 14 449; 16.3.7.43 7,120 119, 12169, 84 7i, 5 6 239, 5 14 461 4.3.5.241 75, 94 — — 119, 10 89, 43 14 479 2.3.19.127 — — 121, 9 14, 69 28, 46 14 489 8.1811 67,100 117, 20133, 40 — — 14 503 2.3.2417 — — 155, 69 106, 33 212, 22 14 519 2.7. 17.61 — — 139, 49 — — 14 533 4-3-7-I73 "3. 42 — 101, 38 215, 21 14 537 8.23.79 61,104 33, 82 137, 46 — — 14 543 2. 1 1. 661 — — 121, 7 — — 14 549 4.3637 25,118 — — — 14 551 2.3- 2 5-97 — 123, 17 74, 55 9 1 , 43 14 557 4.3.1213 101, 66 — — 55, 62 131, 39 14 561 32.5-7-I3 119, 20 69, 70 127, 28 — — 14 563; 2.9.809 — 71, 69 — 100, 39 200, 26 14 591! 2.5.1459 — — 121, 5 — — 14593:256.3.19 97, 72 65, 72 129, 32 119, 12 238, 8 14 621 4.5I7.43 85, 86 — — — — 14 627 2. 71. 103 — 63, 73 — — — 14 629 4.3.2353 65,102 — — 91, 46 229, 15 14 633 8-31-59 83, 88 in, 34 121, 2 — — 14 639 2.i3.5 6 3 — — 121, 1 — — 14 653 4.9.11.37 27,118 — — 121, 2 115, 4i 14 657 64.229 121, 4 117, 22 125, 22 — — 14 669 4.I9-I93 U5, 38 • — — — 14 683 2.3.2447 — 115, 27 — 20, 69 40, 46 14 699 2-7349 — 93, 55 — — — 14 713 8.3.613 117, 32 121, 6 i39, 48 29, 68 233, I 3 44 QUADRATIC PARTITIONS. p P -l a b c d e f A B L M 14 717 4.13.283 59,106 — — — — 14 723 2.17-433 — 105, 43' — — — 14 731 2.3.5.491 — 59, 75 — 112, 27224, 18 14 737 16.3.307 119, 24 25, 84123, 14 73, 5 6 95, 43 14 741 4.5. 11. 67 131, IO — — — — 14 747 2.73. 101 — n7, 23 — — — 14 753 32.461 47,112 81, 64 145, 56 — 14 759 2.47.157 — — 149, 61 . — 14 767 2.3.23.107 — — 167, 81 22, 69 44, 46 14 771 2.5-7.211 — in, 35 — — — 14 779 2.9.821 — 91, 57 — 116, 21 232, 14 14 783 2.19.389 — — 169, 83 — — 14 797 4.27.137 109, 54 — — 113, 26 191, 29 14 813 4.7-23.23 107, 58 — — — — 14 821 4-3-5-I3-I9 in, 50 — — 11, 70 199, 27 14 827 2-3-7-353 — 83, 63 — 80, 53 239, 9 14 831 2.5.1483 — — H3, 53 — — 14 843 2.41. 181 — 69, 71 — — — 14 851 2. 27. 25. 11 — 73, 69 — 76, 55 241, 7 14 867 2-7433 — 33, 83 — — — 14 869 4.9-7-59 105, 62 — — 13, 70 223, 19 14 879 2.43-173 — — 127, 25 — 14 887 2.9.827 — — 123, 11 122, 1 119, 41 14 891 2.5.1489 — 31, 85 — — 14 897 16.49.19 131, 16 105, 44 137, 44 — — 14 923 2.9.829 — io 9, 39 — 104, 37 7, 47 14 929 16.3.311 23,120 131, 12 123, 10 119, 16 7i, 45 14 939 3.7.11.97 — 117, 25 — — — 14 947 2-3-47-53 — ri 3, 33 — 88, 49235, !3 14 951 2.25.13.23 — — 133, 37 — — 14 957 4-3739 61,106 — — — — 14 969 8.1871 85, 88 39, 82 161, 74 — 14 983 2. 3. 11. 227 — — 131. 33 110 , 3 1 17, 47 15 013 427.139 33>n8 — 1 59, 62 245, 1 15 017 8.1877 109, 56 15, 86 163, 76 — 15 031 2.9.5.167 — — 123, 7 122, 7 101, 43 15 053 4-53-71 13,122 — — — — 15 061 4-3-5-25I 119, 3° — — 19, 70 229, 17 15 073 32.3-I57 113, 48 31, 84 129, 28 121, 12 242, 8| 15 077 4.3769 79, 94 — — 1 - 1 QUADRATIC PARTITIONS. 45 V p-l a be d e f A B L M 15 083 2.7541 — - 5i, 79 — — — 15 09l| 2.3.5.503 — 121, 15! 92, 47 233, 15 15 101! 4.25-151 101, 70 — — — — 15 107 2.7.13.83 57, 77: — — — 15 121 16.27.5.7 105, 64 89, 60123, 2 113, 28 29, 47 15131 2.5.17.89 — ^3, i\ — — 15137 32.11.43 41,116 123, 2 173, 86 — — 15139 2.9.29.29 — 1, 87 — 4, 7i 209, 25 15 149 4.7.541 35,u8 — — — — 15 161 8-5-379 115, 44 123, 4127, 22 — — 15 173 4-3793 17,122 — — — — 15 187] 2.3.2531 — 7, 87 — 8, 71 221, 21 15 193 8.9.21 1 123, 8 55, 78i45, 54 91, 48 182, 32 15 199 2. 3. 17. 149 — 159, 7i 86, 51 172, 34 15 217i 16.3.317 121, 24103, 48 153, 6 4 97, 44 35, 47 15 227 2.23.331 — 123, 7 — — — 15 233 128.7.17 103, 68: 21, 86125, 14 — — 15 241 8.3.5.127 29,120 97, 54 137, 42 37, 68 167, 35 15259^.3.2543 — 11, 87 — 64, 61 247, 1 15 263 2.13.587 — — 161, 73 — — 15 269 4.11.347 IJ 3, 5° — — — 15 271 2-3-5-5°9 i39, 45 58, 63 116, 42 1527714.3.19.67 99, 74: — — 47, 66 94, 44 15 287 1 2.7643 i I2 5, 13 — — 15 289,8.3.49-13 117, 40 121, 18 129, 26 67, 60 134, 40 15 299 2.7649 — 39, 83 — — — 15 307! 2.3.2551 13. 87 — 32, 69 64, 46 15 313J 16.3.11.29 87, 88 119, 24 i55, 66 55, 64 247, 3 15 319 2.9.23.37 — — 163, 75 14, 71 227, 19 15 329 32.479 73,100 123, 10 127, 20 — — 15 331 2.3.5.7.73 _ 47, 81 — 116, 25 41, 47 15 349 4.3.1279 57,no ■ — 109, 34 2H, 25 15 359 2.7.1097 — — 151, 61 — — 15 361 1024.3.5 31,120 113, 36 1.3'ij 3° 119, 20 '79, 33 15 373 4.9.7-61 93, 82 — 95, 46 43, 47 15 377 16.31. 31 1,124 93, 58 *33, 34 — — 15 383 2.7691 — — 125, n — — 15 391 2.81. 5.19 — — 129, 25 122, 13 ^3, 45 15 401 825.7.11 5, I2 4 Si, 80 157, 68 — — 15 413 4.3853 23,122 — — — 46 QUADRATIC PARTITIONS. V P -l a b c d . fj A B L M 15 427 2.9.857 — i7, 87 — 112, 31205, 27 15 439 2.3-3 l8 3 — — ■ 169, 81 34, 69 68, 46 15 443 2.7.1103 105, 47 — — — 15 451 2.3.25.103 77, 69 — 124, 5 109, 43 15 461 4-5-773 65,106 — — — — 15 467 2. 11. 19.37 — 123, 13 — — — 15 473 16.967 113, 5 2 45. 82 149, 58 — — 15 493 4.3.1291 97, 78 — — 101, 42 202, 28 15 497 8.13.149 11,124 3, 88 125, 8 — — 15 511 2.3.5.11 47 — — 133, 33 118, 23 49, 47 15 527 2,7.1109 — ' — 125, 7 — — 15 541 4-3 5-7-37 121, 30 — — 29, 70 181, 33 15 551 2. 25. 311 — — 127, 17 — — 15 559 2-3-2593 — — 147, 55 122, 15 244, 10 15 569 16.7-139 55, 112 9, 88 i37, 4o — — 15 581 4.5. 19.41 59, IIQ — — — — 15 583 2 -3-49-53 — — 129, 23 46, 67 247, 7 15 601 16.3.25.13 i5> 12 4 83, 66 151, 60 7, 72 14, 48 15 607 2.27.17 17 — — 125, 3 22, 71 I9 1 , 3i 15 619 2.3.19.137 — 119, 27 — 124, 9 248, 6 15 629 4 39°7 125, 2 — — — — 15 641 8.5.17.23 125, 4 123, 16 133, 32 — — 15 643 2. 9. 11. 79 — 125, 3 — 116, 27 232, 18 15 647 2.7823 — 143, 49 — — 15 649 3 2 -3- l6 3 105, 68 59, 78 141, 46 79, 56 89, 45 15 661 4.27.5.29 125, 6 — — 31, 7° 241, 13 15 667 2.3-7-373 — 23, 87 — 92, 49 55, 47 15 671 2.5.1567 — — 157, 67 — — 15 679 2.9.13.67 — — 127, 15 98, 45 196, 30 15 683 2.7841 — in, 41 — — 15 727 > 2.3 2621 — — >37, 39 38, 69 76, 46 15 731 2-5-121.13 — 57, 79 — — 15 733 4.9.19.23 73,102 — — 125, 6 250, 4 15 737 8.7.281 19,124 117, 32 127, 14 — — 15 739 . 2.3.43.61 — 67, 75 — 124, 11 9 1 , 45 15 749 4-3 T - I2 7 95, 82 — — — — 15 761 16.5. 197 119, 40 87, 64 169, 80 — 15 767 i 2.7883 — — 133, 3 1 — — 15 773 | 4-3943 43>n8 — — — 15 787 1 2.9.877 — 125, 9 — 68, 61 115, 43 QUADRATIC PARTITIONS. 47 p p—1 a b c d e f A B L M 15 791 2.5.1579 127, 13 — 15 797 411.359 121, 34 — . , 15 803 2.7901 — ! 45, 83 15 809 64.13.19 97, 80 81, 68131, 26 15 817j 8.3.659 21,124115, 36 173, 84125, 8149, 39 15 823 2.27.293 — 145, 51 86, 53245, 11 15 859 2.9.881 — 89, 63 — 104, 41227, 21 15 877 ! 4.81.49 1,126 — ! 53, 66106, 44 15 881 8.5.397 125, 16 33, 86137, 38 — 15 887j 2. 13.13.47 — — 127, Hi — — 15 889 16.3.331 65,108 61, 78 *33> 3°H9, 24 238, 16 15 901' 4.3-25-53 5,126 — — 103, 42 206, 28 15 907 2.3.11.241 — 97, 57 28, 7x185, 33 15 913 8.9.13.17 123, 28 125, 12 *35, 34 19, 72; 38, 48 15 919 2.3.7.379 — — 129, 19 74, 59251, 5 15 923 2. 19.419 — Q, 89 — _ j _ 15 937 64.3.83 121, 36 85, 66 157, 66 95, 48190, 32 15 959 2. 79.101 — 139, 4i — - — 15 971 2.5.1597 39, 85 — — 15 973 4-3-1331 33,122 ~~ — 85, 54 170, 36 I599IJ2.3.5.13.41 — T 47, 53 2, 73 217, 25 16001 128.125 25,124 117, 34 127, 8 — — 16 007 2. 53.151 *33, 29 — — 16 033 32.3.167 87, 92 101, 54 159, 68 89, 52 67, 47 16 057, 8.9.223 51,116 107, 48 127, 6 125, 12 250, 8 16061! 4.5.ii.73 85, 94 — — — — 16 063 2.3.2677 — 129, 17 70, 61 253, 3 16 067 2.29.277 — 15, 89 — — 16 069 4-3- i 3 io 3 63,110 — 37, 7o 247, 11 16 073 8.49.41 107, 68 99, 5 6 151, 5^ — — 16 087 2.3-7.383 — — i55, 63 10, 73 229, 21 16 091 2.5.1609 — 93, 61 — — — 16 097 32.5 3 119, 44 123, 22 127, 4 — — 16 103 2.8397 — — *3h 2 3 — — 16111 2.9.5.179 — — 127, 3 118, 27 236, 18 16127 2.11.733 — — 127, 1 — — 16 139 2.8069 — 117, 35 — — — 16 141 4.3.5.269 115, 54 — — 127, 2 121, 43 16183 2.9.29.31 — — 141, 43 14, 73 205, 29 16 187 2.8093 — 123, 2S — — — 48 QUADRATIC PARTITIONS. p p-1 a b c d e f A B 1 L M 16189 4.3.19.71 117, 5° — — 119, 26 i97, 31 16 193 64.11.23 127, 8 in, 44 131, 22 — — 16 217 8.2027 29,124 27, 88 143, 46 — — 16 223 2.8111 — — 145, 49 — — 16 229 4-4057 127, 10 — — — — 16 231 2-3-5-54I — — 133, 27 98, 47 239, 17 16 249 8.3.677 43,120 7, 9° 129, 14 107, 40 13, 49 16 253 4 17.239 37,122 — — — — 16 267 2.3.2711 — 115, 39 — 92, 51 184, 34 16 273 16.9.113 127, 12 125, 18 165, 74 49, 68 155, 39 16 301 4.25.163 125, 26 — — — — 16 319 2.41. 199 — — i37, 35 — — 16 333 4.3.1361 77,102 — — 79, 58 253, 7 16 339 2.3.7.389 — 119, 33 — 116, 31 23, 49 16 349 4.61.67 107, 70 — — — — 16 361 8.5.409 "5. 56 81, 70 131, 20 — — 16 363 2.81. 101 — 35, 87 — 104, 43 25, 49 16 369 16.3. 11. 31 113, 60 13, 90 149, 54 121, 24 242, 16 16 381 4-9-5-7-I3 91, 90 — — 41, 70 169, 37 16 411 2-3-5-547 — 83, 69 — 128, 3 256, 2 16 417 32.27.19 in, 64 127, 12 145, 48 103, 44 29, 49 16 421 4.5.821 95, 86 — — — — 16 427 2.43.191 — 117, 37 — — — 16 433 16.13.79 7,128 105, 52 139, 38 — — 16 447 2.3.2741 — i53, 59 118, 29 3*i 49 16 451 2.25.7.47 — 63, 79 — — — 16 453 4-9-457 127, 18 — — 5, 74 227, 23 16 477 4-3-1373 59,iH — — 7, 74 215, 27 16 481 32.5- io 3 55,n6 123, 26 173, 82 — — 16 487 2.8243 — 163, 7i — — 16 493 4.7.1931 ^3, 98 — — — — 16 519 2.3-2753 — — 141, 41 62, 65 257, 1 16 529 1 16.1033 127, 20 99, 58 151, 56 — — 16 547 1 2.8273 — 87, 67 — — — 16 553 8.2069 13,128 in, 46 179, 88 — — 16 561 16.9.5.23 81,100 19, 90 181, 90 127, 12 254, 8 16 567 2.3.11.251 — 165, 73 38, 71 251, 11 16 573 4.3.1381 123, 38 — 71, 62 257, 3 16 603 2.3.2767 — 59, 81 — 56, 67 145, 4i 16 607 2. 19.19.23 — — 145, 47 — QUADRATIC PARTITIONS. 49 p p-l a b d e f A B L M 16 619 2.7.1187 69, 77 _ _ — 16 631 2.5.1663 — — 133, 23; — — 16 633 8.27. 7.11 107, 72 89, 66 129, 2 85, 56 ^3, 47 16 649 8.2081 125, 32 129, 2 131, 16 — — 16 651 2.9.25.37 — 107, 5 1 — 112, 37 223, 25 16 657" 16.3.347 129, 4 67, 78 J 35> 28113, 36 226, 24 16 661 4-5-49-I7 119, 5° — — — — 16 6731 32.521 17,128 129, 4 161, 68 — 16 691 ; 2.5.1669 — "9, 5 — — — 16 693 4.3. 13. 107 103. 78 — — «5» 34 217, 27 16 699 2.3.121.23 — 101, 57 — 124, 21 248, 14 16703,2.7.1193 — — 169, 77 — — 16 729 ! 8.3.17.41 123, 40 23, 90 *39, 3 6 77, 60 154, 40 16 741 1 4.27-5-31 129, 10 — — 107, 42 214, 28 16 747i 2.3.2791 — 85, 69 — '128, 11 161, 39 16 759 2.9.49.19 — — 171, 79122, 25 47, 49 16 763 2. 17. 17.29 — 99, 59 — — 16 787 2. 7. 11. 109 — 15, 9i — — — 16 811 2.5-41-41 — 123, 29 — — — - 16 823 2.13.647 — — 131, 13 — — 16 829 4.7.601 85, 98 — - — — — 16 831 2.9.5. 1 1. 1 7 — — J59, 65 58, 67 259, 3 16 843 2.3.7.401 — 61, 81 — 80, 59 257, 7 16 871 2.5.7.241 — — — — 16 879 2.3.29.97 — i77, 85 2, 75 4, 5° 16 883 2.23.367 — 129, 11 — — — 16 889 8.21 1 1 83,100 117, 40 133, 20 — — 16 901 4-25.T3.13 1,13° — — — — 16 903 2.27.313 — — i79, 87 13°, 1 *33> 43 16 921 8.9.5.47 125, 36 53, 84143, 42 37, 72 74, 48 16 927 2.3-7.I3-3 1 — — 183, 91 i3°> 3 260, 2 16 931 2.5.1693 — 33, 89 — — — 16 937 8.29.73 59> IJ 6 3, 92167, 74 — — 16 943 2.43.197 — — 161, 67 — — 16 963 2.3.11.257 — 95> 63 — 124, 23 55, 49 16 979 2.13-653 — 129, 13 — — — 16 981 4.3-5.283 9,i3° — — 83, 58 9 1 . 47 16 987 2.3-19.149 — 43, 87 — 52, 69 104, 46 16 993 32.9.59 73>i°8 91, 66 141, 38 121, 28 205, 31 17 011 2.243.5-7 — 127, 21 3 2 , 73 187, 35 50 QUADRATIC PARTITIONS. p p-l a b c d e f | A B L M 17 021 4-5-23-37 11,130 — — — — 17 027! 2.8513 — 57, 83 — — — 17 029 4.9.11.43 J27, 3°j — — 9h 54 182, 36 17 033 8.2129 67,112129, 14 131, 8 — — 17 041 16.3.5.71 129, 20 29, 9° 133, 18 79, 60 158, 40 17 047 2.9.947 — — 163, 69 130, 7 I5 1 , 4i 17 053|4-3-49- 2 9 117, 5 8 — — 25, 74 J97, 33 17 077j 4-3-1423 119, 54 — — 125, 22 59, 49 17 093j 44273 47,122 — — — — 17 099| 2.83.103 — 93, 65 — — — 17 107 2.3.2851 — 103, 57 — 112, 39 224, 26 17 117 4.11.389 9 1 , 94 — — — — 17 123 2.7.1223 — in, 49 — — 17 137 16.9.7. 17 89, 96 55, 84 i53< 5 6 95, 52 61, 49 17 159 2-23-373 — — I3 1 , 1 — — 17167 2.3.2861 — — i35, 23 82, 59 95, 47 17 183! 2.121.71 — — iSh 53 — — 17 189 4-4297 17,13° — — — — 17 191' 2.9.5.191 — — |i47, 47 118, 33236, 22 17 203 2.3.47.61 — - 119, 39| 100, 49247, 17 17 207 2.7.1229 — — Ii57, 61 — - 17 209; 8.9.239 53,i2o 71, 78 161, 66 131, 4 119, 45 17 231 2.5.1723 — 167, 73 — 17239:2.3.13.13.17 — — !33, J 5 46, 71 167, 39 17 257i 8.3.719 101, 84 83, 72 135, 22 107, 44 239, 21 17291:2.5.7.13.19 27, 9 1 — 17 293; 4-3-H.I3I 83,102 — "-- 65, 66 13°, 44 17 299| 2.9.31. 31 — 1, 93 68, 65 263, 1 17 317; 4.9.13.37 129, 26 — — 85, 58 259, 9 17 321j 8.5.433 115, 6 4 in, 50 163, 68 — 17 327 2.8663 — — 145, 43 — — 17 333 4.7.619 103, 82 — — — — 17 341 4-3-5-J7-I7 21,130 — — 121, 30 242, 20 17 351 2.25.347 — — 133, 13 — — 17 359 2.3.11.263 — — i53, 55 22, 75 44, 5° 17 377 32.3. l8r 81,104 113, 48 147, 46 7, 76 235, 23 17 383 2.3.2897 — — 171, 77 74, 63 148, 42 17 387 2.8693 — 117, 43 — — 17 389 ; 4.27.7.23 125, 42 — — 3h 74 191, 35 17 393 16.1087 113, 68 51, 86 151, S 2 - QUADRATIC PARTITIONS. 51 V p-1 a b c d e f A B L M 17 40l| 8.3.25.29 45,124101, 60133, 12 43, 72 86, 48 17 417 8.7.311 131, 16 63, 82 137, 26 — 17 419 2.3.2903 — "> 93 56, 69 112, 46 17 43lj 2.3.5.7.83 — — 141, 35 38, 73 181, 37 17 443 2.27. 17.19 — 89, 69 — 104, 47 245, !9 17 449 ; 8.3.727 5^32 131, 12 157, 60! 11, 76 217, 29 17 467 2. 3.41. 71 — i3> 93 128, 19 7i, 49 17 471; 2.5.1747 — — 161, 65 — 17 4771 4.17.257 79,106 — — — — 17 483 2.8741 — 75, 77 — — — 17 489 16.1093 95, 92 99, 62 i33, 10 — — 17 491 2.3.5.11. 53 — 79, 75 88, 57 176, 3^ 17 497! 8.27.81 91, 96 73, 78 M5, 42 13, 76 241, 21 17 509; 4-3-1459 97, 9° — — 53, 7o 157, 4i I75i9j2.19.461 — — i37, 25 — — 17 539 2.3.37.79 — 49, 87 — 92, 55 73, 49 17 551 2.27.25.13 — — i77, ^3 26, 75 52, 50 17 569! 32.9.61 87,100 37, 90 141, 34 113, 4o 7, 5 1 17 573 4-23.191 127, 38 — — — — 17 579 : 2. 11. 17. 47 — I2 3, 35 — — — 17 581 4-3-5-293 115, 66 — — 127, 22193, 35 17 597 4.53-83 101, 86 — — — — 17 599| 2.3.7.419 — — 151, 5 1 n8, 35; 13, 51 17 609 8.31. 71 35^28 129, 22 169, 74 — — 17 623 12.9.11.89 — — 181, 87 50, 71263, 7 17 627 2.7.1259 — 93, 67 — — — 17 657:8.2207 109, 76 27, 92 *33, 4 — — 17 659 2.81. 109 — 19, 93 — 28, 75 56, 5° 17 669 4.7.631 113, 7o — — — — 17 681 16.5.13.17 65,116 3, 94 133, 2 — — 17 683 2.3.7.421 — 121, 39 — 76, 63152, 42 17 707 2.3.13.227 — 133, 3 — 128, 21256, 14 17 713 16.27.41 17,132 109, 54 135, l6 121, 32 25, 51 17 729 1 64.277 127, 40 in, 52 161, 64 — — 17 737 8.3.739 i$h 24 95, 66 147, 44 133, 4*45, 43 17 747 2.19.467 — 63, 83 — — — 17 749 4.9.17.29 105, 82 — — l$h I4I73, 39 17 761 32.3.5-37 119, 60 *33, 6 173, 78 47, 72 94, 48 17 783 2.17.523 — — 149, 47 — — 17 789 4.4447 133. IO — — — 52 QUADRATIC PARTITIONS. p P -l a b c d e f A B L M 17 791 2 -3-5-593 — — !53, 53 2, 77 233, 25 17 807 2.29.307 — — 167, 71 17 827 2.3.2971 — 23, 93 — 52, 71161, 41 17 837 4.343-J3 131, 26 — — — - — 17 839 2.9.991 — — 159, 61 86, 59263, 9 17 851 2.3.25.7.17 — 133, 9 — 8, 77 239, 23 17 863 2.3.13.229 — — i39, 27 106, 47 35, 5i 17 881 8.3.5.149 59,120 41, 90 177, 82 133, 8 109, 47 17 891 2.5.1789 — 129, 25 — — — 17 903 2.8951 — — l6 9, 73 — — 17 909 4.121.37 55>122 — — — — 17 911 2.9.5.199 — — 147, 43 94, 55 259, 13 17 921 512.5.7 89,100 117, 46 157, 58 — - 17 923 2.3.29.103 — 25, 93 — 44, 73 175, 39 17 929 8.27.83 125, 48 127, 30 179, 84 131, 16 83, 49 17 939 2.8969 — "*> 53 — 17 957 4.67.67 1,134 — — — 17 959 2.3-4I.73 — — 141, 31 134, 1 131, 45 17 971 2.3-5-599 — 113, 5 1 128, 23 J 97, 35 17 977 8.3.7.107 5 X , I2 4 i33, I2 165, 68 125, 28 4i, 51 17 981 4-5-29-3I 5,*34 — — — — 17 987 2.17.23.23 — 105, 59 — — — 17 989 4.3.1499 33>*3° — — 133, 10 163, 41 18 013 4.3.19.79 *33, 18 — — 89, 58 85, 49 18 041 8.5.11.41 85,104 57, 86 187, 92 — — 18 043 2.3.3I.97 — ■ 131, 21 — 16, 77 215, 3i 18 047 2.7.1289 — — r 37, 19 18 049 128.3.47 25,132 43, 9o 189, 94 119, 36 238, 24 18 059 2.9029 3, 95 — - — 18 061 4.3.5-7.43 i3 J , 30 — — 113, 42 226, 28 18 077 4-45 x 9 n,i34 18 089 8.7.17.19 133, 20 51, 88 167, 70 — — 18 097 16.3.13.29 in, 76 77, 78 135, 8 65, 68 269, 1 18119 2.9059 — — 163, 65 — 18121 8.3.5.151 61,120 97, 66 r 37, 18 133, 12 266, 8 18 127 2.9.I9-53 — — 135, 7 62, 69 124, 46 18 131 2-5-49-37 — ' 9, 95 — — — 18 133 4-3-1511 57,122 — — 131, 18 262, 12 18 143 2.47.193 — — i75, 79 — — 18 149 4-I3-349 65,118 — — — — QUADRATIC PARTITIONS. 53 p p — 1 a b c d e f A B L M 18 168 1 8.3-757 75,H2 121, 42 *39i 24 29, 76 199, 35 18181 4.9.5. 101 x 5>i34 — 59, 7° I5 r > 43 18191 2.5.17.107 — — . !37, 17 — — 18198 2.27.337 — — 141, 29 *34, 9 268, 6 18 211 2.3.5.607 — 119, 45 92, 57 184, 38 18 217 8.9.11.23 69,116 125, 36 *35i 2 77, 64 "5, 47 18 223 2-3-3037 — — 135, 1 130, 21 260, 14 18 229 4-3-49 3 J *35> 2 — — 109, 46 247, 21 18 233 8-43-53 43,128 135. 2 161, 62 — . — 18 251 2.125.73 — 99, 65 — — — 18 253 4-27-13-13 93, 98 — — 1, 78 2, 52 18 257 16.7. 163 119, 64 r 35, 4 i37, 16 — 18 269 4-45 6 7 37>i3o — — — 18 287 2.41.223 — — H5» 37 — 18 289 16.9. 127 135, 8 89, 72 *7h 74 3i, 76 259, 15 18 301 4.3.25.61 101, 90 — — 7, 78 14, 52 18 307 2. 81. 113 — 127, 33 — 80, 63 160, 42 18 311 2-5-1831 181, 85 — 18 313 8.3.7.109 117, 68 131, 24 T41, 28 101, 52 55, 51 18 329 8.29.79 I2 5, 52 123, 40 149, 44 — — 18 341 4.5-7-I3I 79,110 — — — — 18 353 16.31.37 103, 88 135, 8 139, 22 — 18 367 2.3.3061 — 167, 69 70, 67271, 1 18 371 2. 5. 11. 167 — IJI , 55 — — — 18 379 2.9.1021 — 109, 57 — 64, 69 128, 46 18 397 4-9-7-73 21,134 — — 73, 66146, 44 18 401 32-25-23 55, I2 4 27, 94 143, 32 — — 18 413 4.4603 6 7 ,it8 — — — — 18 427 2-3-37-83 — H5, 5i — 100, 53 59, 5 1 18 433 2048.9 127, 48 1, 96 H5, 36 95, 56 263, 13 18 439 2-3-7-439 — — i39, 21 106, 49 253, *9 18 443 2.9221 — 5 J , 89 — — — 18 451 2.9.25.41 — 73, 81 — 76, 65 119, 47 18 457 8.3.769 *3h 36 5, 96 *75i 78133, i6| 181, 39 18 461 4.5-I3-7I 85,106 — — — — 18 481 16.3.5.7.11 135, 16 7, 96 i37, 12 127, 28211, 33 18 493 4-3-23-67 123, 58 — — 119, 3^ 2 33, 27 18 503 2. 11. 29.29 — 149, 43 — — 18 517 4-3-1543 119, 66 — — 115, 42230, 28 18 521 8.5463 5,136 87, 74; 139, 20 — - 54 QUADRATIC PARTITIONS p P -l a be d e f j A B L M 18 523 2.27.343 — 35, 93 — 136, 3272, 2 18 539 2.13.23.31 — 69, 83 — — — 18 541 4.9.5.103 125, 54 — — 17, 78 34, 52 18 553 8-3-773 83,108 n, 96 i59, 58: 35, 76 193, 37 18 583 2.3.19.163 — — 171, 73! 94, 57 188, 38 18 587 2.9293 — 45, 9i — — 18 593 32.7.83 47,128 in, 56 179, 82 — — 18 617 8.13.179 11,136, 135, M 155, 52: — — 18 637 4-3-1553 99, 94 — — 47, 74 269, 9 18 661 4-3-5-3 11 81,110 — — 133, 18 266, 12 18 671 2.5.1867 — 137, 7i — — 18 679 2.3-11-283 — — i73, 75 98, 55 67, 5* 18 691 2.3.5.7.89 — 121, 45 - 52, 73 271, 7 18 701 4.25.11.17 115, 74 — — — 18 713 8.2339 133, 32 105, 62 145, 34 — — 18 719 2.49.191 — — i37, 5 — — 18 731 2-5-1873 — 93, 7i — — — 18 743 2.9371 — — 139, n — — 18 749 4.43.109 43, 1 3° — — — — 18 757 4.9.521 129, 46 — — 85, 62 101, 49 18 773 4.13.19.19 i37, 2 — — — — 18 787 2.3.31. 101 — 137, 3 — 8, 79 229, 29 18 793 8.81.29 37,i32 19, 96 189, 92 109, 48 218, 32 18 797 4.37.127 29,134 — — — — 18 803 2.7.17.79 — i35, J 7 — — — 18 839 2.9419 — — 149, 41 — — 18 859 2.3.7.449 — 61, 87 — 136, 11 103, 49 18 869 4-53-89 137, i° — — — — 18 899 2.11.859 9, 97 — — — 18 911 2. 5. 31. 61 — 167, 67 — — 18 913 32.3-I97 137, I2 101, 66 141, 22 71, 68 275, * 18 917 4.4729 ! 3M34 — — • — — 18 919 2.9.1051 — — 179, 81 14, 79 223, 31 18 947 2-9473 — 135, T 9 — — — 18 959 2-9479 — — 161, 59 — — 18 973 4.9.17. 31 123, 62 — — • 121, 38 7, 53 18 979 2.33163 — 4i, 93 — 16, 79 253, 21 19 001 8.125. 19 115, 76 123, 44 149, 40 — 1 - 19 009 64.27.11 135, 28 53, 90 159, 56 41, 76 ,187, 39 19 013 4.49.97 | 97, 98 1 — — QUADRATIC PARTITIONS. 55 1 A B L M 19031 2.5. n. 173 19087 4.4759 19051 2.3.25.127 19069^4.3.7.227 19 073 128.149 19 079 2.9539 19 081 8.9.5.53 19 087 2.3.3181 19121 16.5.239 19139 2.7.1367 19141 4-3-5- XI - 2 9 19 157 4-4789 19 163 2. 11. 13.67 19 181 ! 4.5.7.137 19 183, 2.3.23.139 19 207 19 211i 19 213i 19 219 19 231 19 237 19 249| 19 259 19 267 19 273 19 289 19 301 19 309 19 319 19 333 19 373 19 379 19 381 19 387 19 391 19 403 19 417 19 421 19 423 19 427 101, 94 — ! 77, 5,138 103, 9 2 75, 75,116109, 60 25,136 29, 5° 89,106 35,i34 87, 33, 5 1 , 9i 2.9.11.97 2. 5. 17. 113 4.3.1601 2.3.3203 2.3.5.641 4.3.7.229 16.3.401 2.9629 2.3.13.13.19 8.3.11-73 8.2411 4-25.193 4.3.1609 2.13.743 4.27.179 4.29.167 2.9689 4.3-5- I 7.i9 2.27.359 2.5.7.277 2.89.109 8.3.809 4.5.971 2.9.13.83 2. 11. 883 13, 138 79, 135, 114 32 43, 132 133, 49, "5, 40 130 78 17, 138 67, 122 135, 34 IOI, 139, 96 10 69, 137= 121, 21, 113, 29, 48 97 57 96 98 129, 107, 75, i37, 37 63 83 18 — 87, 77 i57, 53 i75, 76 139, 141, 185, !39, 191, 195, J 59, 139, i39, !39, 124, i37, 9i, 130, 133, 22 70, 22, 3i, 64, 38, 53, 7, 128, 61, — 79, i39, 69 79 78 7i 77 74 80 3i 72 143, 155, 161, 109, 40, 23 - 48133, 5713°, 24 J 9, 53 107, 49 152, 40 260, 18 !99, 37 140, 46 259, 19 62, 52 i49, 45 269, 13 275, 7 233, 29 35, 53 122, 48 158, 44 133, 47 41, 53 9 1 , 39 266, 16 29 43, 53 56 QUADRATIC PARTITIONS. p p-1 a be d e f A B L M 19 429 4.3.1619 95,102 139, 6278, 4 19 433 8-7-347 83,112 15, 98185, 86 — J — 19 441 16.243.5 71,120 73, 84 171, 70 121, 40241, 27 19 447 2-3-7-463 — — 1*57, 5*1 122, 39244, 26 19 457 1024.19 31,136 63, 88 145, 28 — '■ — 19 463 2.37.263 — - 149, 37 — — 19 469 4.3I-I57 125, 62 - — — — 19 471! 2.3.5. 11.59 ; i77, 77 118, 43 247, 25 19 477 5 4.9.541 39,134 — — 35, 78 70, 52 19 483; 2.3.17.191 139, 9 — 124, 37 235, 29 19 489 32.3.7.29 105, 92 133, 3° 141, 14 17, 80 257, 21 19 501 4.3- I2 5-i3 Sh*&\ — 97, 58 27 1 , 13 19 507 2-3-325 1 — 47, 93 — 28, 79 265, 17 19 531 2.9-5-7-3' — 9i, 75 — 116, 45 232, 30 19 541 4-5-977 121, 70 — — — — 19 543 2-3-3257 — 141, 13 T34, 23 203, 37 19 553 32.i3.47 137, 2.8 69, 86 191, 92 — — 19 559 2. 7. 11. 127 — — i79, 79 — — 19 571 2.5.19.103 — 39, 95 — — — 19 577 8.2447 139, * 6 i35, 26 193, 94 — — 19 583 2.9791 — 169, 67 — — 19 597 4-3-23-71 61,126 — — 127, 34 229, 31 19 603 2.81. 121 — 1, 99 — 140, 1 137, 47 19 609 8.3.19.43 3> I 4° 139, 12 149; 3 6 101, 56 269, 15 19 661 4-5-983 13 1 , 5° — — — — 19 681 32-3-5.41 9,140 59, 90 141, 10 113, 48 226, 32 19 687 2-3-17-193 — — 147, 3 1 2, 81 4, 54 19 697 16.1231 79,116 45, 94 167, 64 — — 19 699 2.3.49.67 — 49, 93 — 4, 81 8, 54 19 709 4.I3.379 53»I3« — — — — 19 717 4.3.3I.53 in, 86 — — 133, 26 55, 53 19 727 2.7.1409 — — i43, i9 — — 19 739 2-71-139 — 117, 55 — — — 19 751 2.125.79 — i49, 35 — — 19 753 8.3.823 123, 68 t$h 36 141, 8 139, I2 278, 8 19 759 23-37.89 — — 151, 39 74, 69 148, 46 19 763 2.41. 241 in, 61 — — — 19 777 64.3.103 129, 56 97, 72 177, 76 65, 72 130, 48 19 793 16.1237 137, 32 135, 28 155, 46 — — 19 801 8.9.25. 11 99,100 37, 96 143, l8 1 77, 68 281, 3 QUADRATIC PARTITIONS. 57 p p-1 a b c d e f A B L M 19 813 1 4.3-13-127 97,102 — — 91, 62 95, 5i 19 819 2.27.367 — 109, 63 — 136, 21 272, 14 19 841; 128.5. 31 95> io 4 129, 40 163, 58 — — 19 843 2.1.3307 — 121, 51 — 140, 9 280, 6 19 853' 4.7.709 77,118 — — — — 19 861 4-3-5-331 105, 94 — — 131, 30 262, 20 19 867 2.3,7.11.43 — l 33, 33 — 80, 67 121, 49 19 889 16.11.113 17,140 141, 2 149, 34 — — 19 891 2.9.5.13.17 — 17, 99 — 104, 55 61, 53 19 913 8.19.131 107, 92 141, 4 151, 3^> — — 19 919 ! 2.23.433 — — 191, 91 — — 19 927 2.243.41 — — 147, 29 122, 41 245, 27 19 937 32.7.89 119, 76 27, 98 143, 16 — — 19 949 4.4987 115, 82 — — — — 19 961 8.5.499 19,140 117, 5 6 181, 80 — — 19 963 2.9.1109 — i9, 99 — 140, 11 173, 43 19 973 4-4993 127, 62 19 979 2.7.1427 — Hi, 7 — — . — 19 991 2.5.1999 — 197, 97 — — 19 993 8.3.49.17 *33, 48 119, 54 171, 68 109, 52 265, 19 19 997 4.4999 139, 26 — — — 20 011 2.3.5.23.29 — 83, 81 56, 75 112, 50 20 021 4.5.7. 11. 13 89,110 — — — — 20 023 2.3.47.71 — — 149, 33 70, 71 143, 47 20 029 4.3.1669 123, 70 — — 73, 7° 283, 1 20 047 2.3- I 3- 2 57 — — 153, 4i 98, 59 275, J 3 20 051 2.25.401 — 87, 79 — — 20 063 2.7.I433 — — I5 1 , 37 — 20 071 2.9.5.223 — — 163, 57 86, 65 281, 7 20 089 8.81.31 117, 80 89, 78 161, 54 139, 16 187, 41 20101 4-3.25.67 65,126 — 43, 78 86, 52 20 107 2.9.1117 — 53, 93 — U°, 13 101, 51 20113 16.3.419 87,112 41, 96 185, 84 79, 68 125, 49 20117 4.47.107 121, 74 — — — 20123 2.10061 — 141, 11 — — — 20129 32.i7.37 23,140 I2 3, 5° i73, 7o — — 20 143 2.27.373 — — i45, 21 134, 27 268, 18 20 147 2.7.1439 — i35> 3i — — — 20 149 4.3.23-73 57,13° — 61, 74 161, 45 20161 64.9.5.7 135, 44 107, 66 143, I2 31, 80 209, 37 58 QUADRATIC PARTITIONS. V s A Bj L M 86 1, 82 247, 27 77 62 — — 47 88 131, 32 227, 33 «$ 50 263, 21 5 9 6 43 5°, 77 40, 79 281, 9 277, 13 94 13, 82 112, 51 55, 76 259, 23 224, 34 283, 7 25 26, 81 52, 54 64 98 5 69 i33, 30 266, 20 142, 9 284, 6 3 2 122, 43 7, 55 TOO, 59 77, 53 49 134, 29 221, 35 38 119, 46 139, 20 19, 55 79, 53 7i 19, 82 265, 21 23 118, 47 104, 57 23, 55 208, 38 20 173 20177 20183 20 201 20 219 20 231 20 233 20 249 20 261 20 269 20 287 20 297 20 323 20 327 20 333 20 341 20 347 20 353 20 357 20 359 4.3.41.41 16.13.97 2.10091 8.25. 101 2. 11. 919 2.5.7.17.17 8.9.281 8.2531 4-5- IOI 3 4.9-563 2.9.49.23 8.43.59 2.9.1129 2.10163 4.i3- I 7-23 4-9.5- TI 3 2-3-339 1 128.3.53 4.7.727 2.27.13.29 20 369 16.19.67 20 389 .4.3. 1699 20 393 8.2549 20 399 2.7.31.47 20 407 ; 2.3.19.179 20 411 2.5.13.157 20 431 2.9.5.227 20 441 8.5.7.73 20 443 2.3.3407 20 477 4-5 1 19 20 479 2.3.3413 20 483 2.49.1 1. 19 20 507 20 509 20 521 20 533 20 543 20 549 20 551 20 563 2.10253 4.3.1709 8.27.5.19 4.3-29-59 2.10271 4.1 1.467 2.3- 2 5- J 37 2.3.23.149 3> I 42| — 4i,i3 6 57, 92 187, — i/9, 101,100 93, 76167, — 141, 13J — — 157, 53,132125, 48189, 125, 68 69, 88143, 95,106 35,!38j — — i43, 3^ 56 33, 98163, 55, 93 — 155. i3,M2 35, 46 63,128 49, J 34 85, 8i| 79, 84195, — 147, 87, 80169, 137, 4o i i5,H2 733, S 2 14*1 16I199, 143, 173, 143, M3, — — 159, - 3, 101 29, 39, [40 34 21, 29, 100 99 75, 45, [22 [36 9, 93, 143, 101 77 6 37, 42 43, to 3i, 99 153, 175, 147, QUADRATIC PARTITIONS. 59 V p-l a b c d e f | A B L M 20 593 16.9.11.13 143. I2 109, 66 181, 78 71, 72142, 48 20 599 2 .3.3433 — — 157, 45 74, 71287, T 20 611 2.9.5.229 — M3, 9 — 68, 73, I 5 I , 47 20 627 2.10313 — 15,101 — — — 20 639 2.17.607 — — 191, 89 20 641 32-3-5-43 79,120 47, 96147, 22 143, 8167, 45 20 663 2-10331 — — 155, 4i — — 20 681 8.5. 11.47 85,116 141, 20173, 68 — — 20 693 4-7-739 23,142 — — — — 20 707 2.3.7.17.29 — 113, 63 — 32, 81 64, 54 20 717 4.5*79 109, 941 — — — — 20 719 2 9.1151 — — 161, 51 62, 75 124, 5° 20 731 2.3.5.691 — *33, 39 — 8, 83 257, 25 20 743 2-3-3457 — — 149, 27 94, 63 188, 42 20 747 2. 11. 23. 41 — I2 3, 53 — — 20 749 4-3-7-I3-I9 93>no — . — 143, 10 113, 5 1 20 753 16.1297 127, 68 99, 74 151, 32 — — 20 759 2.97.107 — — *97, 95 — — 20 771 2.5.31.67 — in, 65 — — — 20 773; 4-9-577 143, 18 — — 139, 22 205, 39 20 789 4.5197 25,142 — — — — 20 807 2.101.103 — — 203,101 — — 20 809 8.9.17.17 125, 72 1,102 147, 20 59, 76 169, 45 20 849 16.1303 i43> 20 141, 22 149, 26 — — 20 857 8.3.11.79 11,144 7,102 187, 84 107, 56 275, *7 20 873 8.2609 67,128 129, 46169, 62 — — 2O879j2.11.13.73 — — 15*1 3 1 — — 20 887 2.3.59.59 — — i47, 19 70, 73 289, 1 20 897! 32.653 49,i36 63, 92 145, 8 — — 20 899 2.243.43 — 143, 15 — 76, 71 137, 49 20 903 2.7.1493 — — 181, 77 — — 20 921 8.5.523 139, 40 57, 94i6i, 5° — — 20 929 64.3.109 J 35, 52 11,102 189, 86 127, 40 247, 29 20 939 2. 19. 19.29 — 141, 23 — — — 20 947 2-3-3491 — 137, 33 — 128, 39 256, 26 20 959 2.3.7.499 — — *53, 35 122, 45 244, 3° 20 963 2.47.223 — i35, 37 — — — 20 981 4-5-1049 55,i34 — — — 20 9831 2.3.13.269 155, 39 106, 57 212, 38 21001 8.3.125.7 75, I2 4 83, 84 *5 x i 3o 101, 60 202, 40 60 QUADRATIC PARTITIONS. p p-l a b c d e f A B L M 21011 2.5.11.191 — 81, 85 — — — 21 013 4.3.17.103 103,102 — — 29, 82 217, 37 21 017 8-37-7I 101,104 87, 82 145, 2 — — 21 019 a4.3x.113 — 61, 93 136, 29 49, 55 21 023 2.23.457 — — 145, J - — — 21 031 2.3.5.701 — — 147, *7 142, 17 91, 53 21 059 2.10529 — 129, 47 — — — 21061 4.81.5-13 i45> 6 — — 53, 78 1 106, 52 21 067 2-3-35 11 — 77, 87 — 20, 83 269, 21 21089 32.659 i45> 8 33, IO ° 179, 74 — — 21 101 4.25. 211 125, 74 — — — — 21107 2.61. 173 — i°5, 7i — — : — 21121 128.3.5. n 39 5 i4o i39> 3° 157, 42 i37, 28 53, 55 21139 2.3.13.271 — 121, 57 — 92, 65 287, 9 21 143 2. 11. 31. 31 — — 149, 23 — — 21149 4.17. 311 85,118 — — — — 21157 4- 3-41-43 in, 94 — — 133, 34 235, 33 21 le3 2.3-3527 — 1x5, 6 3 — 100, 61 283, 13 21169 16.27.49 i45> I2 19,102 199, 96 1, 84 2, 56 21179 2.10589 — 123, 55 — — 21187 2.9.11.107 — i45» 9 140, 23 209, 39 21191 2.5.13.163 — — 187, 83 — — 21 193 8.3.883 93, 112 95, 78 201, 98 5, 84 10, 56 21211 2.3.5.7.101 — 131. 45 — 88, 67 289, 7 21 221 4.5.1061 i45> J 4 — — — — 21227 2.10613 3, io 3 — — — 21247 2.3.3541 — — 177, 7i 142, 19 199, 41 21 269 ,4-13-409 ^37, 5o — — — — 21277 4.27.197 91,114 — — 55, 78 no, 52 21 283 2.3.3547 — 4i, 99 — 40, 81 80, 54 21313 64-9-37 127, 72 145, I2 161, 48 95, 64 97, 53 21317 4.73.73 1,146 — — — 21 319 2. 3. 11. 17. 19 — — 149, 21 146, 1 143, 49 21323 2.7.1523 — 69, 9 1 — — — 21341 4.5.11.97 5^46 — — — — — 21347 i 2. 13. 821 — 87, 83 — — 21377 128.167 89,116 117, 62 175, 68 — 2137S i 2.3-7-5°9 — 79, 87 — i3 6 , 3 1 229, 35 21383 2.10691 — 179, 73 — 21 391 | 2.3.5.23.31 — — 167, 57 146, 5 161, 47 QUADRATIC PARTITIONS. 61 f p-l a b c d e f A B L M 21397 4-3-1783 9,146 - 35, 82 211, 39 21401 8.25.107 125, 76 ! 123, 56 149, 20 | — — 21407 2.7. 11. 139 j — — 193, 89 ; — — 21419 2.10709 — 5 1 , 97 — 21 433 8.3.19.47 117, 88 25,102 155, 36125, 44 257, 27 21467 2.10733 — 75, 89 — — — 21481 ! 8.3.5.179 141, 40 113, 66 147, 8 77, 72 154, 48 21487 2.3.3581 — — 153, 3 1 142, 21 284, 14 21491 2.5-7-307 — 33, IOT — — 21 493 4.27.199 87,118 — — 131, 38 245, 3 1 21499 23.3583 — 139, 33 — 68, 75 136, 5° 21503 2.13.827 — — 161, 47 — — 2I517I4.3.11.163 131, 66 — "3, 54 226, 36 21521 16.5.269 55,^6 39,100 187, 82 — — 21523 2.3.17.211 — 65, 93 — 80, 71 293, 3 21529 8.9.13.23 123, 80 73, 90 177, 70 19, 84 38, 56 21557 4.i7-3!7 119, 86 — — 21 559 2-3-3593 — — i47, 5 146, 9 292, 6 21 563 2.10781 — 141, 29 — — — 21569 64.337 95, II2 in, 68 163, 5° — — 21577 8.3.29.31 29,144 97, 78 147, 4 133, 36 266, 24 21587 2.43.251 — i35, 4i — — — 21 589 4.3-7.257 135, 58 — 83, 7° 127, 5 1 21599 2.10799 — — 169, 59 — 21601 32.27.25 145, 24 143, 24 147, 2 49, 80 19 1 , 43 21611 2.5.2161 — 147, 1 — — — 21613 4.3.1801 147, 2 — 145, J 4 103, 53 21617 16.7. 193 79,124 147, 2 167, 56 — — 21647 2.79.137 — — i75, 67 — — 21649 16.3.11.41 65,^32 29,102 I5 1 , 24 143, 20 203, 41 21661 4.3.5. 19.19 69,130 — 119, 5° 269, 23 21673 8.9.7.43 147, 8 145, l8 i79, 72 139, 28 223, 37 21683 2.37.293 — 105, 73 — — 21701 4-25-7-3 1 145, 26 — — 21713 16.23.59 73,128 9,104 155, 34 — — 21 727 2. 9. 17. 71 — — 153, 29 118, 51 1236, 34 21737 8.11. 13.19 91,116 ,147, 8 173, 64 — 21739 2.3.3623 — *33, 45 8, 85 247, 3 1 21751 2.3.125.29 — — 149, J5 142, 23 73, 55 21757 4-3-49-37 21,146 — 73, 74 |i49, 49 62 QUADRATIC PARTITIONS. V p-1 a be d e f A B L M 21767 2.10883 — , i 163, 49 — 21 773' 4-5443 83,122 — — — 21787 2-3-3631 — 67, 93| 140, 27 280, 18 21799 2.9.7.173 — — 171, 61 46, 81 i 92, 54 21803 2. 11. 991 — 141, 3 1 — — — 21817 8.27. 101 141, 44 107, 72 165, 52 67, 76 295, 3 21821 4.5.1091 *39, 5° — — — 21839 2. 61. 179 — — l6 7, 55 — 21841 16.3.5-7.13 105,104 121, 60 i53, 28137, 32 233, 35 21851 2.25.19.23 — 147, 11 — — — 21859 2-3-3643 103, 75 — 56, 79 181, 45 21863 2.17.643 — — '49, 13 — — 21871 2.27.81.5 — — 161, 45 14, 85 241, 33 21881 8-5-547 109,100117, 64 197, 92 — — 21893 4-I3-42I i43, 38 — — — — 21911 2-5-7-3I3 — — 157, 37 — — 21929 8.2741 5,148141, 32199, 94 — — 21937 16.3.457 81,124115, 66183, 76 127, 44 5, 57 21 943 2-9-23.53 — 189, 83 13°, 4i 7, 57 21961 8.9.5.61 35,144127, 54163, 48 *$h 40 Mi 57 21977 8.41.67 59,136105, 74 155, 32 — — 21 991 2.3.5.733 — — 173, 63 146, 15 292, 10 21997 4.9.13.47 141, 46 — — 145, 18 290, 12 22 003 2.3.19.193 — 49, 99 — 124, 47 17, 57 22 013 4-55°3 43^42 — — — — 22 027 2.3.3671 — ^3, 87 — 88, 69 176, 46 22 031 2.5.2203 — — 191, 85 — — 22 037 4.7.787 121, 86 — — — — 22 039 2.3-3673 — — 149, 9 142, 25 217, 39 22 051 2.9.25.49 — 1,105 148, 7 169, 47 22 063 2-3-3677 — — 169, 57 134, 37 23, 57 22 067 2.11.17.59 — 57, 97| — — 22 073 8.31.89 13,148 21,104 149, 8 — — 22 079 2.7.19.83 — — 15', 19 — — 22 091 2.5-47-47 — 123, 59 — — 22 093 4.3.7.263 147, 22 — — 95, 66 190, 44 22 109 4.5527 85,122 — — — — 22 111 2.3.5.11.67 — — 193, 87 3^, 83J 287, 15 22123 2.9.1229 — 125, 57 — 140, 29^ 227, 37 22 129 1 16.3.461 i5,H8i 77, 90 149, 6 3i, 84 1 62, 56 QUADRATIC PARTITIONS. 63 p p-1 a b c d e f A B L M *22 133 4,11.503 137, 58 — — 22 147 2.3.3691 — 95, 81 ■ — 148, 9 296, 6 22 153 83.13-7 1 117, 92 61, 96 151, 18 91, 68 «i 53 22 157 4.29. 191 29 146 — — — — 22 159 2.9.1231 — — r 53, 25 22, 85 277, 21 22 171 2-3-5-739 — 11,105 136, 35 31, 57 22 189 4-3-43-43 45^42 — — 1, 86 257, 29 22 193 16.19.73 17,148 141, 34 149, 2 — — 22 229 4-5557 73,i3o — — — — 22 247 2.49.227 — — 197, 9 1 — — 22 259 2-31-359 — 129, 53 — — — 22 271 2.5.17. 131 — — 167, 53 — — 22 273 256.3.29 103,108149, 6 189, 82 119, 52 37, 57 22 277 4-55 6 9 31,146 — — — — 22 279 2.3.47.79 — — 171, 59 98, 65 293, " 22 283 2-13-857 — 99, 79 — — — 22 291 2-3-5-743 — 113, 6 9 — 112, 57 224, 38 22 303 2.27.7.59 — — 199, 93 94, 67 295, 9 22 307 2.19.587 ! 33,103 — — — 22 343 2.11171 — — 155, 29 — — 22 349 4-37-I5 1 125, 82; — — — — 22 367 2.53.211 185, 77 — • — 22 369 32.3-233 137, 60101, 78 191, 84 71, 76 157, 49 22 381 4-3-5-373 mi, 5° — — 47, 82 199, 43 22 391 2.5.2239 — — 203, 97 — — 22 397 4.11.509 149, 14 — — — — 22 409 8.2801 53,!4oi47> 20 I5 1 , T 4 — — 22 433 32.701 23,148 69, 94 175, 6 4 — — 22 441 8.3.5.11.17 115, 96 79, 9oi53, 22 ^3, 72 166, 48 22 447 2.9.29.43 — — 207,101 130, 43 259, 29 22 453 4.3.1871 87,122 — — 131, 42 262, 28 22 469 4-4I.I37 145, 38 — — — — 22 481 16.5.281 95, 1 * 6 3,106 167, 52 — — 22 483 2.9.1249 — 145, 27 — 140, 3 1 47, 57 22 501 4.9.625 1,150 — — 149, 10 119, 53 22 511 2.5.2251 — — 169, 55 — — 22 531 2-3-5-75I — 97, 81 — 116, 55 49, 57 22 541 4-5-49-23 35,M6 — — — — 22 543 2.3.13.17.17 — — !59, 37 no, 59 287, 17 22 549 4.3.1879 7,150 — — 19, 86 239, 35 64 QUADRATIC PARTITIONS. p p-1 a b c d e f A B L M 22 567 2.3.3761 — — 155, 27 62, 79 175, 47 22 571 2.5.37.61 — 123, 61 — — — 22 573 4.27. n. 19 93>n8 — — 49, 82 295, lI 22 613 4-5653 137, 62 — — — — 22 619 2.43.263 — 141, 37 — — — 22 621 4-3-5-I3-29 11,150 — — 89, 70 121, 53 22 637 4.5659 131, 74 — — — — 22 639 2.3- 343-n — — *$h 9 146, 21292, 14 22 643 2.11321 — 135, 47 — — — 22 651 2.3.25. 151 — 149, J 5 — 76, 75J5 2 , 5° 22 669 4.3.1889 13,15° — — 79, 74M3, 5 1 22 679 2.17.23.29 — — 181, 71 — — 22 691 2.5.2269 — 129, 55 — — — 22 697 8.2837 109,104 15,106 163, 44 — — 22 699 2.9.13.97 107, 75 — 32, 85223, 39 22 709 4.7. 811 103,110 — — — — 22 717 49.631 69,!34! — — 23, 86281, 21 22 721 64.5.71 65^36 33, IQ 4 161, 40 — — 22 727 2. 11. 1033 — — i57, 3 1 — — 22 739 2.11369 — 39,io3 — — — 22 741 4-3-5-379 121, 90 — — 67, 78 134, 52 22 751 2.125.7. 13 — — IS*. 5 — — 22 769 16.1423 ii&ioo^i, 38 I5 1 , 4 — — 22 777 8-3-I3-73 149, 24103, 78 203, 96 85, 72 170, 48 22 783 2.3.3797 — — «.S*i 3 46, 83203, 43 22 787 2.11393 — 63, 97 — 22 807 2.9.7. 181 — — 165, 47 10, 87 20, 58 22 811 2.5.2281 — 69, 95 123, 62 — — — 22 817 32.23.31 *5 f i 4 205, 98 — — 22 853 4.29.197 127, 82 — — — — 22 859 2. 11. 1039 — 147, 25 — — — 22 861 4.9.5.127 i9,!5 — — 113, 58 61, 57 22 871 2.5.2287 — — 163, 43 — — 22 877 4.7.19.43 149, 26 — — — — 22 901 4.25.229 151, 10 — — — — 22 907 2. 13.881 — 3,107 — — — 22 921 8.3.5.191 139, 60 67, 96 189, 80 61, 80 179, 47 22 937 8.47.61 13I1 76 117, 68 175, 62 — — 22 943 2.11471 — — 169, 53 — — 22 961 16.5.7. 41 145, 44 147, 26 181, 70 — — QUADRATIC PARTITIONS. 65 JO p-\ a b c d e f A B L M 22 963 2.3.43.89 — *5 J , 9 — 16, 87 32, 58 22 973 4-5743 53^42 — — — ■ — ■ 22 993; 16.3.479 33.148 *3*i 54 165, 46 151, 8 127, 53 23 003 2-7-3 r -53 — 51,101 — — — 23 011: 2 -3-5- I 3-59 — 31,105 — 128, 47 269, 27 23 017 8-3-7-I37 141, 5 6 47,102 153, H 43, 84 86, 56 23 021 4.5-H5 1 125, 86 — — — — 23 027 2.29.397 — !35, 49 — — — 23 029 4.3.19.101 23,15° — — 29, 86 287, 19 23 039 2.11519 — — 199, 91 — — 23 041 5 I2 -9-5 129, 80 i43, 36 163, 42 127, 48 254, 32 23 053 4-3- I 7-i I 3 147, 38 — 145, 26 67, 57 23 057 16.11.131 151, 16 87, 88 155, 22 — — 23 059 2.27.7.61 — 89, 87 136, 39 272, 26 23 063 2.13.887 — — 179, 67 — — 23 071 2-35-769 — — 153, 13 98, 67 i°3, 55 23 081 8-5-577 59^40 141, 40 157, 28 — — 23 087 2.7.17.97 — — 167, 49 — — 23 099 2.11549 — 93, 85 — — — 23117 4-5779 109,106 — — — — 23 131 2-9-5- 2 57 — 109, 75 — 152, 3 3°4, 2 23 143 2.3.7.19.29 — — 155, 21 106, 63 212, 42 23159 2.11579 — — 203, 95 — — 23167 2.81. 11. 13 — — 153, 11 5°, 83 299, 11 23173 4-3.193I 113,102 — — 149, 18 298, 12 23189 4.11. 17.31 55^42 — — — — 23 197 4.3.1933 101,114 — — 55, 82 301, 9 23 201 32.25.29 151, 20 27,106 i73, 58 — — 23 203 2.9.1289 — 145, 33 — 116, 57 232, 38 23 209 8.3.967 147, 40 49,102 i53, 10 i39, 3^ 278, 24 23 227 2.3.49.79 — 77, 93 — 148, 21 296, 14 23 251 2.3.125-31 — 151, J 5 — 152, 7 131, 53 23 269 4.3.7.277 65,138 — — 101, 66 202, 44 23 279 2.103.113 — — 209,101 — — 23 291 2.5.17.137 — 147, 29 • — — — 23 293 4.9.647 117, 98 — — 7i, 78 142, 52 23 297 256.7.13 89,124 75, 94 i57, 26 — — 23 311 2.9.5.7.37 — — i53, 7 122, 53 281, 23 23 321 23 327 8.5.11.53 61,140 123, 64 197, 88 — — 2. 107. 109 — — 215,107 — — 66 QUADRATIC PARTITIONS. p p-1 a b c d e f A B L M 23 333U-i9-3°7 97,118 — — 23 339! 2.7.1667 — 21, IO) - — — 23357)4-5839 i49> 34 — — — 23 369 8.23.127 125, 88129, 58163, 40 — 23 371 2.3.5.19.41 — !39, 45 52, 83 197, 45 23 399 2. 1 1699 — — T 57, 25 — — 23 417 8.2927 139, 64153, 2 187, 76 — — 23 431 2.3.5. n. 71 — — 173, 57 142, 33 284, 22 23 447 2. 19. 617 — ' — i55, 17 — — 23 459 2-37-3 J 7 — •S3, S — — 23 473 16.9. 163 i53, 8 71, 962OI, 92 89, 72 178, 48 23 497 8.3.11.89 J 49. 36 13,108 157, 24 133, 44 h 59 23 509 4-9- 6 53 '53, 10 — *3h 46 7, 59 23 531 2.5.13.181 — 147, 31 — — — 23 537 16.1471 71,136 153, 8 203, 94 — — 23 539 2-3-3923 — 79, 93 _ 136, 41 13, 59 23 549 4.7.29.29 107,110 — — — — 23 557 4-3- I 3-i5 I 111,106 — — 37, 86221, 41 23 561 8.5.19.31 131, 80 33> IQ 6 169, 50 — — 23 563 2.9.7.11.17 — 125, 63 — 76, 77155. 5i 23 567 2.11783 — — 185, 73 — — 23 581 4-9-5- I 3 I 75^34 — — 73, 78 146, 52 23 593 8.3.983 123, 92 115, 72 205, 96 19, 88 283, 23 23 599 2.27.19.23 — — i59, 29 82, 75 164, 50 23 603 2.11801 — I2 9, 59 — — — 23 609 8.13.227 85,128 *53, 10 161, 34 — — 23 623 2.3.31. 127 — — 171, 53 70, 79 3°7, 3 23 627 2.11813 — 27,107 — — — 23 629 4.3.11.179 115,102 — — 127, 50 23, 59 23 633 16. 7. 211 23,152 J35> 52 !55, H — — 23 663 2.11831 — — 175, 59 — — 23 669 4.61.97 i37, 70 — — — — 23 671 2.9.5.263 — — 197, 87 118, 57 236, 38 23 677 4-3-!973 139, 66 — — 103, 66 206, 44 23 687 2.13.911 — — 155, 13 — — 23 689 8.9.7.47 117,100 19,108 183, 70 67, 80' 173, 49 23 719 2.3.59.67 — — 187, 75; J 54, 1 J 57, 5 1 23 741 4.5.1187 5,154 — — — — 23 743 2.9.1319 — — <6i, 33 154, 3 308, 2 23 747: 2-3i-3 8 3 — i53, 13 — — • — QUADRATIC PARTITIONS. 67 p p~ l a b c d e f A B L M 23 753 8.2969 43,148141, 44 215,106 — 23 761 16.27.5. 11 55» I 44 73, 96 217,108 23, 88241, 37 23 767 2.3- r 7-233 — — 157, 21 2, 89 269, 29 23 773 4.3.7.283 133, 78 — 151, 18302, 12 23 789 4-i9-3 J 3 ; 83,130 — — — — 23 801 8.25.7.17 149, 40 *53, 14 193, 82 — — 23 813 4-5953 !43> 58 — — 1 23 819 2.11909 — 5 x , io 3 — 23 827 2.3.H.E9.I9 — 65, 99 — 8, 89275, 27 23 831 2.5- 2 3 8 3 — — 163, 37 — — 23 833 8-9-331 27,152 55,io2 171, 52 91, 72,182, 48 23 857 16.3.7.71 12 1, 96 23,108 185, 72 25, 88289, 21 23 869 4.27.13.17 37,15° — — 41, 86299, 15 23 873 64.373 127, 88 in, 76 161, 32 — — 23 879 2.11939 — — *73, 55 — — 23 887 2.9.1327 — — 177, 61 98, 69 196, 46 23 893 4.3.11.181 153, 22 — — 61, 82 307, 7 23 899 2.3.7.569 — 43,io5 — 116, 59 293, 19 23 909 4.43.i39 95,122 — — — — 23 911 2.3.5.797 — — 203, 93 106, 65 89, 57 23 917 4.31993 5 I , I 46 — — 143, 34 4i, 59 23 929 8.3.997 45,!48 i39, 48 159, 26 149, 24 298, 16 23 957 4.53.ii3 *$h 34 — — — — 23 971 2.3.5.I7.47 — 137, 51 — 152, 17 203, 45 23 977 8.81.37 141, 64 143, 42 163, 36 53, 84 106, 56 23 981 4.5. 11. 109 109,110 — — — — 23 993 8.2999 107,112 39,106 155, 4 — — 24 001 64 3- I2 5 135, 76 149, 30 157, 18 151, 20 91, 57 24 007 2.3.4001 — — J55, 3 no, 63 220, 42 24 019 2.3.4003 — Il 3, 75 — 16, 89 251, 35 24 023 2.12011 — — J 55, ! — — 24 029 4.6007 155, 2 — — — 24 043 2.3.4007 155, 3 — i3 6 , 43 265, 31 24 049 16.9.167 143, 60 109, 78 181, 66 121, 56 47, 59 24 061 4.3.5.401 155, 6 — — 137, 42 274, 28 24 071 2.5.29.83 — — 157, 17 — — 24 077 4.13.463 19^54 24 083 2.12041 — 129, 61 — — — 24 091 2.3-5 II -73 — 67, 99 — 148, 27 296, 18 24 097 32.3.25 1 *5h 36 155, 6 173, 54 145, 32 49, 59 68 QUADRATIC PARTITIONS. p p-1 a b c d e f A B L M 24103 2.9.13.103 — — 179, 63 130, 49277, 27 24107 2.17.709 — 123, 67 — — — 24109 4.3.49.41 i47, 5° 97, 70 307, 9 24113 16.11.137 47,148 141, 46 199, 88 — 24121 8.9.5.67 75,136 89, 90 161, 30 i39, 4o 259, 33 24133 4.3.2011 63,142 — — i55, 6 3io, 4 24 137 8.7.431 149, 44 93, 88 i57, 16 — — 24151 2.3.25.7.23 — — 213,103 38, 87 76, 58 24169 8-3-I9-53 155, 12 29,108 189, 76 109, 64 3°i, 15 24 179 2.7. 11. 157 — in, 77 — 24181 4-3-5- I 3.3 I 41,15° — — 77, 78 154, 52 24 197 4.23.263 79,i34 — — — 24 203 2.12101 — 21,109 — — 24 223 2.3.11.367 — — 159, 23 i54, 13 193, 47 24 229 4.9.673 127, 90 — — 149, 26 227, 41 24 239 2. 121 19 — — 161, 29 — ' — 24 247 2.27.449 — — 195, 83 22, 89 245, 37 24 251 2.125.97 — 99, 85 — — 24 281 8.5.607 155, 16 9,110 203, 92 — — 24 317 4.6079 149, 46 — — — — 24 329 8.3041 35,152 129, 62 169, 46 — — 24 337 16.9.13.13 1,156 125, 66 165, 38 i43, 36 286, 24 24 359 2. 19.641 — — 197, 85 — — 24 371 2-5-2437 — 63,101 — — — 24 373 4.9.677 73138 — — 125, 54 250, 36 24 379 2.3.17.239 — 149, 33 — 52, 85 307, 11 24 391 2.9.5.271 — — 163, 33 i54, 15 308, 10 24 407 2.12203 — — 157, 11 — — 24 413 4-17-359 i33, 82 — — — 24 419 2.29.421 — 39,io7 — — — 24 421 4.3.5-i i-37 111,110 — — 11, 90 22, 60 24 439 2.3.4073 — — 171, 49 26, 89 293, 21 24 443 2. 1 2 1. 1 01 — 75, 97 — — — 24 469 4.3.2039 87,130 — 13, 90 26, 60 24 473 8.7.19.23 37,152 105, 82 209, 98 — — 24 481 3 2 -9-5- J 7 105,116 91, 90 159, 20 103, 68 101, 57 24 499 2.9.1361 — i43, 45 — 76, 79 3i3, 1 24 509, 4-II.557 i55, 22 — — — 24 517| 4.27 227 81,134 — — 107, 66 214, 44 24 527 2.12263 — 167, 41 — - QUADRATIC PARTITIONS. 69 p P -l a b c d e f A B L M 24 533 4-6133 103,118 — — 24 547 2.3.4091 — 97, 87 — 28, 89 239, 39 24 551 2.25.491 — — i57, 7 — — 24 571 2.27.5.7.13 — 107, 81 — 136, 45 272, 30 24 593 16.29.53 127, 92 99, 86 215,104 — — 24 611 2.5.23.107 — 81, 95 — — — 24 623 2.13.947 — — 1911 77 — — 24 631! 2.3.5.821 — — i57, 3 I22 » 57 244, 3 8 24 659 2.12329 — i53, 25 — — — 24 671! 2.5.2467 — — 161, 25 — — 24 677 4.31. 199 31,154 — — — — 24 683 2.7.41.43 — 141, 49 — — — 24 691 2.3-5-823 — 7,111 — 152, 23 221, 43 24 697 8-9-343 19,15° 37,108197, 84 157, 4 169, 51 24 709 4.3.29.71 47,150 — — 9i, 74 i3i> 55 24 733 4.27.229 123, 98 — — 121, 58 295, 21 24 749 4.23.269 157, 10 — — — — 24 763 2.3.4127 — 11, in — 64, 83 185, 49 24 767 2.7.29.61 — — 193, 79 — 24 781 4-3-5-7-59 141, 70 — — 143, 38 257, 35 24 793 8-3-I033 *57» 12 H9, 3 6 *75, 54 155, 16 107, 57 24 799 2.3-4I33 — — 207, 95 154, 19 211, 45 24 809 8.7.443 i55, 28 147, 40 199, 86 — — 24 821 4-5-I7-73 89,130 — — — — 24 841 8.27.5.23 125, 96 127, 66 179, 60 157, 8 x 33, 55 24 847 2.3.41. 101 — — 167, 39 2, 91 271, 3 1 24 851 2.25.7.71 — 33,109 — — — 24 859 2.9.1381 — 53,105 — 4, 9 1 277, 29 24 877 4.9.691 109,114 — 127, 54 254, 3 6 24 889 8.3. 17. 61 115,108 133, 60 159, 14 61, 84 122, 56 24 907 2.3-7.593 — 155, 21 — 8, 91 265, 33 24 917 4.6229 i$h 46 — — — — 24 919 2.3-4153 — 2H, 99 34, 89 233, 4i 24 923 217-733 — 45, io 7 — — — 24 943 2.3.4I57 — — J 59, 13 10, 91 283, 27 24 953 8.3119 43, J 5 2 135, 58 161, 22 — — 24 967 2.9.19.73 — — 213,101 158, 1 !55, 53 24 971 2. 5. 11. 227 — 147, 4i — — — 2i977. 16.7.223 119,104 153, 28 185, 68 — — 24 979 2.3.23.181 — l 5h 33 — 152, 25 77, 59 70 QUADRATIC PARTITIONS. p p-l a b c d I A B L M 24 989 4.6247 5,i58 — — — 25 013 4.I3.I3.37 7,i58 — — — 25 031 2.5-2503 — — — — 25 033 8.3.7.149 93,128 65,102 125, 56 293, 23 25 037 4.11.569 61,146 — — — 25 057 32.27.29 81,136 143, 48 113, 64 79, 59 25 073 16.1567 143, 68 51,106 — — 25 087 2.3.37-113 — — 118, 61 301, 19 25 097 8.3137 139, 76 3, 112 - - 25111 2.81. 5.31 — — 158, 7 i37, 55 25 117 4.3.7.13.23 149, 54 — i37, 46 1, 61 25121 32.5.157 145, 64 in, 80 — — 25127 2.17.739 — — — — 25 147 2.9.11.127 — 125, 69 140, 43 11, 61 25 153 64.3.131 57,148 i39, 54 151, 28 235, 4i 25163 2.23.547 — 69,101 — — 25 169 16. 121. 13 137, 80 9,112 — — 25171 2-3-5- 8 39 — 23,111 148, 33 296, 22 25 183 2.9.1399 — — 86, 77 3 X 7, 3 25 189 4.3.2099 15,15* 133, 5° 17, 61 25 219 2.27.467 89, 93 112, 65 83, 59 25 229 4-7-I7-53 125, 98 — — — 25 237 4.9.701 39,154 — 157, !4 115, 57 25 243 2.3.7.601 — 149, 39 20, 91 253, 37 25 247 2.13-971 — — — — 25 253 4.59.107 17,158 — — — 25 261 4-3.5.42I 131, 9° — 3 1 , 9° 62, 60 25 301 4.25-11.23 151, 5o — — 25 303 2.3.4217 — — 154, 23 85, 59 25 307 2.12653 — 147, 43 — — 25 309 4.9.I9.37 53,!5° — 103, 70 3i3, » 25 321 8.3.5.211 i55, 36 83, 96 107, 68 3 11 , *3 25 339 2.3.41. 103 i IOI 5 87 92, 75 184, 50 25 343; 2.1 2671 — — — 25 349 4.6337 i43, 7° — — — 25 357 4-3-2II3 141, 74 — 145, 38 3*i 61 25 367 2.11.1153 — — — — 25 373 4.6343 107,118 — — — 25 391 2.5.2539 — — — — 25 409 , 64.397 95, I2 8 ^59, 8 — — QUADRATIC PARTITIONS. 71 p p-l a b c d A B L M 25 411 1 2.3.5.7. 121 — 119, 75* 52, 87104, 58 25 423 2.3.19.223 — — 146, 37 35, 61 25 439 2.7.23.79 — — — — 25 447 2.3.4241 — — 82, 793 J 9, 1 25 453, 4 9 7.101 147, 62 — 95, 74317, 7 25 457 16.37.43 121,104 153, 32 — — 25 463 2.29.439 — — ■ — — 25 469 4.6367 155, 38 — — — 25 471 2.9.5.283 — ^58, i3 XI 9, 57 25 523 2.7.1823 — 159, « — | - 25537,64.3.7.19 159, 16 47,108127, 56 41, 61 25 54l! 4.5.1277 65,146 — — — 25 561 8.9.5.71 35.156 107, 84 13, 92263, 35 25 577; 8.23.139 101,124 93, 92 — 25 579 2.9.49.29 — 91, 93148, 35 43, 61 25 583 2.12791 — — — — 25 589 46397 25,158 — — 25 601 1024.25 1,160 63,104 — — 25 603 2.3.17.251 — 3i,in 160, 1 163, 53 25 609 8.3.11.97 3,160 97, 90 91, 76 3i9, 5 25 621 4.3.5.7.61 135, 86 — i57, 18 3i4, 12 25 633 32.9.89 M3, 72 145, 48 49, ^ 3*3, !3 25 639 2.3-4273 — — 158, 15 316, 10 25 643 2.12821 — 99, 89 — — 25 657 8.3.1069 141, 76 85, 96 67, 84 i34, 56 25 667 241.313 — 135, 61 — — 25 673 8.3209 r 57, 32 i59> i4 — — 25 679 2-37-347 — — — — 25 693 4.3.2141 27,158 — 119, 62 305, !9 25 703 2. 71. 181 — — — — 25 717 4-3-2143 151, 54 — 125, 58 49, 61 25 733 4.7.919 127, 98 — — — 25 741 4.9.5.11.13 45> I 54 — 143, 42 286, 28 25 747 2.3.7.613 — 103, 87 160, 7 181, 51 25 759 2-243-53 — — 134, 5i 268, 34 25 763 2.11.1171 — i5,n3 — — 25 771 2-3-5-859 — 61,105 64, 85 3i9, 7 25 793 64.13.31 97,128 i59, 16 — — 25 799 2.12899 — — — — 25 801 8.3.25. 43 149, 60 i57, 24 133, 52 289, 27 72 QUADRATIC PARTITIONS. p p-\ a b c d A B L M 25 819 2 3 I 3-33 I — i39, 57 124, 59 53, 61 25 841 16.5.17.19 79,140 147, 46 — — 25 847 2.12923. — — — — 25 849 8-9-359 107,120 71,102 i57, 20 97, 59 25 867 2.27.479 — 35,m 32, 9 1 241, 41 25 873 16.3.49.11 63,148 131, 66 151, 32 55, 6l 25 889 32.809 17,160 129, 68 — — 25 903 2.9.1439 — — 154, 27 308, 18 25 913 8.41.79 53^52 i35, ° 2 — — 25 919 2.12959 — — — — 25 931 2.5- 2 593 — Mi, 55 — — 25 933 4.3.2161 83,138 — 161, 2 167, 53 25 939 2.9.11.131 — 161, 3 104, 71 3!7, 11 25 943 2.7. 17. 109 — — — — 25 951 2-325-173 — — 2, 93 4, 62 25 969 16.3.541 135, 88 137, 60 161, 4 i49, 55 25 981 4.3-5-433 59^50 — 41, 90 82, 60 25 997 4.67.97 I3 1 , 94 — — — 25 999 2.3.7.619 — — 34, 91 3°7, 19 26 003 2.13001 — i59, 19 — — 26 017 32.3.271 41,156 5, TI 4 25, 92 251, 39 26 021 4.5.1301 161, 10 — — — 26 029 4.27.241 125,102 — 161, 6 322, 4 26 041 8-3-5-7-3I 21,160 7,n4 53, 88 211, 47 26 053 4.3. 13. 167 33,158 155, 26 233, 43 26 083 2.81.7.23 — 161, 9 80, 81 160, 54 26 099 2.13049 — in, 83 — 26107 2.3.19.229 — 157, 27 160, 13 199, 49 26 111 2-5-7-373 — — — — 26113 5 I2 -3-i7 153, 52 11,114 161, 8 185, 5i 26119 2.9.1451 — — 86, 79 151, 55 26141 4-5-I307 155, 46 — — — 26 153 8.7.467 133, 92 141, 5 6 — 26161 16.3.5.109 81,140 i3> IX 4 103, 72 206, 48 26171 2.5.2617 — 117, 79 — — 26177 64.409 161, 16 33, 112 — — 26183 2.I3-I9-53 — — — — 26189 46547 35,158 — — 26 203 2.3.11.397 — 155, 33 16, 93 32, 62 26 209 32.9-7-13 145, 72 161, 12 71, 84 142, 56 QUADRATIC PARTITIONS. 73 p p-l a b c d A B L M 26 227 2.9.31.47 — H5, 5 1 140, 47 281, 31 26 237 4-7-937 9M34 — — — 26 249 8.I7-I93 157, 40 159, 22 — — 26 251 2.3.625.7 — I49j 45 92, 77 3 2 3, 5 26 261 4.5.13.101 119,110 — — — 26 263 2.9.1459 — — 5°, 89317, 13 26 267 2.23.571 — 27>i'3 — — 26 293[4.3.7-3i3 7,162 — 115, 66230, 44 26 297 8. 19. 1 73 149, 64 153, 38 • — — 26 309 4.6577 97,13° — — 26 317 4.9.17.43 5M54 — i45, 42 290, 28 26 321 16.5.7.47 161, 20 93, 94 — — 26 339 2.13.1013 — J 59, 23 — — 26 347 2-3-4391 — 115, 81 20, 93 40, 62 26 357 4.11.599 71,146 — 26 371 2.9.5.293 — 161, 15 J 5 2 , 33 3°4, 22 26 387 2.79.167 — 87, 97 — — 26 393 8.3299 67,148 69,104 — — 26 399 2.67.197 — — — — 26 407 2.81. 163 — — 82, 81 164, 54 26 417 16.13. 127 89,136 i35, 64 — — 26 423 2.11.1201 — — — — 26 431 2.3.5.881 — — 22, 93 44, 62 26 437 4.3.2203 159, 34 — 133, 54 266, 36 26 449 16.3.19.29 95^32 i57, 30 119, 64 73, 61 26 459 2.13229 — 3,n5 — — 26 479 2.9.1471 — 98, 75^6, 5° 26 489 8.7. 11.43 83,140 117, 80 — — 26 497 128.9.23 161, 24 127, 72 73, 84146, 56 26 501 4.125.53 i45> 74 — • — 26 513 16.1657 137, 88 105, 88 — — 26 539 2-3-4423 — 67,105 124, 61 307, 21 26 557 4.3.2213 149, 66 — 7, 94 289, 29 26 561 64-5-83 31,160 81,100 — — 26 573 4-7-13-73 163, 2 — — — 26 591 2.5.2659 — — — — 26 597 4.61. 109 161, 26 — — — 26 627 2.13313 — 33, IJ 3 — — 26 633 8.3329 163, 8 159, 26 — — 26 641 16.95.37 129,100 163, 6 113, 68 3i7, 15 74 QUADRATIC PARTITIONS. p p-1 a be d A B L M 26 647 2.3.4441 _ _ 130, 57 260, 38 26 669 4-59-II3 163, 10 — — — 26 681 8.5 23.29 115,116123, 76 — — 26 683 2-3-4447 — 131, 69160, 19 217, 47 26 687 2.11.1213 — — — — 26 693 4.6673 113,118, — — — 26 699 2.7.1907 — 93, 95 — — 26 701 4.3.25.89 99>i3o — 49, 90 98, 60 26 711 2.5.2671 — — — — 26 713 8-9-7 53 163, 12, 91, 96 59, 88205, 49 26 717 4.6679 139, 86 — — — 26 723 2. 31. 431 — 129, 7i — — 26 729 8.13.257 i55, 5 2 ; 99, 92 — — 26 731 2.343.5.11 — 163, 9 28, 93 56, 62 26 737 ( 16.3.557 49» I 5 6 , 77,io2 97, 76325, 7 26 759! 2.17.787 — — — — 26 777: 8.3347 91,136 87, 98 — — 26 783.2.7.I9I3 — — — — 26 801 16.25.67 145, 76; 5 1 , 110 — — 26 813 4.6703 43,158 — — — 26 82lU-9-5- I 49 161, 30 — 139, 5° 11, 63 26 833; 16.3.13.43 97,132 29,114 145, 44 13, 63 26 839 2.27.7.71 — — 158, 25 83, 61 26 849 32.839 143, 80159, 28 26 861 4-5-17-79 125,106 — — — 26 863 2.3.121.37 — — 146, 43 J 7, 63 26 879 2.89.151 — — — — 26 881 25 6 -3-5-7 i59, 40 113, 84 i37, 5 2 | 19, 63 26 891 2.5.2689 — 21,115 — — 26 893 4.81.83 163, 18 — 161, 18322, 12 26 903 2.13451 — — — — 26 921 8.5.673 5, l6 4 3,n6 — — 26 927 2.13463 , — — — — 26 947 2.27.499 — i43, 57 14.8, 41 25, 63 26 951 2. 25. 49.11 — — 26 953 8.3.1123 157, 48 3 I , II 4 61, 88325, 9 26 959 2-3-4493 — — 46, 91 319, 15 26 981 4.5.19.71 95,!34 — — — 26 987 2.103.131 — 123, 77 — — 26 993 16.7. 241 103,128 9,116 — — . QUADRATIC PARTITIONS. 75 V P -l a b c d A B L M 27 011 2.5.37.73 57, 1Q 9 _ 27 017 8.11.307 11,164 147, 52 — — 27 031 2.3.5.17.53 — — i34, 55 31, 63 27 043 2.3.4507 — 49,111 164, 7*43, 57 27 059 2.83.163 — 39, ri 3 — — 27 061 ! 4.3.5 u.41 135. 94 — 83, 82 J63, 55 27 067 2.3.13.347 — i55, 39 80, 83329, 1 27 073 64.9.47 63,152 161, 24 41, 9 2 ;3!7, 17 27 077 4.7.967 161, 34 — — — 27 091 2 -9-5-7-43 — 71,105 4, 95,281, 33 27 103 2.3-45 J 7 — — 34, 93 68, 62 27107 2 - I 3553 — J 53, 43 — — 27109 4.27.251 *45i 7 8 — 53, 90 106, 60 27127 2.9.11.137 — — 58, 89 209, 49 27 143 2.41.33 1 — — — — 27179 2. 107. 127 — 27,n5 — — 27 191 2.5.2719 — — — — 27197 4.I3-523 59,^54 — — — 27 211 2.3.5.907 — *33, 69 152, 37 41, 63 27 239 2.13619 — — — — 27 241 8.3.5.227 165, 4 i57, 36 43, 92 233, 45 27 253 4-9-757 153, 62 — 131, 58 43, 63 27 259 2.3.7.11.59 — i39, 63 164, 11 197, 5 1 27 271 2.27.5. 101 — — 14, 95 299, 27 27 277 4-3-2273 141, 86 — 95, 78190, 52 27 281 16.5.11.31 41,160 153, 44 — — 27 283 2-3-4547 — 119, 81 124, 6s 248, 42 27 299 2.13649 — 129, 73 — — 27 329 64.7.61 65,152 i59, 32 — — 27 337 8.3.17.67 21,164 115, 8 4 163, 16 211, 49 27 361 32.9.5.19 55,156 37, JI 4 i43, 48 286, 32 27 367 2.34561 — 142, 49 289, 31 27 397 4.9.761 159, 46 — 85, 82 33h 1 27 407 2.71. 193 — — — — 27 409 16.3.571 105,128151, 48 79, 84 158, 56 27 427 2.3-7-653 — 7,n7 88, 81 176, 54 27 431 2.5.13-211 — — — — 27 437 4.19.19.19 6i 5 i54 — — • — 27 449 8.47.73 43,160 57,no — — 27 457 64.3.11.13 129,104 95, 96 65, 88 i99, 5 1 76 QUADRATIC PARTITIONS. p P -l a b c d A B L M 27 479 2. ii. 1249 — — — 27 481 8.3.5.229 165, 16 137, 66 91, 80149, 57 27 487 2.27.509 — — 158, 29245, 43 27 509, 4.13.23.23 103,130 — — . — 27 527 2.13763 — — — — 27 529 8.3-3 I 37 75>i48 13 1 , 72 101, 76 127, 59 27 539 2.49.281 — 33 5 n5 — - 27 541i 4.81. 5. 17 7M5 — 163, 18 326, 12 27 551 2.25.19.29 — — — — 27 581 4.5-7.I97 5,166 — — — 27 583 2.3.4597 — — 166, 3 332, 2 27 611 2.5.11.251 — 123, 79 — — 27 617 32.863 119,116 165, 14 — — 27 63l| 2.9.5.307 — — 166, 5 15*1 57 27 647| 2.23.601 — — — — 27 653 4-31.223 113,122 — — — 27 673|8.3.ii53 123,112 41,114 5, 96 10, 64 27 68918.3461 133,100 51,112 — — 27 691 2.3.5. 13.71 ■ — 157, 39 '°4, 75 208, 50 27 697 16.3.577 111,124 83,102 7, 96 14, 64 27 701 4.25.277 151, 7o — — — 27 733' 4.3.231 1 87,142 — 35, 94 247, 43 27 737 8.3467 29,164165, 16 — 27 739 2.9.23.67 — 19,117 116, 69 232, 46 27 743 2. 1 1. 13.97 — — — — 27 749 47.991 145, 82 — — — 27 75i; 2.3.125.37 — — 26, 95 3 11 , 23 27 763 2.3.7.661 — 121, 81 164, 17 215, 49 27 767 2.13883 — — — — 27 773 4.53.131 53,158 — — — 27 779 2. 17. 19.43 — 81,103 — — 27 791 2.5.7.397 — — — — 27 793, 16.9.193 127,108125, 78 49, 92 227, 47 27 799 2.3.41.113- — — 166, 9 332, 6 27 803.2.1 390 1 — 165, 17 — — 27 809; 32.11.79 47,160 in, 88 — — 27 817| 8.3.19.61 59,156 67,108 13, 96 26, 64 27 823 2.3.4637 — — 154, 37 265, 39 27 827 2.13913 — 153, 47 — — 27 847 2.9.7.13.17 — — 158, 31 65, 63 QUADRATIC PARTITIONS. 77 p p-1 a b c d A B L M 27 851 2-25.557 — I 99, 95 _ __ 27 883 2.9.1549 — 9i, 99 44, 93 88, 62 27 893 4.19.367 167, 2 — — — 27 901 4.9.25.31 165, 26 — l6 7, 2,173, 55 27 917 4.7.997 19,166 — — — 27 919 2. 27. 11. 47 — ! _ 166, 11133, 59 27 941 4.5.11.127 65,154 — — — 27 943 2-3-4657 — — 146, 47287, S3 27 947 2.89.157 — 165, 19 — — 27 953 16.1747 167, 8105, 92 — — 27 961 8.3.5-233 85,144167, 6 131, 60262, 40 27 967 2.3-59-79 — — T42, 51284, 34 27 983 2.17.823 — — — — 27 997 4-3-2333 21,166 — 167, 6334, 4 28 001 32.125.7 49,160 33,116 — — 28 019 2.14009 — !59, 37 — — 28 027 2.81. 173 — 163, 27 140, 53 299, 29 28 031 2.5.2803 — — — — 28 051 2.3.25. 11. 17 167, 9124, 65 7*i 6 3 28 057 8.3.7.167 61,156 133, 72 ^3, 84 166, 56 28 069 4.3.2339 95>*38 — J 39, 54 278, 36 28 081 16.27.5.13 i45» 84 109, 90 167, 8 *9h 53 28 087 2-3-3 I - I 5 I — - no, 73 109, 61 28 097 64.439 121,116 75,!o6 — — 28 099 2.9.7.223 — 161, 33 32, 95 3 J 7, 21 28109 4.7027 115,122 — — — 28 111 2-3-5-937 — 106, 75 212, 50 28 123 2.3.43.109 — 59,iii 160, 29 73, 63 28 151 2.25 563 — — — — 28163 2.14081 — in, 89 — — 28 181 4.5.1409 25,166 — — — 28 183 2.3.7. 11. 61 — — 74, 87 148, 58 28 201 8.3-25.47 51,160 47,n4 53, 92 329, J 3 28 211 25-7-13.31 — 153, 49 — — 28 219 2-3-4703 — 29,117 164, 21 328, 14 28 229 4.7057 127,110 — — — 28 277 4.7069 l$h 74 — — — 28 279 2.9-i57i — 154, 39 308, 26 28 283 2.79.179 — 165, 23 — — 28 289 128.13.17 167, 20 21,118 1 — — 78 QUADRATIC PARTITIONS. p p-1 a b c d A B L M 28 297 8.27.131 99,136127, 78163, 24326, 16 28 307 2.14153 — 135. 7i — — 28 309 4-3-7-337 153, 7o 109, 74113, 61 28 319 2.14159 — — — 28 349 4-19-373 107,130 — — 28 351 2.81.25.7 — 122, 67 79, 63 28 387 2.9.19.83 — i43, 63 68, 89335, 7 28 393 8.-3-7-*3-»3 13,168 49,114 85, 84170, 56 28 403 2.11.1291 — 9,119 — — 28 409 8.53-67 53>i6o 153, 50 — — 28 411 2-3-5-947 _ 131, 75 88, 83 161, 57 28 429 4.3- 2 3.io3 77,15° — 79, 86179, 55 28 433 16.1777 73,152 39,u6 — — 28 439 2.59.241 — — — — 28 447 2.3.11.431 — — 50, 93100, 62 28 463 2. 7. 19.107 — — — — 28 477 4.9.7. 1 13 69,154 — 167, 14 209, 51 28 493 4.17.419 i57, 62 — — — 28 499 2.14249 — 129, 77 — — 28 513 32. 81. 11 17,168 161, 36 121, 68 83, 63 28 517 4.7129 31,166 — — — 28 537 8.3.29.41 i39, 96 167, 18 157, 36 3M, 24 28 541 4.5.1427 85,146 — — — 28 547 2.7.2039 — i5, JI 9 — — 28 549 4.9.13.61 143, 9° — 149, 46 11, 65 28 559 2.109. 131 — — — — 28 571 2.5.2857 — i47, 59 — — 28 573 4.3.2381 117,122 — 169, 2 163, 57 28 579 2.3.11-433 — 169, 3 116, 71 329, i5 28 591 2.3.5.953 — — 142, 53 17, 65 28 597 4-3-2383 169, 6 — 163, 26 85, 63 28 603 2.9.7.227 — 35>"7 104, 77 335, 9 28 607 2.14303 — — — — 28 619 2.41.349 — 99, 97 — — 28 621 4.3.5.9.53 125,114 — 161, 30 322, 20 28 627 2.3.13.367 — 95, 99 20, 97 271, 39 28 631 2.5.7.409 — — — — 28 643 2.14321 — 159, 4i — — 28 649 8.3581 i55, 68 93,100 — — 28 657 16.9.199 89,144 73,io8 167, 16 119, 61 QUADRATIC PARTITIONS. 79 V p-1 a b c d A B L M 28 661 1 4-5-I433 169, 10 — — 28 663 2.3.17.281 — — 70, 89 ,197, 53 28 669 4.3.2389 165, 38 — 169, 6 338, 4 28 687 2.3.7.683 — — 62, 91 211, 5 1 28 697, 8.17. 211 101,136 105, 94 — — 28 703 2.113.127 — — — — 28 7111 2.9.5. 11. 29 — — 22, 97 3i3, 25 28 723 2.3.4787 — 169, 9 Joo, 79 337, 7 28 729 8.27.7.19 75, J 5 2 89,102 T 39, 56 29, 65 28 751 2.625.23 — — — — 28 753 16.3.599 23,168 121, 84 169, 8 145, 59 28 759 2.3.4793 — — i54, 4i 3i, 65 28 771 : 2.3.5.7.137 — 167, 21 164, 25 89, 63 28 789 4-3-2399 167, 30 — 67, 9° 134, 60 28 793 8.59.61 83,148 165, 28 — — 28 807 2.3.4801 — — 130, 63 260, 42 28 813 4-3-2401 93>i42 — 1, 98 293, 33 28 8171 16.1801 169, 16 r 53, 52 — 28 837 4.81.89 161, 54 5, 98 299, 3i 28 843 2.3.11.19.23 — J 39, 69 124, 67 325, 19 28 859 2.47.307 — 141, 67 — — 28 867 2.3.17.283 — 65,111 160, 33 320, 22 28 871 2.5.2887 — — — — 28 879 2.3.4813 — — 166, 21 332, 14 28 901 4.25-17-17 1,170 — — — ' 28 909 4-9-II.73 3,i7o — 49, 94 33i, 15 28 921 8.3.5.241 45, l6 4 11,120 163, 28 247, 45 28 927 2.9.1607 — — 170, 3 34o, 2 28 933 4.3-2411 63,158 — 11, 98 305, 29 28 949 4.7237 7,170 — — — 28 961 32.5.181 169, 20 69,110 — — 28 979 2.14489 159, 43 — — 29 009 16.49.37 97,140 99, 98 — — 29 017 8.9.13.3T 91,144 55,n4 37, 96 74, 64 29 021 4-5- I 45 I 11,170 — — — 29 023 2.3.7.691 — — 106, 77 125, 61 29 027 2.23.631 — J 53, 53 — — 29 033 8.19. 191 77,152 81,106 — — 29 059 2.3.29.167 41,117 128, 65 323, 21 29 063 2.11.1321 — — — "~ 80 QUADRATIC PARTITIONS. p p-\ a b c (1 A B L M 29 077 4-3-2423 39,166 — 83, 86341, 1 29 101 4-3- 2 5-97 115,126 — 17, 98 3"> 2 7 29 12:3 2.14561 — 129, 79 — — 29 129, $.11,331 85,148 141, 68 — — 29 131 2.3-5-97I — 67,111 92, 83341, 3 29 137 16.3 607 169, 24 137, 72 145, 52301, 31 29 147 2.13.19.59 — 165, 3' — — 29153 32.911 113,128159, 44 — — 29167 2.3.4861 — — 122, 69244, 46 29173 4.3.11. 13.17 137,102 — 19, 98275, 39 29 179 2.9.1621 — i°9» 93 152, 45 304, 30 29 191 2-3-5-7-I39 — — 46, 95 239, 47 29 201 16.25.73 151, 80; 87,104 — — 29 207 2.17.859 — t — — — 29 209 8.3-1217 155, 72169, 18 109, 76 337, « 29 221 4.3-5-487 111,130 — i33, 62 53, 65 29 231 2.5-37-79 — — — — 29 243 2. 1462 1 — 171, 1 — — 29 251 2.9.125. 13 — 127, 81 32, 97 259, 43 29 269 4.27.271 55^62 — 163, 30 326, 20 29 287 2.9.1627 — — 98, 81 196, 54 29 297 16.1831 49,164 147, 62 — — 29 303 2.49.13.23 — — — — 29 311 2-3-5-977 — — 58, 93 116, 62 29 327 2.11. 31.43 — — — — 29 333 4-7333 167, 38 — — — 29 339 2.14669 — 171, 7 — — 29 347 2.3.67.73 — 167, 27 140, 57 280, 38 29 363 2.53-277 — 9,121 — — 29 383 2.3-59-83 — — 34, 97 325, 21 29 387 2.7.2099 — 75>i°9 — — 29 389 4-3-31-79 83,150 — 161, 34 59, 65 29 399 2.14699 — — — — 29 401 8.3.25.49 99,140 149, 60 101, 80 34i, 7 29 411 2.5- J 7-i73 — 33,n9 — — 29 423 2.47-313 — — — — 29 429 4.7.1051 23,170 — — — 29 437 4.3.11.223 171, 14 — 25, 98 269, 41 29 443 2.3.7.701 — 169, 21 ,116, 73 103, 6 3 29 453 4-37-199 67,158 — _ — QUADRATIC PARTITIONS. 81 p p-1 a b c d A B L M 29 473; 3 2 -3-3°7 87,148 59tM4 79, 88 343, 3 29 483 2.14741 — 171, 11 — — 29 50l| 4.125-59 155. 74 — — — 29 527! 2-3-7-I9-37 — — I5 8 , 39 316, 26 29 531 2.5- 2 953 — 117, 89 — — 29 537^ 32.13.71 119,124 165, 34 — — 29 567 2.14783 — — — — 29 569 128.3.7.11 63,160 79,108 137, 60 2 74, 40 29 573 4-7393 97,142 — — — 29 581 4-3-5- I 7-29 45,166 — 97, 82 343, 5 29 587 2.3-4931 — 47,117 172, 1 i75, 57 29 599 2-3-4933 — — 14, 99 28, 66 29 611 2.9.5.7.47 — 163, 39 172, 3 344, 2 29 629 4.9.823 27,170 — 73, 90 146, 60 29 633 64.463 7,172 171, 14 — — 29 641 8.3.5-*3-*9 171, 20 29,120 163, 32 67, 65 29 663 2.14831 — — — — 29 669 4.7417 113^3° — — — 29 671 2.3.5.23.43 — — 38, 97 253, 45 29 683 2.9.17.97 — 71,111 100, 81 200, 54 29 717 4.17.19.23 169, 34 — — — 29 723 2. 7. n. 193 — 21,121 — — 29 741 4.5.1487 29,170 — — — 29 753 8.3719 13,172 171, 16 — — 29 759 2.14879 — — — 29 761 64.3.5.31 95, r 44 31,120 169, 20 109, 63 29 789 4.11.677 i33> 110 — — — 29 803 2.3.4967 — 101, 99 20, 99 40, 66 29 819 2.17.877 — 171, 17 — — 29 833 8.3.11.113 i57, 72 95,102 155, 44 287, 37 29 837 4 7459 109,134 — — — 29 851 2.3.25.199 — 157, 5i 128, 67 73, 65 29 863 2.27.7.79 — — 134, 63 268, 42 29 867 2. 109.137 — 93, io 3 — — 29 873 16.1867 17,172 45» IlS — — 29 879 2.14939 — — — — 29 881 8.9.5.83 141,100 107, 96 67, 92 209, 53 29 917 4.27.277 171, 26 — 167, 26 245, 47 29 921 32.5-n.17 55, l6 4 123, 86 — — 29 927 2.13.1151 — — — — 82 QUADRATIC PARTITIONS. p p-1 a b c d A B L M 29 947 2.3.7.23.31 — *73i 3 172, 11 i39, 61 29 959 2.3.4993 — — 106, 79 343, 9 29 983i 2.3.19.263 — — 170, 19 113, 63 29 989 4.9.49.17 33, J 7o — 59, 94 223, 51 30 011 2.5.3001 — 27,121 — — 30 013 4.3.41.61 123,122 — 169, 22 235, 49 30 029 4-7507 i73, IO — — — 30 047! 2.83. 181 — — — — 30 059 2.7.19.1 13 — i47, 65 — — 30071 2.5.31.97 — — — — 30 089! 8.3761 67,160 129, 82 — — 30 091 2-3-5-!7-59 — 173, 9 172, 13 211, 53 30 097 16.9.11.19 129,116 163, 42 113, 76 IJ 5, 63 30 103 2.3.29.173 — — 86, 87 172, 58 30109 4-3- I 3- I 93 i55, 78 — 89, 86 347, 1 30 113 3 2 -94i 23,172 165, 38 — — 30 119 2.11. 37.37 — — — — 30 133 4-243-31 i53, 82 — 109, 78 218, 52 30 137! 8.3767 139,104 i53, 58 — — 30 139 2.3.5023 — 149, 63 92, 85 163, 59 30161 16.5.13.29 169, 40 57,n6 — — 30169 8.9.419 163, 60 37,120 13,100 3*3, 29 30 181 4-3-5-5°3 159, 7o — 37, 98 257, 45 30187 2.27.13.43 — 53,H7 28, 99 56, 66 30 197 4-7549 151, 86 — — — 30 203 2.15101 — 99,101 — — 30 211 2 -3-5- I 9-53 — io 3, 99 56, 95 34i, 13 30 223 2.9.23.73 — — 170, 21 34o, 14 30 241 32.27.5.7 145, 9 6 127, 84167, 28 83, 65 30 253 4.3.2521 173, 18 — 161, 38 275, 4i 30 259 2.9.41.41 — 1,123 !7 2 , 15 344, 10 30 269 4.7.23.47 37,i7o — — — 30 271 2.3.5.1009 — — 98, 8 3 347, 5 30 293 4-7573 73,i58 — ~ — 30 307 2-3-5051 — 7,123152, 49 5, 67 30 313 8.9.421 27,172 109, 96149, 52 7, 67 30 319 2.3.31. 163 — — 74, 91 i99, 55 30 323 2.15161 — 81,109 — — 30 341 4-5-37-4I 95,^6 — — — 30 347 a.15173 — 45, 1J 9 ~ — QUADRATIC PARTITIONS. 83 p p-l a b c d A B L M 30 367 2.9.7.241 — — , 1 i3°, 67331, 21 30 3b9 4.71. 107 167, 50 — — — 30 391 2.3.5.1013 — — 146, 55 19, 67 30 403 2.27.563 — 55,n7 136, 63272, 42 30 427 2. 3. n. 461 — i3> 12 3 32, 99 64, 66 30 431 2. 5. 17. 179 — — — — 30 449 16.11.173 143,100 51,118 — — 30 467 2.15233 87,107 — — 30 469 4 .3-2539 65,162 — 91, 86 !67, 59 30 491 2-5-3°49 — 171, 25 — 30 493 4.9.7. 121 107,138 — 4i, 98 335, 19 30 497 32.953 169, 44 27,122 — — 30 509 4.29.263 125,122 — — — 30 517 4.3.2543 121,126 — i73, 14^15, 53 30 529j 64.9.53 127,120 161, 48 23,100277, 41 30 539 2.15269 — 141, 73 — — 30 553 8.3.19.67 93,148 85,108 115, 76343, 13 30 557i 4.7639 139,106 — — — 3055912.3.11.463 — — 34, 99 68, 66 30 577 16.3.49-13 79, I 5 6 j i73, 18 97, 84 194, 56 30 593: 128.239 167, 52 171, 26 — — 30 631! 2.3.5.1021 — — 134, 65329, 23 30 637| 4.9-23-37 i9,!74 — 175, 2 169, 59 30 643| 2.3.5107 — 175, 3 160, 41 37, 67 30649^.3.1277 H5, I 32 43,120107, 80 347, 9 30 661! 4-3-5-7-73 i75, 6 43, 98 251, 47 30 671 2.5.3067 — — — — 30 677 4.7669 169, 461 — — — 30 689 32.7.137 J75, 8159, 52 ■ — — 30 697 8.3.1279 141,104175, 6 173, 16 125, 63 30 703 2.3.7.17.43 — — 10,101 293, 37 30 707 2.13.1181 — i35, 79 — — 30 713 8.11.349 i73, 28 75,112 — — 30 727 2.27.569 — — 5°, 97 241, 49 30 757 j4.-3.11.233 159, 74 — i33, 66 266, 44 30 763 1 2.9.1709 — 125, 87 140, 61 43, 6 7 30 773 4-49-157 103,142 — — — 30 781 4.81. 5. 19 9i,i5 — 103, 82 349, 7 30 803 2. 1 540 1 39, 121 — 30 809 ,8.3851 35,!7 2 171, 28 — — QUADRATIC PARTITIONS. p p-1 a b c d A B L M 30 817 32.9.107 1 jin,i36 143, 72175, 8151, 61 30 829 4-3.7-367 173, 30 — 127, 70337, 19 30 839 2.17.907 — — — — 30 841 8.3-5-257 171, 40 I2Ij 90, 29,100 271, 43 30 851 2.25.617 — J 53, 6i| — — 30 853 4-9-857 143,102 — |i39, 62 , 47, 67 30 859| 2.3.37.139 — 59,ii7| 16,101 ,287, 39 30 869' 4.7717 137,110 — — — 30 871 2.9.5.343 — — 122, 73 97, 65 30 881 32.5.193 175. l6 63,116 — — 30 893,4-7723 77,i58 — — 30 911: 2.5. 11. 281 — — — 30 931 2.3.5.1031 — 167, 39' 52, 97 343, 15 30 937J 8.3.1289 101,144 137, 78i55, 48 310, 3 2 3094114.5.7.13.17 85,154 — — 30 949 4.3.2579 i75, 18 149, 54 298, 36 30 971 2. 5. 19.163 — 123, 89 — 30 977 256.121 1,176 *5?«4 — — 30 983; 2.7.2213 — — — 31013 4-7753 127,122 — — — 31019 2.13.1193 — 99,io3 — — 31033 8.9.431 53,i68 71,114 131, 68 335, 21 31 039| 2.3.7.739 — — 158, 45 316, 30 31 051; 2.27.25.23 — 107, 99 176, 5 191, 57 31063 2.3.31. 167 — — 146, 57 292, 38 31 069' 4.9.863 165, 62 — 121, 74 101, 65 31079 2.41.379 — — — — 31081 8.3.5.7.37 i55, 84 i73, 24 109, 80 131, 63 31091 2.5.3109 — 129, 85 — — 31121 16.5.389 65,164 93,106 — — 31 123 2.9.7. 13.19 — 161, 51 176, 7 155, 61 3II392.15569 — in, 97 — 31 147 2.3.29.179 — J 57, 57 160, 43 289, 39 31 151 2.25.7.89 — — — 31 153 16.3. 1 1.59 153, 88 169, 36 89, 88 *75> 59 31159 2.27.577 — — 86, 89 353, 1 31 177 8.9.433 i7r, 44 163, 48 125 72 250, 48 31 181 4.5.1559 H5, J 34 — — — 31183, 2.3.5197 — — 130, 69 260, 46 31 189 4.3-23-113 105,142 — 83, 90 166, 60 QUADRATIC PARTITIONS. 85 P v- abed A B L M 31 193! 8.7.557 31 219 31 223 31 231 31 237 2.3.121.43 2.67.233 2 -9-5-347 4-3-I9-I37 31247! 2.17. 919 31249! 16.9.7. 31 31 253, 4. 13.601 31259: 2.15629 31267 2.81. 193 31 271 2 -5-53-59 31277 4.7.1117 31307 2. 11. 1423 31319 2.7.2237 31321 8.27.5.29 31327 2.3.23.227 31333|4-3-7-373 31337 31357 31379 8.3917 4.9-13-67 2.29.541 31387 2.3.5231 31391 2.5.43.73 31 393 32.9.109 31 397! 4.47.167 31469 4.7867 31477:4.3.43.61 31 481! 8.5.787 31 489| 256.3.41 31511[ 2.5.23.137 31 513^.3.13.101 31 517| 4.7879 31 531 2.3.5.1051 31541 4.5.19.83 3154312.3.7.751 31547 2.15773 31567 2.3.5261 31573:4.9.877 31 583. 2.15791 31601! 16.25.79 31607 2.15803 163, 68 3M74 ! 55> l6 8 21,124 — — 3 I > I2 3 I 76, 935 2 > 6 — J166, 35 ! 61, 67 — 5,102 io, 68 »,io8 143, 60286, 40 167, 58 — j — I — 3,i 2 5! — — 127, 87 112, 79349, 11 6 1', 1 66 65, 64 45> 121 ! — 73,114 77, 9 2 353, 5 — '142, 61325, 27 177, 2 — j 11,102 22, 68 19,176177, 2 — 171, 46 — 167, 34 65, 67 177. 5 — — J173, 27; 28,101275, 43 !77, 8145, 72 175, 16223, 53 |i6i, 74 — — — W* 70. — I169, 54 — 115, 78230, 52 1109,140 27,124 — 167, 60139, 78 119, 76109, 65 1123,128151, 66 91, 88355, 1 101,146! — — — — I 83,111 152, 53311, 33 121,1301 — . — — j 94, 87 188, 58 — I 93>!°7 — ! 82, 91 73,162 — j 19,102 25^76 153, 64 — 355, 3 38, 68 86 QUADRATIC PARTITIONS. • p p-l a b c d A BJ L M 31 627 2.9.7.251 — 37,123 32,101. 535, 23 31 643! 2. 13.1217 [65, 47 — — 31 649 32.23.43 H5, 32 81,112 — — 31 657| 8.3.1319 69,164 115, 9 6 173, 24. 346, 16 31 663 2.9.1759 — — 166, 37 277, 43 31 667 2.71.223 — 177, i3 — — 31 687 2.3.5281 — — 178, 1 181, 59 31 699 2.27.587 — i43, 75 68, 95 353, 9 31 721 8.5.13.61 n5>!3 6 i77, i4 — — 31 723 2. 3.17. 311 — 149, 69 76, 93 152, 62 31 727 2.29.547 — — — — 31 729 16.3. 661 177, 20 i73, 30 161, 44 293, 39 31 741 4-3-5- 2 3- 2 3 I7 1 , 5°; — 23,102 46, 68 31 751 2.125.127 — — — — 31 769, 8.11. 19.19 155, 88 87,110 — — 31 771 2.9-5-353 — 163, 5 1 172, 27 344, 18 31 793 16.1987 47>i72 45,122 — — 31799 2. 13.1223 — — — — 31817 8.41.97 29,176 63,118 — — 31847 2.15923 — — — — 31 849 8.3.1327 165, 68 i57, 60 43,100 343, 19 31859 2.17.937 — i53, 65 — — 31 873 128.3.83 i53> 92 11,126 65, 96 130, 64 31883 2.19.839 — 51,121 — — 31891 2.3.5.1063 — i37, 81 8,103 3 QI , 37 31 907 2.7-43-53 — i77, J 7 — — 31 957 4.3.2663 4i 3 i74 — !i73, 26 251, 49 31963 2.3.7.761 — i55, 63 136, 67 337, 23 31 973 4-7993 17,178 — — — 31981 4.3-5- J 3-4i 141,110 143, 62 329, 27 31 991 2-5-7-457 — — — — 32 003 2.16001 — 135, *2 — 32 009 8.4001 125,12? 159, 5* — 32 027 2.67.239 — 165, 4S i 1 — — 32 028 43.J7.I57 123,13c > — 169, 34 -7', 45 32 051 2.25.641 — 177, ic — 32 057 8.4007 i79, < ^23, 9; i\ — — 32 05< ) 2.9.13.137 — 179, : J 176, i< ► 119, 6 5 32 06; 1 2. 17. 23.41 — — — — 32 06$ ) 4.8017 i75, 3* 5 — — 1 ~~ QUADRATIC PARTITIONS. 87 p p—1 a b c d A B L M 32 077 4.729.11 179, 6 — 175, 22 241, 5 1 32 083 2-3-5347 — 175, 27 16,103 325, 29 32 089 8.3.7. 191 133,120 169, 42 179, 4 167, 61 32 099 2.11.1459 — 81,113 — — 32 117 4-7-3M7 U9 5 i34 — — — 32 119 2.3.53.101 — — 166, 39 332, 26 32 141 4.5.1607 179, 10 — — 32 143 2.3.11.487 — r 54, 53 5, 69 32 159 2.7.2297 — — 32173 4.3-7-383 77,162 — 31,102 62, 68 32183 2.16091 — — — — 32 189 4-i3-6i9 85,158 — — — 32 191 2-3-5- 2 9-37 — — 178, 13 217, 55 32 203 2.9.1789 — 179, 9 40,101 263, 47 32 213 4-8053 23,178 — — — 32 233 8.3.17.79 173, 48 79,n4 179, 8 203, 57 32 237 4.8059 J 79, 14 — — 32 251 2.3-!25-43 — 101,105 124, 75 248, 50 32 257 5 I2 -9-7 89,156 107,102 95, 88 169, 61 32 261 4.5.1613 145,106 — — — 32 297 8.11.367 179, 16 177, 22 — — 32 299 2.3.7.769 — 131, 87 176, 21 352, 14 32 303 2. 31. 521 — — — — 32 309 4-4i.i97 25,178 — — — 32 321 64.5. 101 161, 80 in, 100 — — 32 323 2.3-5387 — 151, 69 64, 97 355, 11 32 327 2.7.2309 — — 32 341 4.3.5.49.11 105,146 — 179, 10 i49, 63 3235332.3.337 177, 32 95,108 i75, 24 35o, 16 32 359 2-3-5393 — — 178, 15 356, 10 32 363 2.11.1471 — 141, 79 — — 32 369 16.7.17.17 113,140 51,122 — — 32 371 2-3-5- I 3-83 — 113, 99 128, 73 91, 67 32 377 8.3.19.71 171, 56 25,126 163, 44 31, 69 32 381 4.5.1619 59^7° — — 32 401 16.81.25 1,180 163, 54 49,100 349, 17 32 411 2.5.7-463 — 93,io9 — 32 413 4.3.37.73 27,178 — 119, 78 238, 52 32 423 2.13.29.43 — — — — 32 429 4.121.67 i73, 5° — — — QUADRATIC PARTITIONS. p p-1 a b c d A B L M 32 441 8.5.811 [79, 20 171, 40 _ — 32 443 2.3-5407 — 139, 81 164, 43 ! 35, 69 32 467 2.37-773 — • 47,123 172, 31 265, 47 32 479 2.3-54I3 — — 146, 6i] 37, 69 32 491 2.9.5.19.19 — 179, 15 104, 85 IS 1 * 6 3 32 497 16.3.677 39>*76 167, 48 7,104 305, 37 32 503 2.3-54I7 — — 26,103 283, 43 32 507 2.16253 — 117, 97 — — 32 531 2-5-3253 — 57,i2i — — 32 533 4.3.2711 87,158 — 61, 98 233, 53 32 537 8.49-83 131,124 75, 116 — — 32 561 16.5.11.37 i75» 44 147, 74 — — 32 563 2.243.67 89, 1 1 1 176, 23 245, 5i 32 569 8.3-23-59 13,180 149, 72 11,104 323, 3 1 32 573 4.17.479 133,122 — — ■ — 32 579 2.7.13.179 — 177, 25 — — 32 587 2-3-543 1 — 157, 63 88, 91 3 6l » J 32 603 2.16301 — 171, 41 — — 32 609 32.1019 $5*172 69,118 — — 32 611 2.3.5.1087 — 169, 45 28,103 337, 25 32 621 4-5-7-233 61,170 — — 32 633 8.4079 i73, 52 165, 52 — — 32 647 2.3-544I — — > 118, 79 355, J 3 32 653 4.9.907 163, 78 — 175, 26 97, 67 32 687 2.59.277 — — . — — 32 693 4.11.743 i37,*i8 — — — 32 707 2.9.23.79 — 1 73,^7 100, 87 200, 58 32 713 8.3.29.47 67,168 ; 31,126 i$t, 72 262, 48 32 717 4.8179 179, 26 — — 32 719 1 2.3.7. 19.41 — "" — 46,101 257, 49 32 749 4.3.2729 i57, 9c — 79, 94 361, 5 32 771 2.5.29.113 — 39,125 — 32 779 2.27.607 — 181, 3 136, 69 272, 46 32 783 2.37-443 — — — — 32 78S 4.7.1 171 167, 7c ' - — — 32 79? 4.9.91 1 181, t > — 103, 86 155, 6 3 32 80] 32.25.41 151,100123, 94 [ \ ~~ — 32 80^ > 2.3.7.11.71 — 175, 3: >i6o, 4c ► 307, 37 32 831 - 2.5.49-67 — — — I - 32 83; : ^64.27.19 57,i7- s 181, ( ) 161, 4$ 1 ,322, 32 QUADRATIC PARTITIONS. 89 p p-1 a b c d 1 A B L M 32 839 2.3.13.421 — — 142, 65 53, 69 32 843 2.16421 — 165, 53 — 32 869 4.9.11.83 63,170 — 181,. 6 362, 4 32 887 2.81.7.29 — — i3°, 73 349, 19 32 909 4-19-433 35>i7* — — — 32 911 2.3.5.1097 — — 106, 85 361, 7 32 917 4.3.13.211 169, 66 163, 46 3 OI > 39 32 933 4.8233 113,142 — — — 32 939 2-43-3 8 3 — i7i 5 43 — — 32 941 4.27.5.61 i79> 30 — 113, 82 *33, 65 32 957 4.7. 11. 107 181, 14 — — — 32 969 8.13-317 163, 80 159, 62 — — 32 971 2.3.5.7.I57 — 173, 39 164, 45 328, 30 32 983 2 -3- 2 3- 2 39 — — 34,103 343, 23 32 987 2.16493 — 27,127 — 32 993 32.1031 143,112 15,128 — — 32 999 2.7.2357 — — — — 33 013 4.9.7.131 i53 ? 98 — 179, 18 358, 12 33 023 2. 11. 19.79 — — — — 33 029 4.23.359 127,130 — — — 33 037 4.3.2753 131,126 — 65, 98 359, IJ 33 049 8.243.17 125,132 181, 12 109, 84I218, 56 33 053 4.8263 37,178 — — — 33 071 2.5.33 7 — — — — 33 073 16.3-13.53 167, 72 121, 96 25,104 287, 43 33 083 2.7-17.139 — 69,119 — — 33 091 2.3.5. 1103 — 167, 51 4,105 8, 70 33107 2.16553 — 87,113 — — 33 113 8.4139 157, 92 I7 1 , 44 — 33 119 2.29.571 — — — 33149 4.8287 5,182 — — — 33151 2.3.25.13.17 — — 182, 3364, 2 33 161 8.5.829 181, 20147, 76 — ! — 33179 2.53.313 — 123, 95 — — 33181 4.3.5.7.79 75^66 — 167, 4*334, 28 33191 2.53319 - — — _ __ 33 199 2.3. 1 1.503 — — 182, 5197, 59 33 203 2. 13.1277 — 129, 91 33211,2.81.5.41 — |i8i, 15 112, 83 137, 65 33 223 2.3.49.1 13 — — 146, 63 292, 42 90 QUADRATIC PARTITIONS. p p-l a be d A B L M 33 247 2.9.1847 _ — 62, 99 124, 66 33 287 2.11.17.89 — — — — 33 289 8.3-I9.73 117,140 67,120 29,104341, 25 33 301 4-9- 2 5-37 55^74 — 67, 98 227, 55 33 311 2-5-3331 — — — — 33 317 4.8329 161, 86 — _ — 33 329 16.2083 i75, 52 141, 82 — — 33 331 2.3.5.11.101 — 7,129 16,105 32, 70 33 343 2-3-5557 — 86, 93 172, 62 33 347 2.16673 33,127 ~ — 33 349 4.3-7.397 15,182 — 181, 14 139, 65 33 353 8.11.379 107,148 51,124 — — 33 359 2. 13.1283 — — — — 33 377 32.7.149 49,176177, 32 — — 33 391 2.9-5-7-53 - - |i58, 53 3i7, 35 33 403 2.3.19.293 — 11,1291160, 51 320, 34 33 409: 128.9.29 153,100181, 18 31,104 281, 45 33 413 4.8353 17,182 — — — 33 427 2.27.619 — I2 7, 93 40,103 349, 21 33 457 16.3.17.41 81,164173, 421127, 76 355, If 33 461 4-5-7-239 169, 70 — 33 469 4.3.2789 85,162 — 137, 70 73, 69 33 479J 2.19.881 — — — — 33 487 2.3.5581 — 182, 11 2<5, 57 33 493 4.3.2791 183, 2 179, 22 113, 67 33 503 2.7.2393 1 — 33 521 16.5.419 89,160183, 4 — — 33 529 8.3. 11. 127 173, 60101,108181, 16 229, 55 33 533 4. 83.101 43,178 — — 33 547 2.3.5591 155, 69152, 59 329, 3i 33 563 2.97.173 99,109 — 33 569 32.1049 145,112129, 92 — 33 577 8.3.1399 51,176113,102 77, 96 i54, 64 33 581| 4.5-23.73 125,134 33 587 2 7.2399 ,183, 7 33 589 4.27.311 183, ioi — 131, 74 353, 19 33 599 2.107. 157 — — — — 33 601 64.3.25.7 i35» I2 4 43,126 151, 60 302, 40 33 613 4.3.2801 93,i58 49,102 98, 68 33 617 16.11.191 151,104 183, 8 — — QUADRATIC PARTITIONS. 91 V p-l a b c d A B L M 33 619 2.3.13.431 — 1 , 79,117136, 71 77, 69 33 623 2.16811 — — — — 33 629 4.7.1201 155, 98 — — — 33 637 4.3.2803 111,146 — 107, 86 365, 7 33 641 8.5.29.29 179, 40 i77, 34 — 33 647 2.16823 — _ | _ — 33 679 2.9.1871 — — I 94, 91 367, 1 33 703 2.3.41. 137 — \ 74, 97 217, 57 33 713 16.49.43 ^3^5 2 *35, 88| — 33 721 8.3.5.281 139,120167, 54 61,100 3 6 i, I 3 33 739 2-3-5 62 3 — 59,123 56,101 359, i5 33 749 4.11. 13.59 25,182 — — — 33 751 2.27.625 — — 26,105 52, 70 33 757 4.3.29.97 59,174 — 7,106 325, 33 33 767 2.16883 — — — — 33 769 8.9.7.67 37,i8o 163, 60 179, 24 358, 16 33 773 4.8443 173, 62 — — — 33 791 2.5.31. 109 — — 33 797 4.7.17.71 79,166! _ — 33 809; 16.2113 65,172 3> I 3°\ — — 33 811 2.3.5.49.23 23,129148, 63 296, 42 33 827 2.13.1301 183, 13 — — 33829:4.3.2819 177, 5o — 11,106 307, 39 33 851; 2.25.677 — ! 5 J , I2 5 — 33 857 64.23.23 1,184! 33,i28 — — 33 863 2.16931 — — — — 33 871 2.3.5.1129 — — 178, 27 356, 18 33 889 32.3.353 183, 20133, 90 79, 96 158, 64 33 893 4.37.229 47,i78 — — — 339112.5.3391 i . — — 33 923 2.7.2423 — 105,107 33 931 2.9.5.13.29 — i°9, io 5 184, 5 169, 63 33 937 ! 16.3.7.101 9,184 103,108 113, 84 226, 56 3394114.5.1697 7I, I 7°; — — — 33 961 8.3.5.283 115,144 47,126 181, 20121, 67 33 967| 2.27.17.37 58,101245, 53 33 997; 4.3.2833 61,174' 17,106301, 41 34 019; 2.73.233 87,115 — — 34 031! 2.5.41.83 — — — — 34 033 16.3.709 177, 52 115,102 161, 52 5, 7i 92 QUADRATIC PARTITIONS. p p-l a b c d A B L M 34 039 2. 9. 3I.61 — — '158, 55 7, 7i 34 057 8.9.II.43 181, 36 125, 96157, 5 6 | 11, 71 34 061 4-5- I 3-i3i I3M3 — — — 34 123 2.3.121.47 — 29,129116, 83365, 11 34 127 2.113.151 — |" • 34129 16.27.79 105,152 73,120 41,104353, 21 34 141 4-3-5-5 6 9 171, 70 73, 98221, 57 34147 2.9.7.271 — 145, 81:172, 39344, 26 34 157 4.8539 179, 46 — 34159 2.3.5693 — — i54, 59 23, 7i 34171 2.3.5.17.67 — 157, 69 128, 77 359, i7 34183 2. 81. 211 — — 166, 47 25, 7i 34 211 2. 5. 11. 311 — 183, 19 — 34 213 4.3.2851 33^82 — (181, 22247, 53 34 217 8.7.13.47 19,184 i77, 38 — — 34 231 2.3.5.7.163 — — 34,105 68, 70 34 253 4.8563 157, 98 — — — 34 259 2.7.2447 — 159, 67 34 261 4.3.5.57I 185, 6 — i73, 38287, 45 34 267 2.3-57II 83,117152, 61 311 7i 34 273 32.9.7.17 183, 28 91,114185, 4173, 63 34 283 2. 61. 281 — 45,127 — 34 297 8.3.1429 21,184185, 6 43,104269, 49 34 301 4.25.343 149,110 — — — 34 303 2.3-57 I 7 — — 70, 99; 140, 66 34 313 8.4289 163, 881129, 94 34 319 2.17159 — — 34 327 2.9.1907 — — 50,103259, 51 34 337 32.29.37 169, 76123, 98 34 351 2.3.25.229 — ~~ 2,107323, 35 34 361 8.5.859 181, 40153, 74 — — 34 367 2.17183 — — — — 34 369 64.3.179 185, 12149, 78 169, 44 37, 7i 34 381 4.9.5.191 109,150 — 127, 781254, 52 34 403 2. 103. 167 9,131 — — 34 421 4.5.1721 185, 14! — — — 34 429 4.3.19.151 155,102 — 89, 94ii93, 61 34 439 2.67.257 — — — — 34 457 8.59.73 59,176183, 22 — 34 469 4.7-1231 i75, 62 ~" — QUADRATIC PARTITIONS. 93 p p-1 a b c d A B L M 34 471 2 -9-5-383 — — S6, 95 37i, 3 34 483 2.3.7.821 — 65,123 136, 73 355, 21 34 487 2.43.401 — — — — 34 499 2.47.367 — 57,125 — — 34 501 4.3.125.23 65,174 101, 90 202, 60 34 511 2.5.7.17.29 — — — — 34 513 16.3.719 183, 32 185, 121175, 36 35°, 24 34 519 2.3. 11.523 — — 38,105 76, 70 34 537 8.3.1439 101,156 J73, 48; S3, 96 166, 64 34 543 2.9.19.101 — ; 14,107 335, 3i 34 549 4.3.2879 185, 18 — j 29,106 289, 45 34 583 2.17291 — — — — 34 589 4.8647 I33,i3 — — — 34 591 ».3-5-«53 — — |n8, 83 131, 67 34 603 2 -3-73-79 — 85,117 16,107 305, 4i 34 607 2.i33 I - I 3 — — — — 34 613 4.17.509 167, 82 — — — 34 631 2.5.3463 — — — — 34 649 8.61. 71 157,100 171, 52 — — 34 651 2. 9.25.7. 11 — 37,129 176, 35 281, 47 34 667 2.17333 — 165, 61 — 34 673 16.11.197 113,148 141, 86 — — 34 679 2.7.2477 — — — — 34 687 2.9.41.47 — — 130, 77 101, 69 34 693 4.3-49-59 177, 58 — 59,102 118, 68 34 703 2-I735 1 — — — — 34 721 32.5-7-3I 175, 64 63,124 34 729 8.3.1447 123,140 77,120 173, 40 53, 7i 34 739 2.11.1579 — 183, 25 — 34 747 2.3-579I — 67,123 20,107 34i, 29 34 757 4.8689 161, 94 — — — 34 759 2.9.1931 — — 166, 49 3i3, 39 34 763 2.7.13.191 — 21,131 — 34 781 4-5-37-47 85,166 — — 34 807 2.3.5801 — — no, 87 220, 58 34 819 2.3.7.829 — u3, io 5 ss, 95 197, 61 34 841 8.5.13.67 155^04 183, 26 — — 34 843 2.3.5807 — 101,111 100, 91 373, 3 34 847 2.7.19.131 — — — — 34 849 32.9.121 143,120 1,132 49, i©4| 263, 51 94 QUADRATIC PARTITIONS. p p-l a b c d A B L M 34 871 2.5.11.317 — 34 877 4.8719 181, 46 — — — 34 883 2. 107. 163 — 81,119 — — 34 897 16.3.727 119,144 7,132 145, 68 59, 7i 34 913 32.1091 73,172; 165, 62 — — 34 919 2.13.17.79 — — — 34 939 2.27.647 181, 33 184, 19 241, 55 34 949 4.8737 145,118 — — — 34 961 16.5.19.23 169, 80 i53, 76 — — 34 963 2.3.5827 — 41,129 5 6 » IQ 3 253, 53 34 981 4-3-5- II -53 175, 66 — 187, 2 181, 63 35 023 2.3.13.449 — 26,107 347, 27 35 027 2. 83. 211 — i77, 43 — — 35 051 2.25.701 — 27,13! — — 35 053 4.3.23.127 157,102 — 79, 98 215, 59 35 059 2.3.5843 — 169, 57 124, 81248, 54 35 069 4.11.797 187, 10 — — — 35 081 8.5.877 35, l8 4 i59, 7o — — 35 083 s 2.9.1949 — 179, 39 176, 37 ( 65, 71 35 089 16.3.17.43 183, 40 167, 60 IS* 6 4 343, 29 35 099! 2.7.23.109 — 93, JI 5 — — 351071 2.3.5851 — 185, 21 128, 79 109, 69 35111:2.5.3511 — — — — 35 117; 4.8779 I3M34 — — 35129 8.4391 115,148 123,100 — 35141 4.5.7.251 79,170 — — 35 149 4.3. 29.101 45^82 — 143, 7o 67, 7i 35153! 16.13.13.13 137,128 135, 92 — — 35 159, 2.17579 — — — — 35171 2.5.3517 — 183, 29 — — 35 20l! 1 28.25. 1 1 65,176 177, 44 — — 35 221 1 4.3-5-587 25,186 — 173, 42 346, 28 35 227 2.9.19.103 — 125, 99 68,101 371, « 35 251 2.3.125.47 — 103,111 112, 87 224, 58 35 257 8.3.13.113 141,124 187, 12 53,i°4 365> 17 35 267 2.7.11.229 — 153, 77 — 1 35 2791 2.31.569 — — — 35 281 16.9.5.49 159,10c 163, 66 17,108 34, 72 35 291 2.5.3529 — 171, 55 — 35 311 L 2.3.5.11.107 — 182, 27 364, 18 QUADRATIC PARTITIONS. 95 p p-l a b c d A B L M 35 317 4.81. 109 71,174 — 163, 54:326, 36 35 323 2.3.7.29.29 — 149, 81 164, 53i3 2 3, 37 35 327 2.17.1039 — — — — 35 339 2.17669 99, "3 — — 35 353 8.9.491 3,188181, 36 19,108; 38, 72 35 363 2.17681 — H59, 7i — — 35 381 4.5.29.61 185, 34 — — — 35 393 64.7.79 7,188! 75,122 — — 35 401 8.3.25-59 99,160 97,114 187, 12374, 8 35 407 2.9.7.281 — 158, 59 335, 33 35 419 2.3.59 3 — 187, 15 188, 5203, 61 35 423 2.89.199 — — — — 35 437 4.3.2953 29,186 — 65,102 130, 68 35 447 2.37.479 — — — — 35 449 8.3.7. 211 85,168 121,102 157, 60314, 40 35 461 4.9.5.197 81,170 181, 30362, 20 35 491 2.3.5.7.I3 T 3 — 47,129 188, 7 167, 65 35 507 2.4I-433 — 57,127 — — 35 509 4.3. 1 1.269 i53>no — J 79, 34; 77, 7* 35 521 64.3.5.37 185, 3^ J 39, 9° 23,108, 46, 72 35 527 2.3.31. 191 — — 170, 47 3ii, 4i 35 531 2.5.11.17.19 — — — 35 533 4.27.7.47 147,118 — 95, 94187, 63 35 537 16.2221 41,184 183, 32 — — 35 543 2. 1 3. 1 367 — — — — 35 569 16.9.13.19 ! 15,188 179, 42 89, 96178, 64 35 573 4.8893 103,158 — __ — 35 591 2.5-3559 — — — , — 35 593 8.3.1483 117,148 I3 1 , 96 101, 92377, 3 35 597 4.1 1.809 109,154 — — 35 603 2-7-2543 — i5,!33 — — 35 617 32.3.7.53 169, 84 187, 18 25, Io8 5°, 72 35 671 2.3.5.29.41 — — 62,103247, 55 35 677 4.9.991 181, 54 — 185, 22119, 69 35 729 16.7. n.29 127,140 189, 2 — — 35 731 2.9-5-397 — 127, 99' 184, 25,259, 53 35 747 2.61.293 — 177, 47 35 753 8.41. 109 187, 28 189, 4 — i — 35 759 2.19.941 — — i — — 35 771 2.5.49.73 — 189, 5 — - 1 96 QUADRATIC PARTITIONS. V 35 797 35 801 35 803 35 809 35 831 35 837 35 839 35 851 35 863 35 869 35 879 35 897 35 899 35 911 35 923 35 933 35 951 35 963 35 969 35 977 35 983 35 993 35 999 36 007 36 011 36 013 36 017 36 037 36 061 36 067 36 073 36 083 36 097 36 107 36109 36131 36 137 36 151 36161 p-1 4-3- I 9- I 57 8.25.179 2.81. 13.17 3 2 -3-373 2.5-3583 4.17.17.31 2.9.11.181 2.3.25-239 2.3-43- J 39 4.3.49.61 2.17939 8.7.641 2-3-3 I - I 93 2.27.5.7.19 2.3-5987 4.13.691 2.25.719 2.17981 128.281 8.3.1499 2.9.1999 8. 1 1.409 2.41.439 2-3-I7-353 2.5.13.277 4.3.3001 16.2251 4-9-7- II - I 3 4.3.5.601 2.3.6011 8.27.167 2.18041 256.3-47 2.7.2579 4.9.17.59 2.5-3 6l 3 8.4517 2.3.25.241 64.5.113 i5">""4 — 101,160183, 34 — ,181, 39 "75> 7 2 ! 31,132 91,166 1187, 30. 181, 56 53,i82 25,188 189, 16 i _ 187, 32 78,173 1 7M76 87, 21 i35> 94 i57, 75 151, 81 A B L M 125, 82 80, 99 121, 84 14,109 188, 13 no, 89 151, 66 16,109 94, 95 121, 69 160, 66 242, 56 3'3> 4i 149, 67 377, 7 302, 44 343, 3i I9 1 * 63 64,io3 373, I 3 36 187| 2.3.37.163 III, 154 165, 94 27, 188 159, 104 3, 190 179, 64 185, 44 163, 56 5, 73 166, 53 7, 73 182, 31 89, 71 161, 58 13, 73 189, II «7'*i 58 65,126 9,i34 69,125 57,128 137, 93 ss,^ 2 111,109 113,108 27,i33 177, 49 i5,i34 142, 73361, 23 117,106 77,1231148, 69296, 46 85, 98209, 61 169, 50 19, 73 128, 81 256, 54 149, 68 137, 76 49,106 353, 27 9 1 , 7i 367, 19 QUADRATIC PARTITIONS. 97 P p-l a b c d A B L M 36 191 2. 5.7. n.47 36 209 16.31.73 103,160 153, 80 — 36 217 8-9-503 109,156 37^32 35, IQ 8 70, 72 36 229 4-3-3 OI 9 177, 70 — 181, 34 283, 49 36 241 16.3.5.151 129,140 67,126 79,100 379, 7 36 251 2.625.29 — 99,115 — — 36 263 2.18131 — — — 36 269 4.9067 ^^o — — — 36 277 4-3-3023 41,186 — 173, 46 35, 73 36 293 4.43.21 1 127,142 — — 36 299 2.18149 — 189, 17 — — 36 307 2.9.2017 — 55, I2 9 112, 89 i55, 67 36 313 8.3.17.89 157,108 149, 84 155, 6 4 37, 73 36 319 2.3- 6 o53 — — 26,109 3.01, 45 36 341 4-5- 2 3-79 185, 46 — — — 36 343 2.27.673 — — 190, 9 380, 6 36 353 512.71 167, 92 21,134 — — 36 373 4-3-7-433 57,182 — i79, 3^ 293, 47 36 383 2.18191 — — — 36 389 4.11.827 17,190 — — — 36 433 16. 9. 11. 23 33,i88 125,102 175, 44 43, 73 36 451 2.729.25 — i,i35 68,103 241, 57 36 457| 8.3.49.31 51,184175, 54 115, 88 379, 9 36 467 ; 2.18233 33,i33 — — 36 469 4.9.1013 87,170 13,110 3i7, 4i 36 473l 8.47.97 83,172 165, 68 — — 36 479 2.13.23.61 — — — — 36 493 4.3.3041 147,122 — 191, 2 i97, 63 36 497 16.2281 191, 4 93, IlS — — 36 523 2.9.2029 109,111 176, 43 47, 73 36 527 2.7.2609 — — — — 36 529 16. 3.761 185, 48 41,132 191, 4 i79, 65 36 541 4.9.5.7.29 21,190 — 73,102 146,' 68 36 551j 2.25.17.43 — — — — 36 559 2.27.677 — — 122, 85133, 69 36 563 2.101.181 — 105,113 — — 36 57l| 2.3.5.23.53 — n,i35 152, 67, 49, 73 36 583 2.3.7.13.67 — — 130, 81260, 54 36 587| 2.11.166^ — 117,107 36 599 2.29.631 — _ — 98 QUADRATIC PARTITIONS. p P -l a b c d A B L M 36 607 12.3.6101 — — i9°» J 3 229, 59 36 629! 4-9*57 23,190 — — — 36 (537i 4.3-43.7I 171, 86 — 167, 54 334, 36 36 643 2.3.31. 197 — 191, 9 164, 57 328, 38 36 653 4.49. 1 J- 1 7 i73> 82 — — — 36 671 2.5.19.193 — — ' — — 36 677 4.53.I73 191, 14 — — — 36 683 2.18341 — 171, 61 — — 36 691 2.3.5.1223 — 121,105 92, 97 J99, 63 36 697 8.3.11.139 99,164 43^32 187, 24 374, 16 36 709 4-3.7-i9.23 i75, 78 — jioi, 94 181, 65 36 713 8.13.353 37>i88 99,116 — — 36 721 16.27.5. 17 i35>i36 89,120161, 60 322, 40 36 739 2.9.13.157 — I7,i35!i84, 31 277, 5 1 36 749 4.9187 157,110 — — — 36 761 8.5.919 131,140 123,104 — — 36 767 2 -3 I -593 — — — — 36 779 2.7.37.71 — 189, 23 — — 36 781 4.3.5-613 141,130 — 191, 10 161, 67 36 787 2.3.6131 — 97,n7 172, 49 3*9, 4i 36 791 2.5.13.283 — — — — 36 793 8.9.7.73 "7>*5 2 71,126 125, 84 25°, 56 36 809 8.43.107 85,172 141, 92 — — 36 821 4.5.7.263 89,170 — — — 36 833 32.1151 143,128 159, 76 — — 36 847 2.9.23.89 — — 5°, io 7 37i, 19 36 857 8.17. 271 181, 64 153, 82 — — 36 871 2.3.5.1229 — — 158, 63 316, 42 36 877 4.3.7.439 189, 34 — i43, 74 365, 23 36 887 2.18443 — — — — 36 899 2. 19.971 — 39,i33 1 36 901 4.9.25.41 145,126 — 149, 70 61, 73 36 913, 16.3.769 7,192 15 1 , 84 191, 12382, 8 36 919, 2.9.7.293 — — 62,105124, 70 36 923 2.18461 — 5M31 — — 36 929' 64.577 185, 52 171, 62 — — 36 931 2.3.5.1231 — 191, 15 188, 23257, 55 36 943 2.3.47. 131 — — no, 91 163, 67 36 947 2.49.13.29 — i77, 53 36 973 4.9.13.79 163,102 175, 46 3i3, 43 QUADRATIC PARTITIONS. 99 p p-1 a b c d A B L M 36 979; 2.3.6163 1 _ 23,135 4,111 8, 74 36 997 4-3.3083 49,186 — 187, 26109, 7 1 37003:2.3.7.881 — 61,129 80,1011383, 7 37013,4.19.487 73,178 — — — 37 019! 2,83.223 — 69,127 — — 37 021 '4.3.5.617 i55t"4 — i37, 78 274, 52 37 039 2.36173 — — 142, 75 284, 50 37 049 8.11.421 107,160 57,i3o — 37 057 64.3- J 93 191, 24 47,i32 97, 96 194, 64 37 061 4.5. 17.109 3M90 — — — 37 087 2.3.7.883 — — 38,109 289, 49 37 097 8.4637 101,164 147, 88 — — 37 117 4.9.1031 181, 66 — 103, 94 3^5, 3 37 123 2.3.23.269 — i75, 57 184, 33 368, 22 37139 2.3 I -599 — i59, 77 — — 37 159 2.3.11- 563 — — . 14,111 28, 74 37 171 2 .9.5.7.59 — 161, 75 64,105 128, 70 37181 4-5- II > 1 3- I 3 91,170 — — — 37189 4.9-1033 33^90 — 59,106 259, 55 37 199| 2.7.2657 — — 37 201 16.3.25.31 151,120 i37, 96 47,108 94, 72 37 217! 32.1163 79,176 !5,!36 — — 37223)2.37.503 — — - — — 37 243 2.9.2069 — i79, 5 1 40,109 367, ^3 37 253 4.67.139 193, 2 — — — 37 273! 8.3.1553 187, 48 169, 66 109, 92 167, 67 37 277 4-93*9 I39>134 — — — 37 307 2. 23. 811 — 165, 7 1 — • — ■ 37 309 4.3-3 io 9 75,178 169, 54 338, 36 37 313 64.11.53 193, 8 81,124 — — 37 321 8.3-5-3ii 189, 40 193, 6 187, 28 271, 53 37 337 8.13-359 59,184 87,122 — — 37 339 2.3.49.127 — 149, 87 164, 59 34i, 35 37 357 4.3.11-283 99,166 — 193, 6 386, 4 37 361 16.5.467 185, 56 183, 44 — — 37 363 2.3.I3.479 — II9 1 * 21 20,111 40, 74 37 369 8.27.173 45,188181, 48 163, 60 326, 40 37 379i 2. 1 1. 1699 — i77, 55 — — 37 397 4.9349 169, 94 1 37 409 32.7.167 145,128 111,112 - ! 100 QUADRATIC PARTITIONS. p p-l a b c d A B L M 37 423 2. 243.7. 11 — — 190, 21 380, 14 37 441 64.9.5.13 71,180 107,114 193, 8:169, 67 37 447 2.3.79.79 — — 22,111! 44, 74 37 463 2.18731 — — — ., — 37 483 2.3.6247 — 85,123 56,107377, 17 37 489 16.3.11.71 25,192 119,108 71,104:383, 11 37 493 4.7.13.103 167, 98 — — 37 501 4.3.3125 85,174 — I5 1 , 7o 361, 27 37 507 2.3.7.19.47 — 65,129 160, 63320, 42 37 511 2.5.121.31 — — — — 37 517 4.83.113 i79> 74 — — — 37 529 8.4691 125,148 69,128 — — 37 537 3 2 -3- I 7.23 81,176 193, I2 i75, 4835°, 32 37 547 2.18773 — 3,i37 — , — 37 549 4.9.7.149 93>i7° — 193, 10223, 61 37 561 8.3.5-313 H5>i56 187, 36 181, 403 01 , 47 37 567 2.9.2087 — — 130, 83119, 71 37 571 2.5.13.17.17 — 57,i3i — — 37 573 4.3.31. 101 193, 18 139, 78278, 52 37 579 2.3.6263 — 101,117 44,109283, 51 37 589 4-9397 185, 58 — — — 37 591 2-3-5-7-I79 — — 122, 87244, 58 37 607 2.18803 — — — — 37 619 2.7.2687 — 9,i37 — — 37 633 256.3-49 97,168 191, 24 1,112337, 37 37 643 2. 11. 29.59 — 189, 3 1 — — 37 649 16.13. 181 193, 20 99,118 — — 37 657 8.9.523 189, 44 53,132 5, 112 33i, 39 37 663 2.3.6277 — — *94, 3 388, 2 37 691 2-5-3769 — 171, 65 — — 37 693 4.27.349 107,162 — 185, 34 83, 73 37 699; 2.3.61. 103 — J93, 15 68,105 136, 70 37 717| 4.3.7.449 9,194 — 157, 66 3 J 4, 44 37 747 2.81.233 — M3, 93 28,111 56, 74 37 781 4.5.1889 41,190 — — — 37 783 2.9.2099 — — i94, 7 173, 67 37 799 2.18899 — — — — 37 811 2.5-19-199 — . 81,125 — — 37 813 4.3-23-I37 137,138 — , 125, 86 383, 13 37 831 2-3-5-I3-97 — 1 — 98, 97 193, 65 QUADRATIC PARTITIONS. 101 p p-1 a b c d A B L M 37 847 2. I27. I49 37 853 4.9463 I33.M2 — — 37 861 4-3-5-63I 15^94 i33, 82 379, 17 37 871 2.5-7.54I — — — — 37 878 2.3.59.107 — — 194, 9 388, 6 37 889 1024.37 167,10c 117,110 — — 37 897 8-3-1579 13^144 i93, 18 i55, 68 359, 29 37 907 2. 11. 1723 — 183, 47 — — 37 951 2.3.25.11.23 — 142, 77 89, 73 37 957 4-3-3163 129,146 107, 94 175, 67 37 963 2.27.19.37 — 181, 51 184, 37 295, 49 37 967 2.41.463 — — — — 37 987 2.3.13.487 — 103,117 32,111 64, 74 37 991 2.5.29.131 — — — — 37 993 8.3.1583 147,128 79,126 19,112 355, 3i 37 997 4.7-23-59 19,194 — — — 38 011 2.3.5-7-181 — 187, 39 172, 53 13, 75 38 039 2.7. 11. 13. 19 — — — — 38 047 2-3-I7-373 — — no, 93 220, 62 38 053 4-9-7-I5 1 177, 82 — 181, 42 362, 28 38 069 4.31-307 185, 62 — — — 38 083 2.3-11.577 — 169, 69 124, 87 248, 58 38 113 32.3.397 183, 68 5,i38 185, 36 37o, 24 38 119 2.3-6353 — 34,in 68, 74 38149 4.3.11.17.17 193, 30 — 43,no 287, 51 38153 8.19.251 53,i88 195, 8 — — 38 167 2.3.6361 — ' 182, 41 305, 47 38177 32.1193 151,124 165, 74 — 38183 2.17.1123 — — — 38189 4-9547 115,158 — — — 38197 4.9.1061 89,174 — 67,106 385, 13 38 201 8.25. 191 85,176 153, 86 — 38 219 2.97.197 — 171, 67 — — 38 231 2.5.3823 — — — — 38 237 4.121.79 181, 74 — — — 38 239 2.3-6373 — — 94, 99 188, 66 38 261 4-5-1913 25,i94 — — 38 273 128.13.23 193, 32 129,104 — — 38 281 8.3.5. 11. 29 195, J 6 191, 30 91,100 39i, 3 38 287 2.27.709 — — 190, 27 380, 18 102 QUADRATIC PARTITIONS. jP p-l a b c d A B L M 38 299 2.3.13.491 — 43,135 116, 91 i57, 69 38 303 2.11.1741 — — — — 38 317 4.3.31. 103 61,186 — 127, 86 13 1 , 7 1 38 321 16.5.479 185, 64 87,124 — — 38 327 2.19163 — — — — 38 329 8.3.1597 77,180! 59,132 13 1 , 84 262, 56 38 333| 4.7.37.37 187, 58 — — 38 351| 2.25.13.59 — — 38371:2.3.5.1279 — 137, 991 8,113 347, 35 38 377 8.9.13.41 141,136 i7, I 3 8 ' 77,io4 389, 9 38 393 8.4799 173, 92 75, I2 8 — 38 431 2.9.5.7.61 — — 158, 67 43, 75 38 447 2.47.409 — — — — 38 449 16.27.89 145^32 i9,!38 193, 20 i33, 7 1 38 453 4.9613 73>i82 — — — 38 459 2.7.41.67 — 189, 37 — — 38 461 4.3.5.641 165,106 — 119, 9° 238, 60 38 501 4.125.7. 11 49,190 — — — 38 543 2.7.2753 — — — — 38 557 4.81. 7.17 9M74 — 185, 38 299, 49 38 561 32.5.241 169,100 69,130 — 38 567 2.11.1753 — — — — 38 569 8.3.1607 187, 60 61,132 181, 44 49, 75 38 593' 64.9.67 57,i88 181, 54 31,112 367, 27 38 603 2.19301 — i95, I 7 — — 38 609 16.19.127 95^72 189, 38 — — 38 611 2. 27. 5. 11. 13 — 73, I2 9 188, 33 376, 22 38 629 4.9.29.37 127,150 — 149, 74 37i, 25 38 639 2.19319 — — — — 38 651 2.25.773 — 3, x 39 — — 38 653 4.3.3221 117,158 — 169, 58 343, 37 38 669 4.7.1381 163,110 — — 38 671 2.3.5.1289 — — 182, 43 53, 75 38 677 4.3.11.293 ;i5i,i26 173, 54 346, 36 38 693 4.17.569 1*93, 38 — — 38 699 2. 11. 1759 141, 97 1 — 38 707 2.3.6451 — 193, 2 7 20,113 359, 3 1 38 711 2.5.49.79 — — — 38 713 8.3.1613 43, J 9 2 25,i3 8 61,108 >I22, 72 38 723 2.19.1019 — 9,i35 , ~ i QUADRATIC PARTITIONS. 103 p p-1 a b c d f A B L M 38 729 8.47.103 125,152 159, 82 — — 38 737 16.9.269 159,116 163, 78 i75, 52 33 1 , 4i 38 747 2.19373 — J95, 19 — — 38 749 4.3.3229 75> l82 — 71,106 247, 59 38 767 2.3.7.13.71 — — 118, 91 39i, 9 38 783 2.19391 — — 38 791 2.9-5-43 1 — — 22,1131317, 45 38 803 2.3.29.223 — 119,111 164, 63328, 42 38 821 4-3-5- 6 47 65,186 — i97, 2 203, 65 38 833 16.3.809 103,168 185, 48 191, 28107, 73 38 839 2.3- 6 473 — — 154, 7i 59, 75 38 851 2.3.25-7.37 — 49> I 35 76,105 152, 7° 38 861 4.5.29.67 35**94 — — — 38 867 2.19433 — i5,!39 — 38 873 8.43.1 13 197, 8 105,118 — — 38 891 2.5.3889 123,109 — — 38 903 2.53.3 6 7 — — — — 38 917 4.9.23.47 161,114 — 197, 6 394, 4 38 921 8.5.7.I39 139,140189, 40 — — 38 923 2.3.13.499 — 139, 99 196, 13 235> 61 38 933 4-9733 137,142 — — — 38 953 8.9.541 197, 12:125,108 179, 48 358, 32 38 959 2.3-43-I5 1 194, 21 388, 14 38 971 2.9-5-433 — ,197, 9 68,107 389, 13 38 977 64.3.7.29 121,1561 85,126 193, 24 386, 16 38 993 16.2437 97,172195, 22 — — 39 019 2.3.7.929 — 187, 45 188, 35 293, 5i 39 023 2. 109.179 — — — 39 041 128.5.61 25,196171* 7o — — 39 043 2. 81. 241 — 161, 81 104, 97 187, 67 39 047 2.7.2789 — — — — 39 079 2.9.13.167 — — 46,111 92, 74 39 089 16.7.349 175, 92 141, 98 — — 39 097 8.27.181 179, 84197, 12 107, 96 214, 64 39103 2.3-343.I9 — — 146, 77 377, 23 39 107 2.19553 — 1183, 53 — — 39113 8.4889 163,112 129,106 — 39119 2.19559 — ■ — ■ 39133 4.9.1087 197, 18 — 89,102 178, 68 39 139 2.3- II -593 - 167, 75 124, 89 143, 7i 104 QUADRATIC PARTITIONS. p p-i a b c d A B L M 39157 4-3-I3-25 1 39,194 — 13,114 26, 76 39161 8.5.11.89 181, 80 57,134 — — 39 163 2.3.61. 107 — 155, 87 136, 83 xi3i 73 39 181 4.3.5-653 195, 34 — 19X1 3° 382, 20 39 191 2.5-39!9 — — — — 39 199 2.3.47.I39 — 1 — 182, 45 364, 30 39 209 8.13.13.29 197, 20 3,140 — — 39 217 16.3.19.43 111,164115,114 65,108 130, 72 39 227 2.11.1783 — 117,113 — — 39 229 4.3.7.467 5,i98 — I5 1 , 74 7*i 75 39 233 64.613 127,152111,116 — — 39 239| 2.23.853 — — — — 39 24i; 8.9.5.109 171,100179, 60 197, 12 394, 8 3925ij2.125.157 — 153, 89 — — 39 293 4. 1 1. 19.47 197, 22 — — — 393OlU.3-25.13* 95,!74 — 187, 38 73, 75 39 313 16.27. 7.13 63,188! 35,138 41,112 295, 5 1 39 317 4.9829 41,194 — — — 39 323 2.19661 — I7X| 7 1 — — 39 341 4.5.7.281 125,154 — — 39 343; 2.3.79.83 — — T7°, 59 347, 37 39 359 2.11.1789 — — — — 39 367! 2.27.729 — 19°, 33 380, 22 39 371 2.5.31. 127 — 27,139 — — 39 373 4.3- I 7- I 93 13^98 — '75> 54 35°, 36 39 383 2.7.29.97 — — — — 39 397 4.3.49.67 I9 1 , 54 — i97, 14 239, 61 39 409 16.3. 821 185, 72 103,120 97,100 397, 1 39 419 2.19709 — 189, 43 — — 39 439 2.9-7.3I3 — — 94,101 209, 65 39 443 2.13.37-41 — i35,i°3 — — 39 451 2.3.25.263 — ^73, 69 188, 37 77, 75 39 461 4-5-I973 i75, 94 — 39 499 2.3.29.227 — 149, 93 196, 19 253, 59 39 503 2.19751 — — — — 39 509 4.7.17.83 103,170 — — — 39 511 2.9-5-439 — — i94, 25 119, 73 39 521 32.5-13-19 i45, J 36 177, 64 — — 39 541 4-3-5-659 i35, x 46 — i79, 5° 329, 43 39 551 2.25.7.113 — — — ~ QUADRATIC PARTITIONS. 105 p p-1 a b c d A B L M 39 563 2.131.151 _ 45,137 — — 39 569 16.2473 65,188 99,122 — — 39 581 4-5- I 979 59, I 9° i — — ■ — 39 607 2.3.7.23.41 — 1 — 13°, 87 260, 58 39 619 2.9.31.71 — *99, 3 112, 95 i73, 69 39 623 2.11.1801 — — — — 39 631 2.3.5.1321 — 134, 85 121, 73 39 659 2.79.251 — ! H7, 95 — — 39 667 2. 3. 11. 601 97,!23 52,111 104, 74 39 671 2-5-3967 — i — — — 39 679 2.3.17.389 — — 2,115 343, 39 39 703 2-3-i3-5°9 — — i54, 73 373, 27 39 709 4.9.1 103 *97, 3° — 199, 6 398, 4 39 719 2.7.2837 — — — — 39 727 2.9.2207 — — 122, 91 151, 7i 39 733 4-3-7-H-43 23,198 — 115, 94 397, 7 39 749 4-i9-5 2 3 *93, 5o — — — 39 761 16.5.7.71 119,160 183, 56 — — 39 769 8.3.1657 165,112 41,138 187, 40 307, 49 39 779 2.19889 — i77, 65 — — 39 791 2.5- 2 3- 1 73 — — — — 39 799 2. 27. 11. 67 — — 82,105 164, 70 39 821 4.5.11.181 61,190 — — — 39 827 2.19913 — 87,127 — — 39 829 4-3-33J9 25,198 — 29,114 58, 76 39 839 2.19919 — — — — 39 841 32.3.5.83 175. 96 i93, 36 47,112 289, 53 39 847 2.3.29.229 — — 142, 81 284, 54 39 857 16.47-53 199, 16 i35, T °4 — — 39 863 2. 19. 1049 — — — — 39 869 4.9967 187, 70 — — — 39 877 4.33323 111,166 — 133, 86 ,125, 73 39 883 2. 3.17. 17. 23 — 11,141 160, 69 ,320, 46 39 887 2.49.11.37 — — — — 39 901 4.3.25.7.19 155^26 — 199, 10 229, 63 39 929 8.7.23.31 173,100 27,140 — — 39 937 i 1024.3.13 ! 39,196 43,138 137, 84 274, 56 39 953 ! 16.II. 227 »93. 52 189, 46 — 39 971 | 2.5.7.571 — i53, 9i — — 39 97S 2.9.2221 — J 79, 63 152, 75 !3°4, 5° 106 QUADRATIC PARTITIONS. p p-1 a b c d A B L M 39 983 2.19991 — — 39 989 4.13.769 167,110 — i 40 009 8.3.1667 3,200191, 42 197, 20257, 59 40 013 4.7.1429 83,182 — — — 40 031 2.5.4003 — — — — 40 037 4. 10009 49,194 s — — i — 40 039 2.3.6673 — — 146, 79 91, 75 40 063 2. 3. 11. 607 — — 170, 61 13, 77 40 087 2. 9.17. 131 — — 158, 7i37*i 29 40 093 4.3-I3.257 123,158 169, 62 17, 77 40 099 2.3.41. 163 — i$h 93 56,111 112, 74 40111 2.3.5.7. 191 — — 178, 53 *9, 77 40123 2.27.743 — 19,141 76,107245, 61 40127 2.20063 — — — 1 " — 40129 64.3.11.19 135^48139^02 151, 76379, 25 40151 2. 25. 11. 73 1 — — 40153 8.3.7.239 187, 721119,114 i79, 52 23, 77 40163 2.43.467 — 39^39 — — 40169 8.5021 13,200 111,118 — — 40177 16.81. 31 i99> 24 73,132 167, 64 25, 77 40189 4.3.17. 197 i33 J I 5°| ™ i99, 14 i57, 7 1 40193 256.157 103,172:171, 74 — , — 40 213 4.9.1117 183, 82 35, IX 4 70, 76 40 231 2.27.5.149 — — 166, 65 29, 77 40 237 4-3-7-479 5M94 — 95, 102 ^0, 68 40 241 16.5.503 121,160 57,136 40 253 4.29.347 i97> 38 — — — 40 277 4.10069 199, 26 — — — 40 283 2.11.1831 — 141,101 — 40 289 32.1259 17,200 33^40 — — 40 343 2.23.877 — — — — 40 351 2.3.25.269 — — 26,115319, 47 40 357 4.9.19.59 129,154 37,114 74, 76 40 361 8.5.1009 19,200 81,130 — — 40 387 2-3-53- I 27 — 5,14! 188, 41 311, 49 40 423 2.3.6737 — — 46,113 293, 53 40 427 2. 17. 29. 41 — 147, 97 — — 40 429 4.9.1123 35>i98 — 127, 90 254, 60 40 433 16.7. 19. 19 167,112 201, 4 — — 40 459 2. 3. 11. 613 101,123 28,115 373, 29 QUADRATIC PARTITIONS. 107 p p-l a b c d A B L M 40 47l' 2.3.5.19.71 — — 86,105 172, 70 40 483 2.9.13.173 — 199, 21 184, 47 43, 77 40 487 2.31.653 — — — — 40 493 4.53-i9i 163,118 — — — 40 499 2.20249 — 201, 7 — — 40 507 2.3-43-J57 — 85,129 200, 13 161, 71 40 519! 2.9.2251 -— — i94, 3 1 101, 75 40 529 16.17. 149 23,200 201, 8 — — 40 531 2-3-5-7- T 93 — 19 1 , 45 116, 95 401, 7 40 543 2.3.29.233 — — 70,109 397, 1 3 40 559! 2.7.2897 — — — — 40 577| 128.317 191, 64 177, 68 — — 40 583 2.103.197 — — — — 40 591 2.9.5.11.41 — — i54, 75 308, 50 40 597 4.3.17.199 201, 14 — 83,106 235, 6 3 40 609 32.27.47 105,172 197, 3° 103,100 403, 1 40 627 2.9.37.61 — H5, 99 148, 79 385, 23 40 637 4-10159 139,146 — — — 40 639 2-3-I3-5 21 — — 106, 99 212, 66 40 693 4-3-339 1 87,182 — 109, 98 185, 69 40 697 8.5087 149,136 i35> 106 — — 40 699 2.9.7.17. 19 — 181, 63 32,115 3 J 3, 49 40 709 4.10177 95^78 — — — 40 739 2.20369 — 201, 13 — — 40 751 2. 125. 163 — — — — 40 759 2.3.6793 — — 178, 55 343, 4i 40 763 2.89.229 — *95, 37 — — 40 771 2.27.5. 151 — 127,111 112, 97 403, 5 40 787 2.20393 — 57,137 — — 40 801 3 2 .3- 2 5- I 7 201, 20 187, 54 199, 20 i39, 73 40 813 4.3.19.179 3,202 — 19*1 38 305, 5 1 40 819 2.3.6803 — 137,105 88,105 176, 70 40 823 2.20411 — — — — 40 829 4-59-173 5,202 — — — 40 841 8.5.1021 29,200 129,110 — 40 847 2.13.1571 — — — — 40 849 16.3.23.37 193, 60 157, 9 C 169, 64 361, 35 40 853 4.7.1459 7,202 — — — 40 867 2.3.49.139 — 103,123 200, 17 251, 61 40 87S 2.27.757 — — 202, 5 187, 69 108 QUADRATIC PARTITIONS. p p-l a b c d A B L M 40 883 2.20441 81,131 40 897 64.9.71 i99> 36 53,i38 23,116371, 31 40 903 2.3.17.401 — — 194, 33^388, 22 40 927 2-3-I9-359 — — 182, 51364, 34 40 933 4.27.379 i77, 98 — 85,106403, 7 40 939 2.3.6823 — 67,135 196, 29109, 75 40 949 4-29-353 185, 82 — — 1 — 40 961 8192.5 31,200 63,136 — — 40 973 4.10243 13,202 — — — 40 993 32.3.7.61 113,168 i75, 72 25,116323, 47 41011 2.3.5-1367 — 167, 81 52,n 3 i 287, 55 41017 8.3.1709 5M96 i33,i°8 125, 92401, 11 41023 2.9-43-53 — — 166, 67367, 33 41 039 2. 17. 17. 71 — — — — 41047 2.3.6841 — — 202, 9 404, 6 41051 2.25.821 — 99,125 — — 41057 32.1283 119,164 27,142 — — 41077 4.9.7.163 201, 26 — 157, 74 65, 77 41081 8-5-13-79 85,184 153, 94 — — 41113 8.9.571 197, 48 55,138 59,H2 277, 57 41117 4-i9-54i 59,194 — — — 41131 2-9-5-457 — 37,Mi 8,117 16, 78 41141 4.5. 121. 17 71,190 — — — 41 143 2.3.6857 — 190, 41 67, 77 41149 4.81.127 165,118 — 121, 94 403, 9 41161 8.3-5-343 i95, 56 97,126 197, 28 113, 75 41177 8.5H7 101,176 183, 62 — — 41179 2.3.6863 i73, 75 164, 69 328, 46 41183 2-59-349 — — — 41189 4.7.1471 145,142 — — — 41201 16.25.103 199, 40 201, 20 — — 41203 2.27.7.109 89,129 136, 87 272, 58 41213 4.10303 203, 2 — — — 41221 4.9.5.229 111,170 — 203, 2 209, 67 41227 2.3.6871 — 203, 3 128, 91 145, 73 41231 2.5.7. 19.31 — — — 41233 16.3.859 183, 88 *$h 96 79,108 158, 72 41243 2.17.1213 5M39 — — 41257 8.27. 191 179, 96 143,102 203, 4 191, 69 41 263 2.3.13.23.23 1 — 14,117 28, 78 QUADRATIC PARTITIONS. 109 p p-l a be d A B L M 41269 4.3.19.181 1 37,i5 c — 163, 70 373, 3i 41281 64.3-5-43 185, 84 203, 6,191, 40 7i, 77 41299 2.3.6883 — 193, 45 J 96, 3 1 289, 55 41 333 4.10333 23,202 — — — 41341 4-3-5- z 3<53 171,110 71,110 401, 13 41 351 2.25.827 — — — — 41357 4.49.211 61,194 — — 41381 4.5.2069 191, 70 — — 41387 2.20693 — 195, 4i — — 41389 4-3-3449 195. 58 — 49,114 98, 76 41399 2.7.2957 — — — — 41411 2.5.41. 101 — 177, 7i — 41413 4.3.7.17.29 47,198 IOI,I02i202, 68 41443 2.3.6907 — 41,141 56,ii3395, 19 41 453 4.43.241 163,122 — — 41467 2.3.6911 — 187, 57 20,117 4°, 78 41479 2.3.31.223 — — 202, 15404, 10 41491 2.9.5.461 — 71,135 172, 63344, 42 41507 2.20753 — 63,i37 — 41513 8.5189 i97, 52 141,104 — — 41519 2.20759 — — — — 41521 I6.3.5-I73 39,200 7,i44 127, 92 149, 73 41539 2.3.7.23.43 — 119,117 92,105 184, 70 41543! 2.20771 — — — — 41549 4.13.17.47 157,130 ~~ — — 41579 2.20789 — 123,115 — — 41593 8.3.1733 173,108 11,144 35,n6 383, 27 41 597j 4.10399 181, 94 — — 41603 2.11.31.61 — 111,121 — — 41609 8.7.743 203, 20 147,100 — — 41611 2.3-5-19-73 — 43, x 4i 44,n5 301, 53 41617; 16.9.17.17 1,204 125,114 i43, 84 286, 56 41 621, 4.5.2081 185, 86 — — — • 41627 1 2.13.1601 — . 27,H3 — — [41 641 8.3.5.347 5,204 i3,M4 203, 13 406, 8 1 41647j 2.3.11.631 — — 190, 43 319, 49 j 41 651 2.25.49.17 — 201, 25 — — i41659| 2.3.53.131 — 203, 15 184, 51 368, 34 41669 ; 4. 1 1.947 113,170. — — 41 681; 16.5. 521 4i,2oo| 183, 64 — 110 QUADRATIC PARTITIONS. p p-l a b c d A B L M 41687 2. 19.1097 1 — — — 41719 2.3.17.409 — — i34, 89! 401, 15 41729 256.163 127,160 129,112 — — 41737 8-3-37-47 11,204 83.132 37,ii6' 3ii, 5i 41759 2.20879 — — - 1 41761 32.9.5.29 145^44 17.144 167, 68 ! 37.1, 33 41771 2.5.4177 — 189, 55 — — 41777 16.7.373 89,184! 105,124 — — 41801 8.25. 11. 19 149,140 5M4° — — 41809 16.3.13.67 97,180 61,138 119, 96 238, 64 41813 4-10453 167,118 — — — 41843 2.20921 — i59. 9i — — 41849 8.5231 43,200 39.M2 — — 41851 2.27.25.31 — 197, 39 28,117 56, 78 41863 2.3.6977 — — 70,111 140, 74 41879 2.20939 — — — — 41887 2.9.13.179 — — 202, 19 259, 6l 41893 4-3-349 1 33,202 — 11,118 343. 43 41897 8-5237 59.196 195. 44 — — 41903 2.7.41.73 — — — — 41911 2.3.5.11.127 — — 94,io5 188, 70 41927 2.20963 — — — — 41 941 4.9.5.233 I35.I54 — 13,118 367, 35 41 947 2.3.6991 — 157. 93 112, 99 224, 66 41 953' 32.3.19.23 183, 92 101,126 199, 28 283, 57 41957;4.i7.6i7 19 1 , 74 — — 41959, 2.81.7.37 — — 122, 95 407. 9 41 969 16.43.61 185, 88 201, 28 — — 41981 4.5.2099 155^34 — — — 41 983; 2.3.6997 — |i46, 83 395. 21 41999 2. 1 1. 23.83 — — — 42 013 4-27.389 53,198 55,U4 no, 76 42 017 32. 13.101 169,116 165, 86 — — 42 019 1 2.3.47.149 — 121,117 164, 71 377, 3i 42 023 2.21011 — — — — 42 042 2.3.49.11.13 205, 2 80,109 247. 63 42 061 ! 4-3-5-7 01 205, 6 — I7,n2 337. 45 42 071 - 2.5.7.601 — — — 42 07^ ^| 8-3-1753 I57.I32 85,i3 2 205, a r;2l7, 67 42 08c * 2.53.397 — 20I, 2C ) — i ~ QUADRATIC PARTITIONS. Ill A B L M 42 089 8.5261 42iOlU.25.421 42131 2.5.11.383 42 139; 2.9.2341 42 157 4.9. 1 17 1 42 169 8.3.7.251 42 179 2.21089 42 181 4.3.5-I9.37 42187 2.3.79.89 42 193 16.9.293 42197 4.7.11-137 42 209 32.1319 42 221 4.5.2111 42223)2.3.31.227 42 227 2.43.491 42 239 2.49.431 42 2571 16.19.139 42 281 8.5.7.151 42 283 2.729.29 42 293 4-97.109 42 299 42 307 42 323 42 331 42 337 42 349 42 359 42 373 42 379 42 391 42 397 42 403 42 407 42 409 42 433 42 437 42 443 42 451 42 457 42 461 2.21149 2. 3. 11. 641 2.7.3023 2.3-5.17.83 32.27.49 4.3.3529 2.21179 4.9.11.107 2.3.7.1009 2.27.5.157 4-3-3533 2.3.37.191 2.7.13.233 8.9.19.31 64.3.13.17 4.103.103 2.21221 2.3.25.283 8.3.29.61 4.5. 11. 193 111,122 7, 79 «, 79 13, 79 205, 5 i99, 5° 9, J 45i — 1109,123176, 61 109,174 — 175, 62 205, 12 187, 60 181, 56 — 129,113: — ! I 59> I 3° — 203, 18406, 12 — 205, 9200, 271400, 18 73,192199, 36145, 84I290, 56 121,1661 — — — I 47,200159, 92! — I205, 14I — — 34,ii7| 68, 78 153, 97! — — 191, 76 205, 16 103,178 195, 46 177, 74 181, 69 184, 53 — 69,137 95, I2 9 201, 31 201, 44 I33,!! 1 197, 42 205, 18 — 127,162 — — 77,i35 194, 69 *5*. 99 197, 60 i93, 72 179, 72 3!, x 44 1,206 — 29,204 5,206 195, 47 i93, 5 1 155, 96 140, 87 128, 93 185, 52 161, 74 149, 82 52,115 202, 23 25,118 64,113 25, 79 280, 58 256, 62 29, 79 3*3, 29 97, 77 397, 21 i33, 75 379, 3i 275, 59 203, 20263, 61 169, 68 35, 79 124, 95 205, 12 161, 73 410, 8 112 QUADRATIC PARTITIONS. V p-i a b c d A B L M 42 463* 2.9.7.337 — — 206, 3 412, 2 42 467 2. 1 7. 1 249 — 183, 67 — — 42 473 8.5309 173,112; 81,134 — 42 487 2.3.73.97 — — 2,119 359, 39 42 491 2.5.7.607 21,145 — 42 499 2.27.787 — 143.105 4,119 353, 4i 42 509 4.10627 205, 22 — — — 42 533 4-343-3 1 97,182 — 42 557 4.10639 11,206 — — 42 569 8.I7-3I3 85,188 99,128 42 571 2.9.5.11.43 53^41 148, 83101, 77 42 577 16.3.887 31,204 67,138 47>n6»395, 23 42 589 4-9-7I3I3 117,170' — 167, 70; 43, 79 42 611 2.5.4261 — | 63,139 — — 42 641 16.5.13.41 65,196 3> J 46 ! 42 643 2.9.23.103 — 199, 39 104,103 205, 69 42 649 8.3.1777 195, 68 139,108 101,104 413, 1 42 667 2.3-I3-547 — 203, 27 40,117 80, 78 42 677 4.47.227 7 I , I 94 — — — 42 683 2.21341 — 189, 59 — — 42 689 64.23.29 185, 92 171, 82 — — 42 697 8-9-593 171,116 35, r 44 197, 36 394, 24 42 701 4.25.7.61 205, 26 — — — 42 703 2 .3."i 1.647 — — 110,101 4i3, 3 42 709 4-3-3559 105,178 — 61,114 122, 76 42 719 2-i3-3 I -53 — — — — 42 727 2.3.7121 — — 190, 47 49, 79 42 737 16.2671 i99> 5 6 183, 68 — — 42 743 2.7.43.71 — — — 42 751 2.9.125. 19 — — 158, 77 389, 27 42 767 2.21383 — — — — 42 773 4.i7-!7-37 167,122 — — — 42 787 2.9.2377 — 55^41 152, 81 3°4, 54 42 793 8.3.1783 77,192 i75, 78 205, 16 253, 63 42 797 4.13.823 1 19,206 — — — 42 821 4.5.2141 161,130 — — — 42 829 4-3-43-83 ; 45> 2 ° 2 — 191, 46 53, 79 42 839 2.21419 — — — — 42 841 8.9.5.7.17 1 35,204 37,i44 179, 6c 358, 40 42 853 4-3-3571 207, 2 181, 58 355, 4i QUADRATIC PARTITIONS. 113 p p- 1 a b c d A B L M 42 859 2.9.2381 — *97, 45 116, 99 232, 66 42 863 2.29.739 — — — — 42 899 2.89.241 — 207, 5 — — 42 901 4.3. 25. 11. 13 201, 50 — i57, 78 314, 52 42 923 2.11.1951 — 45,*43 — — 42 929 16.2683 145,148 5M42 — — 42 937 8.3.1789 149,144 185, 66 203, 24 406, 16 42 943 2. 3. 17. 421 — — 206, 13 167, 73 42 953 8.7.13.59 163,128 159, 94 — — 42 961 16.3.5.179 169,120 119,120 73, 112 409, 13 42 967 2.9.7.11.31 — — 22,119 335, 47 42 979 2.3.13.19.29 — !9i> 57 196, 39 392, 26 42 989 4-H-977 83,190 — — — 43 003j 2.9.2389 — 125,117 44,n7 88, 78 43 013| 4.10753 47,202 — — — 43 019| 2. 137. 157 — \*7h 8 3 — — 43 037; 4.7.29.53 I 39 ) I 54! — — — 43 049 8.5381 205, 32207, 10 — — 43 051; 2.3.25.7.41 — 173, 81 172, 67 373, 35 43 063 2.3.7177 — — 106,103 4i5> 1 43 0671 2.61.353 — 165, 89 — — 43 093 4-81.7.19 183, 98 109,102 218, 68 43103, 2.23.937 — — — — 43 117! 4.3.3593 189, 86\ — '• 97,106 4i5, 3 43 133 4.41.263 107,178! — — 43 151 2.25.863 — — — — 43 159 2.3.7193 — 26,119 383, 3i 43177 8.3.7.257 69,196 205, 24 53,116 401, 21 43189 4.3-59.61 135^58 — 83,110 4i3, 9 43 201; 64.27.25 199, 60107,126 1,120 2, 80 43 207 2.3.19.379 7°>H3 269, 61 43 223, 2.2 161 1 — — — — 43 237! 4.9. 1 20T T 59>*34 : — 203, 26 281, 59 43261:4.3.5.7.103 75,194 — 169, 70 379, 33 43 271j 2.5.4327 — — — — 43 283 2. 17.19. 67 — 105,1271 — 43 29l| 2.9.5.13.37 — i79, 75208, 3416, 2 43 313; 16.2707 7,208135,112 — 43 319 2. 11. n. 179 43 321 8.3.5.19.19 205, 36 43, J 44 11,120 22, 80 114 QUADRATIC PARTITIONS. p-1 d A B | L M 43 331 2.5.7.619 43 391 2.5.4339 43 397 4.19.57* 43 399 2.9.241 1 43 403 2. 2 1 701 43 411 2.3.5.1447 43 427 2.21713 43 441 16.3.5. 181 43 451 2. 25. 11. 79 43 457 64.7.97 43 481 8.5.1087 43 487 ( 2. 17. 1279 43 499 2.7.13.239 43 517 4. 1 1. 23.43 43 541; 4.5.7.31 1 43 543 2.9.41.59 43 5734.3.3631 43 577 8.13.419 43 579 2.81.269 43 591 2.3.5.1453 43 597 4-9.7. !73 43 607 2.21803 43 609 8.3.23.79 43 613 4.10903 43 6271 2.3.11.661 43 633 16.27. 101 43 649 1 28. 1 1. 3 1 43 651 2.9.25.97 43 661; 4.5.37.59 43 669! 4.9. 12 13 43 691 2.5.17.257 43 711 2.3.5.31.47 43 717| 4.3.3643 43 721 8.5.1093 43 753 8.3.1823 43 759 2.9.11.13.1 43 777 256.9.19 43 781 4.5.1 1. 199 43 783 2.3.7297 43 787 2.21893 iS9> 95 167, 72 334, 48 31,206 154, 81308, 54 69,i39 [37,111208, 7229, 67 207, 17 185, 96 121,120 — 123,119 71,196 117,122 , 59,200 87,134 — 5M43 149,146 — 121,170 — 153,142 — 181,104 57,142 i9,!47 i4i,i54 — 166, 73 385, 3i 179, 62365, 39 148, 85403, 21 178, 63356, 42 193, 46 33 1 , 49 165,128151,102197, 40 77, 79 53,202 — |i55, 99208, 11 175, 73 207, 28109,126185, 56353, 43 193, 80207, 20 — |i99, 45ii76, 65371, 37 35,2o6, 87,190 209, 6 ; 61,200 I 83,192 1 59^36 209, 10 13 1 , 94I5 1 , 75 171, 85 — I — 194, 45 388, 30 — '187, 54374, 36 33,M6 — 209, 6205, 24410, 16 — 206, 21 412, 14 143,108127, 96254, 64 165, 9V 74,113413, 13 QUADRATIC PARTITIONS. 115 p j,-l a b c d | A B L M 43 789 ! 4.341.89 205, 42 — . 209, 6 418, 4 43793116.7.17.23 t 23,208 105,128 — — 43 801 8.3.25-73 195. 76 203, 36 173, 68 377, 35 43 853 4.I9.577 i73>n8 — — — 43 867 2.9.2437 — 163, 93! 172, 69 344, 46 43 889 16. 13. 211 25,208 9,148 — — 43 891 2.3.5.7. 11. 19 — 103,129 104,105 208, 70 43 913 8.11.499 203, 52 189, 64 — — 43 933 4.3.7.5 2 3 133,162 — 199, 38 85, 79 43 943 2. 127. 173 — — — — 43 951 2.3.25.293 — — 98,107 4i9, 3 43 961 8.5.7.157 205, 44 69,140 — — 43 963, 2.3.17.431 — 139,111 196, 43 325, 5 1 43 969 64.3.229 63,200 209, 12 I5 1 , 84 3 02 , 56 43 973 4.10993 193, 82 — — 43 987 2.3.7331 — 65,141 8,121 355, 43 43 991 2.5-53.83 — — — 43 997 4.17.647 181,106 — — — 44 017 16.3.7. 131 49,204 77,138 95,108 190, 72 44 021 4.5-3i.7i 89,190 — — — 44 027 2.22013 — 93,133 — 44 029 4.9.1223 123,170 71,114 142, 76 44 041 8.3.5.367 75>i96 173, 84 29,120 58, 80 44 053 4.3.367 1 57,202 — 205, 26 127, 77 44059 2.3.7.1049 — 29,147 116,101 419, 5 44 071 2.3.5.13.113 — — 202, 33 404, 2 2 44 087 2.7.47.67 44 089 8.3.11.167 85,192 167, 90 61,116 287, 59 44101 4.9.25.49 1,210 — 197, 42 394, 28 44111 2. 5. n. 401 — — — — 44119 2.27.19.43 - — 14,121 349, 45 44123 2. 13.1697 99,i3i — — 44129 32.7.197 145^52 ;I77, 80 — — 44131 2.3.5.1471 — 1209, 15 208, 17 :i57, 75 44159 2.22079 — — — — 44171 2.5.7.631 — 189, 65 — 44179 2.3.37.I99 — 3M4J 16,121 379, 35 44189 4.11047 155^42 — 44 201 8.25. 13.17 115^7^ 207, 26 44 203 2.3-53.I39 ! — 205, 32 > 56,n/ 112, 78 116 QUADRATIC PARTITIONS. V p-1 a b c d A B ; L M 44 207 2.23.31. 31 — — — 44 221 4.3.5.11.67 11,210 — 89,110419, 7 44 249 8.5531 157,140 21,148 44 257 32.3.461 209, 24 97,i32 145, 88409, 19 44 263 2.9.2459 — — 194, 471335, 49 44 267 2.22133 — 75,i39 — — 44 269 4-3-7-I7-3 1 13,210 209, 14 251, 65 44 273 16.2767 167,128201, 44 — — 44 279 2.i3- I 3- I 3 I — — — 44 281 8.27.5.41 109,180 53,H4 203, 32 299, 57 44 293 4-3-369 1 207, 38 181, 62 5, 81 44 351 2.25.887 — — — — 44 357 4.I3-853 209, 26 — — 44 371 2.9.5.17.29 — 89,135 112,103 421, 3 44 381 4-5-7-3I7 91,190 — — — 44 383 2.3.13.569 — — 154, 83 95, 79 44 389 4.81.137 17,210 — 149, 86 407, 21 44 417 128.347 161,136 207, 28 — — 44 449 32-3-463 207, 40 193, 60 209, 16 161, 75 44 453 4.11113 113,178 — — — 44 483 2.23.967 — 9, J 49 — — 44 491 2.3-5- I 483 — 187, 69196, 45 392, 30 44 497 16.27.103 201, 64 55,*44 175, 68 29, 81 44 501 4.125.89 199, 70 — — — 44 507 2. 7. 11. 17. 17 — 147,107 — — 44 519 2.22259 — — — — 44 531 2.5.61.73 — 207, 29 — 44 533 4.9.1237 73,198 — 211, 2 205, 71 44 537 8.19.293 211, 4 27,148 — 44 543 2.22271 — — 44 549 4.7.37.43 i75, JI 8 — — — 44 563 2.3.7. 1061 — 209, 21 200, 39 400, 26 44 579 2.31. 719 — 111,127 — 44 587 2.9.2477 — 37,i47 208, 21 416, 14 44 617 8.3.11. 13.13 171,124 205, 36 197, 44 329, 5 1 44 621 45.23.97 211, 10 — — 44 623 2.9.37.67 — — 206, 27 412, 18 44 633 8.7.797 37,208 201, 46 — — 44 641 32.9.5-31 55,204 197, 54| 121,100 421, 7 44 647 1 2.3.7.1063 — — ! 158, 81 316, 54 QUADRATIC PARTITIONS. 117 V P -l a b c d A B L M 44 651 2.25.19.47 — 5^145 — — 44 657 16.2791 79,196 45^46 — 44 683 2.3.11.677 — 211, 9 164, 77395, 29 44 687 2.22343 — — — 44 699 2.22349 — 189, 67 — — 44 701 4.3.25.149 149,150 7,122359, 43 44711 2.5.17.263 — — — 1 — 44 729 8.5591 205, 52 171, 88 — 44 741 4-5- 22 37 145^54 i j ' ___ 44 753 16.2797 97,188 195, 58 1 1 44 771 2.5. 11. 11.37 — 207, 31 — — 44 773 4.3.7.13.41 63,202 11,122 377, 37 44 777 8.29.193 211, 16 177, 82 — — 44 789 4.11197 167,130 — — — 44 797 4-3-3733 101,186 — 55,n8 409, 21 44 809 8.3.1867 203, 60 211, 12 131, 96 262, 64 44 819 2.22409 — 201, 47 — — 44 839 2-9-47-53 — — 194, 49 47, 81 44 843 2.7.3203 — 21,149 — 44 851 2.3.25.13.23 — 151,105:208, 23 J39, 77 44 867 2.22433 — 63 5 H3 — — 44 879 2.19.1181 — — — — 44 887 2.3.7481 — — 170, 73 49, 81 44 893 4.9.29.43 197, 73 — 199, 42 398, 28 44 909 4.103.109 115,178 — — — 44 917 4.3.19.197 121,174 — 77,H4 154, 76 44 927 2.7.3209 — — — — 44 939 2.22469 — 117,125 — 44 953 8.3.1873 3,212 59,144 211, 12 422, 8 44 959 2.3.59.127 — — 206, 29 293, 59 44 963 2.22481 — 129,119 — 44 971 2.3.5.1499 — 211, 15 212, 3 424, 2 44 983 2.27.49.17 — — 5°, 1 19 407, 23 44 987 2.83.271 — i95, 59 — . — 45 007 2 -3-i3-577 — 142, 91 4i5, l 1 45 013 4-3.121.31 137,162 — 19,122 347, 47 45 053 4.7.1609 203, 62 _ — — 45 061 45 077 4-3-5-751 3I,2IOJ — 187, 58 361, 43 4.59.191 *99, 74 — — 45 083, 2.22541 — 171, 89 — - 1 118 QUADRATIC PARTITIONS. bed 45 119 2. 17. 1327 45 121 64.3.5.47 45 127 2.9.23.109 45131 45 137 45139 45 161 45179 45 181 45 19.1 45 197 45 233 45 247 45 259 45 263 45 281 45 289 45 293 45 307 45 317 2.5-45!3 16.7. 13.31 2 -3-75 2 3 8.5.1129 2.49.461 4.9.5.251 2.5.4519 4. 1 1 299 16.11.257 2-3-7541 2.3-!9-397 2.7.53.61 32.5-283 8.9.17.37 4.13.13.67 2.27.839 4.11329 45 319 2.3.7.13.83 45 329 16.2833 45 337 8.3.1889 45 341 4.5.2267 45 343 2.9. 1 1.229 45 361 45 377 45 389 45 403 45 413 16.81. 5.7 64.709 4.7.1621 2-3-7-23-47 4-II353 35, l6 4 11,15° 119,176 27,149 i35> 116 A B L M 161, 80 i3°> 97 208, 25 401, 27 421, 11 283, 61 209, 27 205, 56^07, 34 — i 99,1331 165,134 — I 23,1221389, 33 |2II, 26 17,212 51^46 j 98,109229, 69 203, 45>7°> 69352, 46 45 427 2.3.67. 1 13 45 433| 8.9.631 45 439 2.3.7573 45 481, 8.3.5.379 45 491j 2.5.4549 45 497j8.i2i.47 45 503! 2.22751 45 523 2.81.281 45 533 4. 1 1 383 45 541 4.9.5.11.23 209, 40159,100 208, 45| 17,1501211, 16259, 65 67,202j — — 197, 57212, 11 245, 67 19 1 , 94| — — 206, 31 113, 79 73,200 39,148 — 61,204187, 72133, 9°266, 64 155^46, — — I — — 166, 77 65, 81 145,156' 19,150193, 52349, 47 i99, 76213, 2 — 205, 58 — — 211, 21! 4,123 8, 82 143,158! — — 47,147 92,11 r T84, 74 213, 8199, 54149, 881115, 79 — 194, 51 3S8, 34 [141,160209, 30173, 72346, 48 33,*49 — 179,116213, 8 — 197, 82 129,170 161, 99 40,121:403, 27 — 203, 38317, 55 QUADRATIC PARTITIONS. 119 p p-l a b c d A B L M 45 553 16.3.13-73 207, 52205, 42 89,112247, 67 45 557 4.7.1627 89,194 — — 45 569 512.89 25,212 213, 10 45 587 2.23.991 — 207, 37 — — 45 589 4.3.29.131 183,110 — [109,106427, 1 45 599 2.7-3 2 57 — — — — 45 613 4.9.7.181 163,1381 3M22335, 51 45 631 2.27. 5. 13.13 158, 83407, 25 45 641 8.5.7.163 85.196 93,136 — 45 659 2.37.617 — 69,143 — — 45 667 2.9-43-59 — I45, 111 148, 89 119, 79 45 673 8.3.11.173 27,212 211, 24 115,104,197, 73 45 677 4.19. 601 211, 34 — 45 691 2.3-5- I 523 — 77,i4i 68,117136, 78 45 697 128.3.7.17 191, 96 65,144 73, II 6275, 63 45 707 2.22853 — 213, 13 — — 45 737 8.5717 109,184 207, 38 — — 45 751 2.3.125. 61 — — 118,103427, 5 45 757 4.9.31.41 181,114 — 1185, 62371, 41 45 763 2.3.29.263 — i75, 87 184, 63368, 42 45 767 2.49.467 — — — — 45 779 2 47.487 — '77, 85 — — 45 817 8.3.23.83 211, 36 203, 48157, 84314, 56 45 821 4.5.29.79 5,214 — — — 45 823 2.3.7.1091 — 214, 3428, 2 45 827 2. 11. 2083 — 15,151 — — 45 833 8.17.337 203, 68 45,!48; — — 45 841 16.3.5.191 65,204 2 9, I 5 OI 43, 92419, J 7 45 853 4.3.3821 213, 22 — 121,1021242, 68 45 863 2.23.997 — — — 45 869 4.1x467 205, 62 — — — 45 887 2.22943 — — — — 45 893; 4.7. 11. 149 113,182 — — — 45 943 2.3.13.19.31 — 214, 7235, 69 45 949 4-3-7-547 43,210 |!99, 46337, 5 1 45 953 128.359 103,188 75,!42 — 45 959 2.1 1.2089 — — — — 45 971| 2.5.4597 — 183, 79i — 45 979 2.3.79.97 — 211, 27 124,101 i79, 75 45 989 4. 1 1497 i45>!58 — — 120 QUADRATIC PARTITIONS. p P -l a b c d A B L M 46 021 4.3-5- r 3-59 15,214 — 37,122 329, 53 46 027 2-9-2557 — 53,147 212, 19 155, 77 46 049 32.1439 143,160207, 40 — — 46 051 2.3.25.307 — xi3t*»9 88,113 251, 67 46 061| 4.5.49.47 131,170 — — 46 073 8.13.443 53,2o8|i35,n8 — — 46091 2.5.11.419 — J2i3> 19 1 46 093 4.3.23.167 83,198' 161, 82 85, 81 46 099 2.9.13.197 — i99> 57 176, 71389, 35 46 103 2.7.37.89 — — — — 46 133 4.19.607 73,202 — — — 46141 4-3-5-769 171,130 167, 78 334, 52 46147 2.3.7691 — i37 5 n7 208, 31 301, 59 46 153 8.9.641 213, 28179, 84 5, I2 4 3 6 7, 43 46171 2.243.5.19 — 1*63, 99 28,123 56, 82 46181 4.5.2309 209, 5°; — — — 46183 2.3-43-!79 — — 134, 97 i57, 77 46 187 2.7.3299 i 93>!37 — — 46199 2.23099 — — — 46 219 2.3.7703 — 187, 75 i9 6 > 5 1 39 2 , 34 46 229 4.7.13.127 215, 2 — — — 46 237l 4 -3-3853 21,214 — 215, 2 221, 71 46 261! 4.9-5.257 215, 6 — 67,118 421, 17 46 27l| 2.5.7.661 — — — — 46273:64.3.241 97,192 209, 36215, 4 203, 73 46 279 1 2.27.857 — — 166, 79 403, 29 46 301' 4 25.463 101,190 — 46 307j2.i3.i3.i37 — i53> IQ 7 — — 46 309| 4.3.17.227 47,210 — 197, 50 347, 49 46 327 2.3.7.1103 — — 62,119 419, 19 46 337 256.181 89,196 213, 22 46 349 4.11587 115,182 — — — 46 351 2.9.25.103 — — 202, 43 33i, 53 46 381 4-3-5-773 205, 66 209, 30418, 20 46 399 2.3.11. 19.37 — — 82,115427, 11 46 411 2.3-5-7. I3-I7 ■ — 203 51 32,123; 64, 82 46 439 2.7.31. 107 — — 46 441 8.27.5.43 179,120 143,114107,108214, 72 46 447 2.3.7741 — — 110,107431, 1 46 451 2.25.929 — 201, 55 — — QUADRATIC PARTITIONS. 121 p j>-1 a b C d A B L M 46 457 8.5807 211, 44 117,128 — — 46 471 2-3-5-!549 — 214, 15 428, 10 46 477 4.9.1291 109,186 113,106 205, 73 46 489 8.3.13.149 195. 92 133,120 19,124 39i, 35 46 499 2.67.347 — i59> 10 3 — — 46 507 2.3-23-337 — 115,129 188, 61 5, 83 46 511 2.5.4651 — — — — 46 523 2-7-3323 75^43 — — 46 549 4.27.431 215, 18 — 211, 26 i33, 79 46 559 2.23279 — — — — 46 567 2.9.13.199 — — 98,111 196, 74 46 573 4.3.3881 147,158 — 191, 58 17, ^3 46 589 4.19.613 133^7° — — — 46 591 2-3-5- I 553 — — 182, 67 19, 83 46 601 8.25.233 125,176 63,146 — — 46 619 2.11. 13.163 — 213, 25 — — 46 633 8.3.29.67 187,108 205, 48 181, 68 23, 83 46 639 2.9.2591 — — 158, 85 97, 81 46 643 2.23321 — 111,131 — — 46 649 8-343-17 205, 68 21,152 — — 46 663 2.3.7.11.101 — — 214, 17 163, 77 46 679 2.23339 — — — — 46 681 8.3-5-389 5,216 41,15° 59, I2 o 118, 80 46 687 2.3.31. 251 — — 170, 77 401, 3 1 46 691 2.5.7.23.29 — 33,15* — — 46 703 2. 19.1229 — — — 46 723 2.3- r 3-599 — 209, 39 i3 6 > 97 427, 13 46 727 I 2.61.383 — — — — 46 747 I2.9-49-53 — i97, 63 148, 91 421, 19 46 751 j 2. 125. 11. 17 — — — 46 757 14. 1 1 689 3^214 — — — 46 769 16.37.79 185,112 87,140 — — 46 77] 2.3-5- I 559 — i93, 6 9 92,113 43 1 , 7 46 807 2.3.29.269 — — 178, 71 35, 83 46 811 2-5-3I-I5 1 — 69,H5 — — 46 817 I32. 7. 11. 19 209, 56 177, 88 — 46 819 2. 81. 17. 17 — i,i53 212, 25 i37, 79 46 829 j 4.23.509 ji73>i3c — — — 46 831 2.3-5-7-223 — — 38,123 76, 82 46 853 4-i3-i7-53 i93» 9 8 R ~ ! ~ 122 QUADRATIC PARTITIONS. p P -l a b c d A B L M 46 861 4.3.5. ii. 71 195, 94 47,122 413, 25 46 867 2.3.73.107 — 7,i53 ^52, 89 419, 21 46 877 4.11719 139,166 — — — 46 889 8.5861 83,200 81,142 — — 46 901 4.25.7.67 215, 26 — — 46 919 2.23459 — — — — 46 933 4-3-391 1 167,138 — 115,106 433, 3 46 957 4-3.7-I3-43 189,106 — 143, 94 139, 79 46 993 16.3. 11. 89 137,168 169, 96 215, 16 167, 77 46 997 4-31-379 199, 86 — — 47 017 8.9.653 19,216 I45,H4 203, 44 335, 53 47 041 64-3-5-49 121,180 203, 54 97,112 433, 5 47 051 2 25.941 — 213, 29 — 47 057 16.17.173 169,136 57,148 — — 47 059 2.3.11.23.31 — !03,i35 56,121 307, 59 47 087 2.13.1811 — — — — 47 093 ! 4.61. 193 217, 2 — — — 47111 2.5.7.673 — — — — 47 119 2-3-7853 — — 214, 21 428, 14 47 123 2.23561 — 39,15! — — 47 129 8-43-!37 155,152 201, 58 — — 47 137j 32-3-49 1 151,156 187, 78 217, 4 229, 71 47 143 2.243.97 — — 94,H3 245, 69 47 147 2. 11. 2143 — i47,n3 — — 47 149 4-3-3929 I57,i5 — 209, 34 107, 81 47 161j 8.9.5.131 181,120 217, 6 131,100 169, 77 47 189 4.47.251 217, 10 — — — 47 207 2.23603 — — — — 47 221 4.3-5.787 185,114 — 211, 30 422, 20 47 237: 4.49.241 161,146 — — — 47 251 2.27.125.7 — 217, 9 188, 63 376, 42 47 269 4.9.13.101 145,162 — 91,114 182, 76 47 279 2. 7. 11. 307 — — — — 47 287 2.9.37.71 — — 58,121 421, 21 47 293 4-3-7.563 203, 78 — 185, 66 37o, 44 47 297 64.739 191,104 33,152 — — 47 303 2.67.353 — — — — 47 309 4.11827 125,178 — — — 47 317 4-3-3943 39,214 — 205, 42 410, 28 47 339 1 • 1 2.23669 — 99,137 — — QUADRATIC PARTITIONS. 123 p j>-1 a be d A B 1 L M 47 351 2.25.947 _ 47 353 8-3-1973 173^32 i55> 108 35, I2 4 337, 53 47 363 2.7.17.199 — 201, 59 — — 47 381 4.5.23.103 215, 34 — — 47 387 2.19.29.43 123,127 — — 47 389 4-3-H-359 165,142 — 217, 10 247, 69 47 407 2.3.7901 — — 182, 69 364, 46 47 417 8.5927 179,124 213, 32 — — 47 419 2.3.7.1129 — i3!> 12 3 88,115 433, 9 47 431 2.9.5.17.31 — — 202, 47 61, 83 47 441 16.5.593 95^96 3,154 — — 47 459 2.61.389 — 81,143 — — 47 491 2.3-5.^583 — 167, 99 196, 55 361, 47 47 497 8.3.1979 29,216 97,138 37,124 409, 29 47 501 4.625.19 205, 74 — — — 47 507 2-23753 — i35> I2 i — — 47 513 8-5939 187,112 9,154 — — 47 521 32. 27. 5. 11 215, 36 197, 66 217, 12 434, 8 47 527 2.3.89.89 — — 218, 1 215, 73 47 533 4-3-17.233 3,218 — 145, 94 427, 17 47 543 2.11.2161 — — — — 47 563 2.3.7927 — 211, 39 164, 83 413, 27 47 569 16.3.991 87,200 137,120 209, 36 418, 24 47 581 4.3.5. 13.61 59,210 — 137, 98 43i, 13 47 591 2.5.4759 — — 47 599 2.3.7933 — — 218, 5 233, 7i 47 609 8.11.541 203, 80 i53,no — — 47 623 2-3-7937 — — 170, 79 67, 83 47 629 4.243.49 *95, 98 — 1,126 2, 84 47 639 2.23819 — — — — 47 653 4.3.11. 19.19 193,102 — 5,126 10, 84 47 657 8.7.23.37 211, 56 i5,!54 — — 47 659 2.3.13.13.47 — 29,i53 28,125 347, 5 1 47 681 64.5.149 185,116 213, 34 — 47 699 2.7.3407 — in,i33 — — 47 701 4-9-25.53 199, 90 — 77,118 277, 65 47 711 2.5- I 3-367 — — — 47 713j 32.3.7.71 177,128 79, J 44 199, 52 355, 49 47 717 4.79.151 191,106 — 47 737 8.27. 13.17 171,136 217, 18 163, 84 326, 56 124 QUADRATIC PARTITIONS. p ^-1 a b c d A B L M 47 741 4.5.7. 11. 31 I55>i54 — — 47 743 2.3.73.109 — — 110,109217, 73 47 777 3 2 - I 493 209, 64 63,148 — — 47 779 2.3.7963 — 3i 5 i53 104,111208, 74 47 791 2.81.5.59 ■ — 82,117 164, 78 47 797 4-3-7-5 6 9 201, 86 — 13,126 26, 84 47 807 2.11.41.53 — — — — 47 809 64.9.83 135^72 53,15° 41,124 33i, 55 47 819 2.23909 — 213, 35 — — 47 837 4-H959 101,194 — — — 47 843 2. 19. 1 259 — 201, 61 — — 47 857 16.3.997 79,204 205, 54 217, 16:265, 67 47 869 4-3.3989 2i3> 5° — 119,106199, 75 47 881 8.9.5.7.19 35>2i6 127,126157, g 421, 23 47 903 2-43-557 — — — — 47 911 2.3.5.I597 — — 98,113 437, 5 47 917 4-9-I33 1 179,126 — 17,126 34, 84 47 933 4.23.521 203, 82 — — — 47 939 2. 11. 2179 — 183, 85 — — 47 947 2. 3. 61. 131 — ^S3y^3 t 5^i 9 1 121, 81 47 951 2-25.7.137 — — — — 47 963 2.23981" — 219, 1 — — 47 969 32.1499 55>2I2 219, 2 — 47 977 8.3.1999 219, 4 157,108 43,* 24 4i5, 27 47 981 4.5.2399 109,190 — — — 48 017 16.3001 119,184 ioS,^ — — 48 023 2. 13.1847 — — — — 48 029 4.12007 85,202 — — — 48 049 16.3.7. 11. 13 I 75, 1 3 2 211, 42 193, 60 386, 40 48 073 8.3.2003 213, 52 115,132 125,104 437, 7 48 079 2.9.2671 — — i94, 59 37i, 45 48 091 2.3.5.7.229 — 187, 81 52,123 104, 82 48109 4.3.19.211 205, 78 r 161, 86 419, 25 48119 2.49.491 — — 48121 8.3.5.401 211, 60 139,120 203, 48 406, 32 48131 2.5.4813 ■ — 9,155 — — 48157 4-3-4013 219, 14 23,126 46, 84 48163 2.3-23.349 — 169, 99 196, 57 392, 3^ 48179 2.13. 17. 109 — i59,io7 — — 48 187j 2.9.2677 — 37,i53 112,109 439, 1 QUADRATIC PARTITIONS. 125 p ji-.l a be d A B L M 48193 64.3.251 57,212 149,114 I5 1 , 92125, 81 48197 4.12049 49,214 — — 48 221 45.2411 139,170 — — 48 238 2.89.271 — — — — 48 247 2.3.11.T7.43 — 182, 71395, 37 48 25S 2.9.7.383 — 7i>i47 76,119281, 65 48 271 2.3.5.1609 — — 118,107^03, 75 48 281 8.5.17.71 91,200 183, 86 48 299 2. 19.31. 41 — 219, 13 — — 48 311 2.5-4831 — — — 48 313 8.9. 11. 61 107,192 199, 66 181, 72362, 48 48 337 '6-3-I9-53 41,216 185, 84 47,124 325, 57 48 341 4.5.2417 215, 46 — — — 48 353 32. 15 11 137,172 219, 14 — — 48 371 2.5.7.691 — 63^49 — — 48 383 2. 17. 1423 — • — — — 48 397 4-3-37-IQ9 5^214 — 97,1*4 194, 76 48 407 2.24203 — — — — 48 409 8.3.2017 3,220 203, 60 211, 36 422, 24 48 413 4.49. 1 3. 1 9 197, 98 — — — 48 437 4. 1 2 109 199, 94 — — — 48 449 64-757 7,220 171, 98 — — 48 463 2.3.41. 197 — — 86,117 172, 78 48 473 8-73-83 163,148 219, 16 — — 48 479 2.24239 — — — 48 481 3 2 -3-5- IQI 9,220 59,15° 209, 40 89, 83 48 487 2.3.8081 — — 10,127 39i, 39 48 491 2 -5-i3-373 — 2i,i55 — 48 497 16.7.433 121,184 I53,H2 — 48 523 2.3.8087 — 205, 57 56,123 112, 82 48 527 2.19. 1277 — — — — 48 533 4.11.1103 217. 3^> — — — 48 539, 2.7.3467 — 219, 17 — — 48 541! 4.3.5.809 165,146 — 217, 22 283, 65 48 563| 2.24281 — IQ 5,i37 — — 48 571 2.3.5. 1619 — 211, 45 164, 85 9i, ^3 48 589j 4.3.4049 67,210 — 31,126 62, 84 48 593 16.3037 73,208 201, 64 — — 48 611 2.5.4861 — 81,145 — — 48 619 2 -9-37-73 — 163,105 212, 35 3!7, 59 126 QUADRATIC PARTITIONS. V p-l A B L M 48 623 2.7. 23.151 48 647 2. 13. 187 1 48 649 8.3.2027 48 661 4.3.5 811 48 673j 32.9.13.13 48 677! 4-43-283 48 679 2.3.7.1961 48 731 2.5. 1 1.443 48 733 4.3-31-131 48 751 2.3.625.13 48 757; 4.3.17.239 48 761! 8.5.23.53 48 767 2.37 659 48 779 2.29.29.29 48 781 4.9.5.271 48 787 48 799 48 809 48 817 48 821 48 823 48 847 48 857 48 859 48 869 48 871 48 883 48 889 48 907 48 947 48 953 48 973 48 989 48 991 49 003 49 009 49 019 49 031 49 033 49 037 93.200 105,194 i43' 168 79,206 213, 58 119,186 19,220 141,170 [91, 781 91,116257, 69 I 83,118271, 67 1,156145, 96290, 64 2-3-47-I73 2.9.2711 8.6101 16.27. 113 4.5.2441 2-3-79- io 3 2.3.7. 1163 8.31. 197 2.3.17.479 4.19.643 2.27.5. 181 2.3.8147 8.9.7.97 2.9.11. 13.19 2.24473 8. 29. 211 4-3-7-H-53 4-37-33 1 2.3-5-23-7I 2.3.8167 16.3.1021 2.24509 2.5-4903 8.27.227 4.13.23.41 197,100 199, 96 55,214 213, 4i 219, 2C 27,155 95,!4i 51,152 215, 36 214, 3 1 169, 82 58,123 163, 86 307, 61 4i5, 29 116, 82 95, 83 221, 4 113,190 75,208 165,104 221, 209, 51 217, 30 125,129 i53,n3 203, 881 39,154 173,138! i55,i58 193, 62 20,127 194, 61 217, 24 70,121 218, 21 196, 59 22,127 80,119 221, 4 220, 13 209, 42 7, 85 361, 49 11, 85 434, 16 433, 43 6 , 221, 153,160119,132 219, 23 117,188 19,156 221, 14I — 17 14 19, 85 403, 35 437, 13 209, 75 259, 6 9 418, 28 46, 140, 99 199, 56 25329, 57 280, 66 3i, 85 221, 8 245, 7 QUADRATIC PARTITIONS. 127 p p-l a b c d A B L M 49 043 2.7.31. 1 13 — 159,109 — 49 057i 32.3.7-73 49,216 i75» 96 167, 84 334, 56 49 069, 4.9-29.47 163,150 — 113,110443, 1 49 08l! 8.3.5.409 205, 84 187, 84 107,112229, 73 49103 2.24551 — — — — 49109 4.12277 185,122 — — — 49 117 4-3 4093 2i9> 34 — 217, 26139, 81 49121 32.5.307 175^36 207, 56 — — 49123 2.9.2729 — 199, 69 104,113 443, 3 49139 2. 79.311 — 33,155 — — 49 157 4.12289 209, 74 — — — 49169 16.7.439 65,212 189, 82 — — 49 171 2.3.5.11.149 — 97,141 28,127 409, 33 49177 8.9.683 189,116 197, 72 5,128 389, 4i 49193 8.11. 13.43 77,208 81,146 — — 49199 2.17. 1447 — — — — 49 201 16.3.25.41 135^76 23*156 7,128 377, 45 49 207 2.3.59.I39 — — 82,119 275, 67 49 211 2.5-7.19.37 — 219, 25 — — 49 223 2.24611 — — — — 49 253 4-7-I759 127,182 — — — 49 261 4.3.5.821 195,106 — i43, 98 437, 15 49 277 4.97.127 59>2i4 — — — 49 279 2.3.43.191 — — 98,115 247, 71 49 297 16.3.13.79 169,144 25,156 215, 32 311, 61 49 307 2.89.277 — 3,i57 — 49 331 2-5-4933 — 183, 89 — — 49 333 4.3.4111 7,222 — 125,106 193, 77 49 339 2.9.2741 — 179, 93 208, 45 416, 30 49 363 2 .3.i9.433 — 185, 87 160, 89 107, 83 49 367 2.24683 — — — — 49 369 8.3.121.17 187,120 169,102 '79, 76 49, 85 49 391 2.5.11.449 — — 49 393 16.9-343 217, 48 89,144 95, Ij6 443, 7 49 409 256.193 97,200 129,128 — — 49 411 2. 81. 5. 61 — 127,129 32,127 349, 53 49 417 8.3.29.71 221, 24 193. 78 155, 92 43i, 21 49 429 4.9.I373 73,210 — 221, 14 263, 69 49 433 8.37.167 67,212 75,i48 — — 49 451 2.25.23.43 — 123,131 — 128 QUADRATIC PARTITIONS. V p-\ a be d A B L M 49 4591 2.3.8243 1 79,H7 128,105256, 70 49 463| 2.7.3533 — — — — 49 477 43-7-I9-3 1 191,114 — 43,126 86, 84 49 481 8.5.1237 125,184 159,110 — — 49 499 2.24749 — 189, 83 . 49 523 2. 11. 2251 — i5,i57 — — 49 529 8.41. 151 i73^4o 219, 28 — — 49 531 2.3.5.i3-**7 — 173, 99 92,117 184, 78 49 537 128.9.43 89,204 107,138 193, 64385, 43 49 547 2-7-3539 — 93,143 — — 49 549 4.3.4129 45,218 — 191, 66382, 44 49 559 2.71.349 — — — — 49 597 4-3-4 x 33 139^74 — 103,114206, 76 49 603 2.3.7. 1181 — 191, 81 164, 87328, 58 49 613 4-79-157 157,158 — — — 49 627 2.27.919 — 53.153 188, 69376, 46 49 633 32.3.11.47 113,192 31.156 121,108 242, 72 49 639 2.3.8273 — — 206, 49 59, 85 49 663 2.9.31.89 — — 154, 93 308, 62 49 667 2. 19.1307 — 105,139 — — 49 669 4-3-4I39 175,138 — 187, 70 397, 39 49 681 16.27.5.23 55>2i6 217, 36 23,128 407, 35 49 697 32-I553 151,164 165,106 — — 49 711 2-3-5- l6 57 — 218, 27 436, 18 49 727 2.23.23.47 — — — 49 739 2.13.1913 — 2i,i57 — 49 741 4.3.5.829 221, 30 — 223, 2 217, 75 49 747 2.3.8291 — < 223, 3 200, 57 400, 38 49 757 4-7-1777 149,166 — — — 49 783 2.3.8297 — — i34,io3 I75i 79 49 787 2.11.31.73 — 213, 47 — — 49 789 4.27.461 117,190 — 217, 30 434, 20 49 801 8.3.25.83 99,200 223, 6 163, 88 427, 25 49 807 2.9.2767 — — 158, 9 1 115, 83 49 811 2.5.17.293 — 207, 59 — — 49 823 2.29.859 • — — — — 49 831 2.3.5.11.151 — — 1 38,127 343, 55 49 848 2. 27. 13.71 — 55>*53 184, 73 403, 37 49 853 4.121.103 187,122 — — 49 871 2.5.4987 — — • — — QUADRATIC PARTITIONS. 129 p p-1 a b c d A B L M 49 877 4-37-337 I 169,1461 — — — 49 891 2.3.5.1663 — 223, 9 208, 47 67, 85 49 919 2. 11. 2269 — — — — 49 921 256.3-5-!3 39,220203, 66 223, 8 i99, 77 49 927 2-3-53- I 57 — — 2,129 4, 86 49 937 16.3121 191,116 3,158 — — 49 939 2.3.7.29.41 — 167,105 4,129 8, 86 49 943 2.24971 — — — — 49 957 4.3.23.181 iii 5 i94 203, 54 406, 36 49 991 2.5.4999 — — 49 993 8.3.2083 213, 68221, 24 29,128 4i3, 33 49 999 2.3.13.641 — — 182, 75 3 6 4, 5° 50 021 4.5.41. 61 65,214 — — 50 023 2.9.7.397 — — 10,129 20, 86 50 033 i6.53-59 143^72 5i 5 i54 — — 50 047 2.3.19.439 — — 218, 29 3o5, 63 50 051 2.25.7. 11. 13 — 183, 91 — — 50 053 4-3-43-97 223, 18 91,118 445, 9 50 069 4-12517 215, 62 — — 50 077 4.9.13.107 219, 46 — 167, 86 425, 27 50 087 2.79.317 — — — — 50 093 4.7.1789 I73>I42 — — 50 101 4.3.25.167 185,126 173, 82 73, 85 50111 2.5.5011 — — — — 50119 2-3- 8 353 — — 14,129 28, 86 50123 2.19.1319 — 165,107 — — 50129 16. 13.241 223, 20 99,142 — — 50131 2-9-5-557 — 217, 39 148, 97 439, I? 50147 2.25073 — i77, 97 — — 50153 8.6269 83,208 15,158 — — 50159 1 2.31.809 — — . — . — 50177 1024.49 1,224 63,152 — — 50 207 2.13.1931 — — — — 50 221 4.81. 5.31 125,186 — 161, 90 322, 60 50 227 2. 3. 11. 761 — 175, 99 88,119 269, 69 ' 50 231 | 2.5.5023 — — — — 50 261 1 4-5-7-359 119,190 — — — 50 263 2.3.8377 — — 166, 87 332, 58 50 273 32.1571 73,212 219, 34 — — 50 287 2. 3.17. 17. 29 — 70,123 140, 82 180 QUADRATIC PARTITIONS. p P -l a b c a A B L M 50 291 2.5.47.107 — 207, 61! — — 50 311 2-9-5- I 3-43 — — 194, 65389, 43 50 321 J6.5-I7-37 215, 64153,1161 50 329 8.27.233 165,152 73,150211, 44 79, 85 50 333 4.12583 53>2i8 — — — 50 341; 4.3-5-839 79,210 — 197, 62383, 45 50 359 2. 3.7. 11. 109 — — 214, 39428, 26 50 363 2.13.13.149 — 69> I 5 I i 50 377 8.3.2099 61,216 223, 18 35,128419, 31 50 383 2. 81. 311 — — 190, 69380, 46 50 387 2.7.59.61 — 33,157 — 50 411 2.5.71. 71 — 219, 35 — 50 417 16.23.137 199,104 183, 92 — 50 423 2. 17.1483 — — — — 50 441 8.5.I3-97 221, 40 129,130 — 50 459 2.25229 — i7 I J I °3 | — 50 461 4.3.5.29.29 219, 50 — 119,110449, 3 50 497 64.3.263 129,184 95^44 223, 16 271, 69 50 503 2.3.19.443 — • -— 46,127427, 27 50 513 16. 7. 11. 41 223, 28 189, 86 — — 50 527 2.9.7.401 — — 122,109205, 77 50 539 2.3.8423 — 61,153 224, 11257, 71 50 543 2.37.683 50 549 4.12637 55>2i8 — 50 551 2.3.25.337 — 202, 57,404, 38 50 581 4.9.5.281 215, 66 1 77,122443, 15 50 587 2.3.8431 — 5,159220, 27440, 18 50 591 2.5.5059 — — 50 593 32.3.17.31 207, 88 191, 84 209, 481418, 32 50 5991 2.27.937 — 26,129: 52, 86 50 627 2.17. 1489 — 225, 1 50 647 2.3.23.367 — — 82,121:445, 13 50 651 2-25.1013 — 5M55 — — 50 671 2. 9.5-5 6 3 — 98,117)196, 78 50 683 2.3.8447 ! — IM59 224, 13185, 79 50 707 2.81. 313 . i43> 12 3 28,129 56, 86 50 723 2.7.3623 — 225, 7 — — 50 741 4-5-43-59 121,190 — 50 753 64.13.61 223, 32 225, 81 50 767 2.3.8461 i 142,101161, 81 QUADRATIC PARTITIONS. 131 p p-l a be d A B L M 50 773 4-3-4231 57,218 205, 54 410, 36 50 777 8.11.577 221, 44 213, 52 — — 50 789 4.12697 175^42 — — 5082114.3.5.7.11.11 225, 14 — - 11,130 379, 47 50 833 16.9.353 87,208 215, 48 41,128 425, 29 50 839 2.3.37.229 — 214, 41 9i, 85 50 849 32.7.227 215, 68 219, 38 — — 50 857 8.3.13.163 141,176 113^38 115,112 45i, ! 50 867] 2.29.877 — 225, 11 — — 50 87a 8.6359 77,212 171,104 — 50 891 1 2.5.7.727 — 147,121 — 50 893 4.3.4241 157,162 — 79,122 287, 67 50909 4.11. 13.89 197,110 — — — 50 923 2.27.23.41 i9>i59 220, 29 133, 83 50 929 16.3.1061 177,140 77,15° 223, 20 163, 81 50 951! 2.25. 1019 — — — ■ — 50 957 4-12739 221, 46 — — — 50 969 8.23.277 125,188 69,152 — 50 971 1 2.3.5.1699 — 133,129 64,125 3 IT , 63 50 989! 4.3-7-607 83,210 — 17,13° 373, 49 50 993 16.3187 167,152 135,128 — — 51001 8.3.125.17 51,220 149,120 43,128 34i, 57 51 031 2.729.5.7 — — i34,i°5 268, 70 51043 2.3.47.181 — 65,153 224, 17 275, 69 51 047 2.25523 — ~ 51 059 2.49.521 — 201, 73 — 51061 4-3-5- 2 3-37 169,150 19,13° 4°9, 37 51071 2.5.5107 — — — 51 109 4-3-4259 225, 22 — 59,126 118, 84 51131 2.5.5113 — 141,125 — — 51 133 j 4.3-4261 43,222 — 199, 62 13, 87 51 137 64.17.47 31,224 225, 16 — 51 151 2. 3.25. n. 31 — 226, 5 211, 77 51 157 4.9.49.29 9,226 — 157, 94 439, 21 51 169 ,32.3.13.41 137,180 187, 90 71,124 3 QI , 65 51 193| 8.81.79 147,172 181, 96 221, 28 137, 83 51197 4.12799 11,226 — — — 51 199j 2.3.7.23.53 — 218, 35 323, 61 51203 2.25601 225, 17 1 — 5121^ n 16.3.11.97 201,104 167,108 ,137, i°4 449, H 1 132 QUADRATIC PARTITIONS. V p-1 a b c d A B ! L M 51229 4.9.1423 123,190 — 23> 1 3 3 6 7 5 5 1 51239 2. 11. 17. 137 — — 51 241 8.3.5.7.61 205, 96; 79, I 5 OI 79> 80419, 33 51257 8.43.149 181,136153,118, — 51263 2. 19. 19. 71 51283 2. 9.7. 11. 37 — 145,123220, 31313* 63 51287 2.25643 — — — 1 51 307 2.3- I 7'5°3 — 67,1531148, 99 296, 66 51329 128.401 223, 40177,100! — 51341 45.I7I5 1 221, 50 — — — 51 343 2-3-43- I 99 — — 214, 43!343i 57 51347 2.25673 — 225, 19 — — 51349 4.3. 11. 389 I 35 5 I 82 — 61,126 122, 84 51361 32.3.5.107 175,144193, 84 47,128 43 1 , 27 51383 2.23.1117 — — — — 51407 2.25703 — — — — 51 413 4.12853 103,202 — 51419 2-47-547 — 213, 55 — — 51421 4-3-5-8.S7 75,214 — 217, 38103, 85 51427 2.9.2857 — 215, 51 140,103 169, 81 51431 2-5-37-139 — — — — 51437 4.7. 11. 167 19,226 — — — 51439 2.3-8573 — 226, 11 193, 79 51449 8.59.109 107,200 39,158! — 51461 4- 5-3I-83 95,206 — 51473 16.3217 127,188195, 82 — — 51 479 2.7.3677 — — — — 51481 8.9.5.11.13 I95.H6 53,156' 9M2Q 182, 80 51487 2.3.8581 2,i3 J 395> 43 51 503 2. 11. 2341 — — — — 51511 2.3.5. 17. 101 — 206, 55 41, 87 51517 4-243-53 21,226 — 215, 42430, 28 51 521 64-5-7.23 161,160111,140 — 51 539 2-73-353 — 183, 95 — 51551 2.25. 1031 — — — 51 563 2.7.29.127 — 189, 89 — 51577 8.3-7-3°7 211, 84203, 72227, 4 2i5> 77 51 581 4-5-2579 155,166 — — — 51593 8.6449 227, 8225, 22 — ■ — 51599 2.25799 — QUADRATIC PARTITIONS. 133 p p — 1 a b c d A B L M 51607 2.9.47.61 — 170, 87:340, 58 51613 4.3.11.17.23203,102; 151, 98 143, ^3 51 631 2.3.5.1721 — 218, 37 107, 85 51637 4-3- I 3-33 I 201,106 — 227, 6454, 4 51 647 2.49.17. 31 51659 2. 23.1123 — 219, 43 — 51673 8.3.2153 227, i2 ! ioi,i44Ji55, 96I310, 64 51679 2. 81. 11. 29 14,131407, 39 51683 2.25841 — J225, 2 3j — 51691 2-3-5-I723 — 327, 9208, 53 49, 87 51713 512. 101 217, 68171,106 51 719 2.19.1361 51721 8.3.5-431 I39,l802II, 60227, 8251, 73 51749 4.17.761 65,218 — — i — 51 767 2. II. 13. l8l — — 51769 8.9.719 213, 80199, 78 i39 > I °4 | i73 ) 8l 51787 2.27.7-I37 ! — 35^59 80,1231160, 82 51 797; 4.23-5 6 3 119,194 t 51 8031 2.59.439 — ,195, %3' — 51 817! 8.3.17. 127 101,2041227, 12107,116455, 3 51827 2.25913 — J207, 67 — — 51829!4.3.7.6i7 105,202 — 227, 10 197, 79 51839 2.25919 — — — 51 853 4.3.29.149 227, 18 65,126130, 84 51 859 : 2.9.43.67 7M53 44,129; 88, 86 51 869| 4.12967 187,130 — — — 51 871 2.3.5.7. 13.19 — — 214, 45 428, 30 51893 4.12973 137,182 — — — 51899 2.7.II.337 5M57 — — 51 907 2. 3. 41. 211 — 223, 33 200, 63400, 42 51913 8.9.7.103 93,208 161,114 221, 32 3 J 7> 6 3 51 929; 8.6491 227, 20 27,160 — — 51 94l| 4.5-49.53 175^46 — — — 51 949j 4.27.13.37 195,118 — 193, 7o 4°3> 4i 51971 2.5.5197 — 87,149 — — 51973 4.361. 71 113,198 — 101,118 253, 73 51977 8.73.89 221, 56 225, 26 — — 51991 2.3.5.1733 — 142,103 45 1 , J 3 52 009 8.3. 1 1. 197 5,228 I3M3 2 203, 60 406, 40 52 021 4-9.5.I7-I7 89,2IO 211, 50 61, 87 134 QUADRATIC PARTITIONS. p p-1 a b c d A B L M 52 027 2.3.13.23.29 — 157,117128,109 i99, 79 52 05J ! 2.3-25-347 — 137,129224, 25 M9, 83 52 057j 8.27.241 219, 64 215, 54 77,124 295, 67 52 067 2.7.3719 — 15,161 — 52 069 4-3-4339 225, 38 — 37,130 427, 3 1 52 081 I6-3-5-7-3 1 135^84 103,144 223, 28 307, 65 52 103 2.109.239 — — — 52 121 8.5-1303 61,220 123,136 — 52 127 2.67.389 — — — 52147 2.9.2897 — 73,153 212, 49 65, 87 52 153 8-3-4I-53 13,228 59,156 I3T,108 262, 72 52 163 2. n. 2371 — 81,151 — 52 177 16.3.1087 159,164 227, 18 55,128 329, 61 52 181 4.5.2609 185,134 — — — 52183 2.9.13.223 — — 206, 57 412, 38 52189 4-3-4349 165,158 — 167, 90 334, 60 52 201 8.9.25.29 45,224 143,126 149,100 I5 1 , 83 52 223 2.26111 — — — — 52 237 4.9.1451 99,206 — 145,102 290, 68 52 249 8.3.7.311 I55,* 68 119,138 109,116 239, 75 52 253 4.13063 107,202 — — — 52 259 2.17.29.53 — 201, 77 — — 52 267 2.3.31. 281 — 187, 93 28,131 365, 53 52 289 64.19.43 95,208 33>!6o — — 52 291 2.9.5.7.83 — 217, 5 1 172, 87 344, 58 52 301 4.25.523 35>226 — — 52 313 8.i3.5 3 227, 28 165,112 — 52 321 32.3-5- io 9 111,200 223, 36 7,132 14, 88 52 361 8.5.7.11.17 181,140 147,124 — — 52 363 2.9.2909 — 181, 99 224, 27 448, 18 52 369 16.3. 1091 63,220 221, 42 79,124 45 1, *5 52 379 2.26189 — 219, 47 — — 52 387 2.3.8731 — i93, 87 92,121 271, 71 52 391 2.5- I 3- I 3-3 I — — — — 52 433 16.29.113 223, 52 99,146 — 52 453 4.9.31.47 207, 98 — 229, 2 223, 77 52 457 8.79.83 229, 4 93^48 — — 52 489 8.81. 81 125,192 1,162 229, 4 241, 75 52 501 14.3-625.7 201,110 — 227, 18 454, 12 52 511 1 2.5.59-89 — — — QUADRATIC PARTITIONS. 135 p p-1 a b c d A B L M 52 517 4. 19.691 209, 94 — 52 529 16.49.67 175^48 5i 5 i58 — — 52 541 4-5-37-7I 229, 10 — — — 52 543 2.27.7.139 — — 130,109 457, 7 52 553 8.6569 227, 32 129,134 — — 52 561 16.9.5-73 225, 44 163,114 17,132 34, 88 52 567 2.3.8761 218, 41 34i, 59 52 571 2-5-7-75 1 — 27,161 — 52 579 2.9.23.127 — 1127,1351184, 79 421, 35 52 583 2. 61. 431 — — — — 52 609 128.3.137 25,228 11,162! 97,120 194, 80 52 627 2.3.49.179 — 97,147 52,129 104, 86 52 631 2.5.19.277. — — - — 52 639 2.3.31.283 — — 34,i3i 359, 55 52 667 2.17.1549 — 123,137 — — 52 673 64.823 97,208 225, 32 — ■ — 52 691 2.5. 11. 479 — *53i 12 * — — 52 697 8.7.941 229, 16 183, 98: — 52 709 4-13*77 145,178 — — — 52 711 2.3,5.7-251 — — 202, 63 404, 42 52 721 16.5.659 185,136! 39,160 52 727 2.41.643 — — 52 733 4-13183 197,118, — — — 52 747 2.3.59.149 — ! 77,153 212, 51424, 34 52 757 4. 1 2 1. 109 4I,226j — — — 52 769 32.17.97 113,200; 81,152 — — 52 783 2.3.19.463 86,123172, 82 52 807 2.3.13.677 182, 81364, 54 52 813 4.81. T63 163,162; — 175, 86 83, 87 52 817 16.3301 161,164195, 86 — ; — 52 837 4.3-7-17.37 159,166 — J 55, 98449, 19 52 859 2.13.19.107 — ! i47>i25 52 861 4.3.5-881 219, 70 — l6 9, 9 338, 60 52 879 2.3.7.1259 — — 206, 59383, 49 52 883 2. 137.193 — 201, 79 — — 52 889 8. 11. 601 67,220 117,140 — ! — 52 901 4.25.23.23 1,230 — 1 52 903 2.9.2939 — — 230, 1 227, 77 52 919 2.26459 — — — 52 937 8.13.509 221, 64 225, 34 — — 136 QUADRATIC PARTITIONS. p p-l a b c d A B L M 52 951 2-3-25-353 — 226, 25 301, 67 52 957 4.9.1471 I7M54 — 73,126 146, 84 52 963 2-3-7-I3-97 — 49,159 220, 39 440, 26 52 967 2-7 J -373 — — — — 52 973 4.17. 19.41 227, 38 — — 52 981 4-3.5-883 9.230 227, 22 161, 83 52 999 2.3.121.73 — 214, 49 361, 55 53 003 2.26501 — 171,109 — — 53 017 8.3.47.47 229, 24 23,162 83,124 289, 69 53 047 2.9.7.421 — 230, 7 209, 79 53 051 2. 25.1061 — 93,149 — — 53 069 4.13267 i3, 2 3° — — — 53 077 4-3-4423 i5 I > I 74 — 163, 94 445, 23 53 087 2. 11. 19. 127 — — — — 53 089 32-3-7-79 183,140 229, 18 209, 56 377, 5i 53 093 4.13. 1021 223, 58 — — — ■ 53101 4-9-25-59 45,226 — 49, 1 3° 439, 27 53 113 8.3.2213 213, 88 25,162 29,132 58, 88 53 117 4.49.271 229, 26 — — — 53129 8.29.229 227, 40 159,118 — — 53147 2.26573 — 3,163 — — 53 149 4-3-43- io 3 75>2i8 — 119,114 238, 76 53 161 8.3-5-443 69,220 67,i5 6 173, 88; 91, 87 53 171 2.5.13.409 — 87,15! ! 53173 4.9.7.21 1 217, 78 — 221, 38,335, 61 53189 4.13297 17,230 — 53 197 4-3- II - I 3-3 I 221, 66 — 223, 34 3 2 5, 63 53 201 16.25.7.19 55>224 201, 80 — — 53 231 2.5-5323 — — 53 233 16.3.1109 177,148 211, 66 31,132 62, 88 53 239 2.3.19.467 — — 142,105284, 70 53 267 2.26633 — 63,157 — — 53 269 4.3- 2 3- I 93 185,138 211, 54422, 36 53 279 2.17.1567 — — — — 53 281 32.9-5-37 215, 84 9i,i5 167, 92443, 25 53 299 2.81.7.47 — 161,117 104,119461, 5 53 309 4.13327 203,110 — 53 323 2.3.8887 — 229, 21 16,133415, 39 53 327 2.7.13.293 — — — 53 353 8.27.13.19 37,228 109,144 85,124 457, i3 QUADRATIC PARTITIONS. 137 p ,-1 a b c d A B L M 53 359 2.3.8893 — . — . 178, 85 433, 3 1 53 377 128.3.139 231* 4 203, 78 65,128 449, 21 53 381 4-5- I 7-i57 191,130 — — — 53 401 8.3.25.89 195,124 187, 96 101,120 202, 80 53 407 2.27.23.43 — — 230, 13 191, 81 53 411 2.5.49.109 — 231, 5 — — o3 419 2.3.29.307 — 101,147 44,13! 437^ 29 53 437 43.61.73 219, 74 — 217, 46 355, 57 53 441 64.5.167 71,220 171,110 — — 53 453 4-7-23-83 77,218 — — — 53 479 2.9.2971 — — 202, 65 7, 89 53 503 2.3.37.241 — — 166, 93 332, 62 53 507 2.31.863 — 207, 73 — — 53 527 2.3.11.811 — — 98,121 265, 73 53 549 4.11.1217 i57 ? i7o — — — 53 551 2.9.25.7.17 — — 22,133 421, 37 53 569 64.27.31 i35,i88!i8i,io2 161, 96 322, 64 53 591 2.5.23-233 — — — — 53 593 8.3.7. 11. 29 93,212 229, 24 115,116 233, 77 53 597 4.13399 229, 34 — — — 53 609 8.6701 I 55 > 1 72! 99^48 — — 53 611 2.3.5.1787 — I3M35 112,117 224, 78 53 617 16.3.1117 231, 16)137,132 223, 36 446, 24 53 623 2.81. 331 — — i94, 73 25, 89 53 629 4.3.41. 109 27*230 — 121,114 242, 76 53 633 128.419 193,128129,136 — — 53 639 2.13.2063 — — — — 53 653 4.3.17.263 183,142 — 109,118 463, 3 53 657 8.19.353 59,224105,146 — — 53 681 16.5. 11. 61 209,100 141,130 — — 53 693 4.3I.433 197,122 — — — 53 699 2.26849 — 231, 13 — — 53 717 4-i3 I0 33 89,214 — — — 53 719 2.3.7.1279 — 106,119 25 1 , 75 53 731 2.27.5.199 — 143^29 148,103 457, 15 53 759 2.26879 — — 53 773 4.3.4481 67,222 — 209, 58 35, 89 53 777 16.3361 151,176! 87,152 — — 53 783 2.26891 — — — 53 791 2.3.5. 11. 163 1 — 182, 83 43i, 33 138 QUADRATIC PARTITIONS. p p-1 a b c d A B L M 53 813 4.11.1223 217, 82 — — — 53 819 2.71.379 — 213, 65 — — 53 831| 2.5.7.769 — — — — 53 849 8.53.127 5,232 201, 82 — — 53 857 32.9.11.17 201,116 37,162 175, 88 439, 29 53 861 4.5.2693 31,230 — — — 53 881 8.3-5-449 85,216 167,114 227, 28 143, 85 53 887 2.3.7.1283 — — 190, 77 41, 89 53 891 2-5-17-317 — 183,101 — — 53 897 8.6737 61,224 63,158 — — 53899,2.3.13.691 — 229, 27 232, 5 217, 79 53 917 4-3-4493 139,186 — 7,i34 395, 47 53 923 2.3.11.19.43 119,141 100,121 463, 7 53 927 2-59-457 — — — 53 939 2. 149. 181 — 231, !7 — — 53 951 2.25.13.83 — — — — 53 959 2.3.17.23.23 — — 226, 31 3*9, 65 53 987 2.26993 — 225, 41 — — 53 993 8.17.397 13,232 81,154 — — 54 001 16.27.125 199,120 73,156 217, 48 434, 32 54 011 2.5. 11. 491 — 219, 55 — 54 013 4-3-7-643 187,138 — 151,102 302, 68 54 037 4.9.19.79 231, 26 i3,i34 389, 49 54 049 32.3-563 15,232 209, 72 89,124 283, 71 54 059 2. 151. 179 69,i57 — — 54 083 2.7.3863 231, J 9 — — 54 091 2.9.5.601 — 179,105 32,133 367, 55 54101 4.25-54I 55,226 — — — 54 121 8.3.5. 11.41 165,164 227, 36 43,132 86, 88 54133 4-3.13.347 167,162 — 221, 42 442, 28 54139 2.3.7.1289 — 133,135 136,109 463, 9 54 151 2.3.25. 19.19 — — j2i8, 47 359, 57 54 163 2.27.17.59 — 215, 63 76,127 457, i7 54167 2-7.53-73 — — — 54181 4.9-5-7.43 159,170 59,i3o 33 1 , 63 54193 16.3.1129 47,228 205, 78 71,128 455, J 9 54 217 8.27.251 189,136 1127,138 163, 96 326, 64 54 251 2. 125. 7. 31 — i 93, I 5 I — — 54 26c 4-I3567 37,230 — — — 54 277 ' 4.3-4523 129,194 203, 66 1 406, 44 QUADRATIC PARTITIONS. 139 p p—1 a b c d A B L M 54 287 2.27143 54 293 4.49.277 I233, 2 — i — — 54 311 2-5-5431 — 54 319 2.3.11.823 — I54.IOI i49, 85 54 323 2 -!57-i73 225, 43 — 54 331 2.3.5.1811 — 203, 81 23 2 , I 3 271, 73 54 347 2.29.937 — 213, 67 — 54 361 8.9.5. 151 219, 80 233, 6 197, 72 394, 48 54 367 2. 3. 13.17. 41 — — 158, 99 316, 66 54 3711 2.5.5437 — in,i45 — — 54 377 8.7.971 229, 44 147,128 — — 54 401 128.25.17 65,224 207, 76 — — 54 403J2.3.9O67 121,141 196, 73 415, 4i 54 409 8.3. 2267 195,128 97,15° 91,124 463, 11 54 413 4.61.223 83,218 — — — 54 419 2.7. 13.13.23 — 23 1 , 23 — — 54 421 4-3-5-9°7 39,230 — 61,130 45i, 23 54 437 4-31-439 I9M34 — — — 54 443 2. 163. 167 — 51,161 — — 54 449| 16.41.83 25,232 57,i6o — — 54 469 4-9- 1 7-89 225, 62 — 229, 26 151, 85 54 493: 4.3.19.239 117,202 25,134 377, 53 54 497 32. 13. 131 209,104 225, 44 — — 54 499, 2.3.31.293 — 7,165232, 15 464, 10 54 503 2.7.17.229 — — 54 517 4-3-7-H-59 231, 34 — 83,126 166, 84 54 521 8.5.29.47 211,100 27,164 — — 54 539 2. n. 37. 67 — 189, 97 — — 54 541 4.27.5. 101 179,15° — iH3, I][ 8 241, 77 54 547 2.3.9091 — r 93, 93! 68,129 136, 86 54 559 2 -9-7-433 — — 122,115 223, 79 54 563 2.27281 — 159,121 — — 54 577 16.9.379 89,216 233, 12193, 76 421, 39 54 581 4.5.2729 41,230 — — 54 583 2.3.11.827 — — 110,119 467, 3 54 601 8-3-25.7-13 149,180 77,156 227, 32 323, 65 54 617 8.6827 221, 76 213, 68 — 54 623 2.31. 881 — — 54 629 4.7.1951 223, 70 — — — 54 631 2.9.5.607 — — 166, 95 119, 87 140 QUADRATIC PARTITIONS. p p- 1 a be d A B L M 54 647 2.89.307 : — 54 667 2.9.3037 — I07,I47| 40,133 439, 3i 54 673 16.3.17.67 193,132221, 54 49,132 98, 88 54 679 2.3.13.701 — — 2,135 4, 9° 54 709 4.3-47-97 103,210 — 29,134 43i, 35 54 713 8.7.977 107,208231, 26 — — 54 721 64.9.5.19 225, 64 161,120 233, 12 466, 8 54 727 2.3-7- 13°3 — — 218, 49 7i, 89 54 751 2.3.125.73 — — 226, 35 121, 87 54 767 2.139.197 — — 54 773 4-I3693 233, 22 — — — 54 779 2.61.449 — 171,113 — — 54 787 2.3.23-397 — i 65,159 80,127 301, 69 54 799 2.3-9J33 — — 182, 85 73, 89 54 829 4-9- I 5 2 3 125,198 — 3i,i34 37i, 55 54 833 16.23.149 217, 88!io 5 ,i 4 8 — — 54 851 2.25.1097 — 201, 85 — — 54 869 4.11. 29.43 137,190 — — 54 877 4.3.17.269 11,234 — 233, 14 275, 73 54 881 32. 5-343 145,184 33,164 — — 54 907 2.3.9151 — i57, I2 3232, 19 289, 71 54 917 4.13729 209,106 — — — 54 919 2. 243.113 i34,ni 268, 74 54 941 4.5.41.67 229, 501 — — 54 949 4.3.19.241 207,110 — 181, 86 77, 89 54 959 2.27479 — — — — 54 973 4.27.509 213, 98 — 215, 54 43°, 36 54 979 2.3.49.11.17 — 23,^5 148,105 296, 70 54 983 2-37-743 — — — — 55 001 8.625. 11 155,176 87,154 — 1 — 55 009 32.9.191 55,228 197, 90 121,116 227, 79 55 021 4.3.5-7.i3i 205,114 — 223, 42 446, 28 55 049 8.7.983 35>232 159,122 — — 55 051 2.3-25.367 67,159 124,115 469, 3 55 057 I 6-33 I -37 129,196 227, 42 233« l6 185, 83 55 061 4-5-2753 215, 94 — — — 55 073 32.1721 233, 2 ^ 165,118 — — 55 079 2.27539 ' — — — — 55 103 2.27551 — — — — 55109 4-23-599 47,230 — — QUADRATIC PARTITIONS. 141 p ^-1 a b c d A B L M 55117 U.9^53 1 19,234 — 127,114 254, 76 55 127 2.43.641 — ■ — — — 55 147 2.3.7.13.101 — 205, 81 232, 21 464, M 55 163j 2.27581 — ! 45, l6 3 — — 55 171 2.9.5.613 — 233, 21 208, 63 416, 42 55 201 3 2 -3-25-23 151,180 101,150 217, 52 373, 55 55 207 2.9.3067 — — *3©»"3 209, 81 55 213 4.3.43.107 77,222! 209, 62 395, 49 55 217 16.7. 17. 29 7i>224|i35,i36 — — 55 219j 2.3.9203 — |i37 5 i35 224, 41 347, 61 55 229 4.13807 235, 2! — — — 55 243) 2.81. n. 31 — '235, 3 140,109 187, 83 55 249 16.3.1151 225, 681131,138 151. 104 161, 85 55 259 2-7-3947 — ii4i>i33 — — 55 291 2.3-5- I 9.97 — 29,165 196, 75 392, 5° 55 313 16.3457 233> 32 3$i64 — — 55 331 2. 5. 11. 503 — 207, 79 — — 55 333 4-929.53 127,198 — 235, 6 47o, 4 55 337 8.6917 211,104 15,166 1 55 339 2.3.23.401 — 221, 57 92,125467, 11 55 343 2.7.59.67 — — — — 55 351 2.27.25.41 — — 26,135 52, 90 55 373 4. 109. 127 227, 62 — — — 55 381 4.3-5- I 3.7i 25,234 — 163, 98^131, 87 55 399 2.3.7.1319 — — 74,129148, 86 55 411 2.3.5.1847 — 31,165 232, 23163, 85 55 439 2-53.523 — : | 55 441 16.9.5. 7. 11 215, 96 233, 24 143,108 286, 72 55 457 32.1733 169,164 123,142 — — 55 469 4.49.283 163,170 — — 55 487 2 27743 — — 55 501 4 3- I2 5-37 5M30 — 193, 78 386, 52 55 511 2 5.7. 13.61 — — 55 529 8 n. 631 173,160 l77,IIO — — 55 541 4 5.2777 185,146 1 — 55 547 2 27773 — l65,II9 55 579 2 3-59-I57 — 227, 45 64,131329, 65 55 589 4 13.1069 I75>I5S — — — 55 603 2 93089 — 71,159220, 49 367, 57 55 609 8 3.7.33I 203,120 103,15° 11,136 397, 49 142 QUADRATIC PARTITIONS. p ,-i a b c d A B L M 55 619 2.27809 — 87,155 55 621 4.27.5.103 145,186 139,110 191, 83 55 631 2-5-5563 — — — — 55 633 16.3. 19.61 192,137 119,144 215, 56 383, 53 55 639 2.9.11.281 — — 226, 39 452, 26 55 661 4.5.121.23 115,206 — — — 55 663 2.3.9277 — — 146,107 467, 13 55 667 2.13.2141 — 153^27 — — 55 673 8.6959 43^32 231* 34 — — 55 681 128.3.5.29 95,216 i93, 96 191, 80 43*> 37 55 691 2-5-5569 — 171,115 — — 55 697 16.59-59 1,236 195, 94 — — 55 711 2.9.5.619 — — 94,125 281, 73 55 717 4-3-4643 3^234 — 43>!34 359, 59 55 721 8.5.7.199 5.236 1 89, 1 00 — — 55 733 4.13933 233, 38 — — — 55 763 2.49.569 — 135,137 — — 55 787 2.27893 — 3,167 — — 55 793 16.11.317 143,188 141,134 — — 55 799 2.23. 1213 — — — — 55 807 2.3.71. 131 — — 142,109 469, II 55 813 4-3-4651 223, 78 — 235, 14 i93, 83 55 817 8.6977 11,236 45,164 — — 55 819 2.9.7.443 — 37,1651176, 91 97, 89 55 823 2.13.19.113 — — — — 55 829 4. 1 7.82 1 215, 98 — — — 55 837 4-27-U-47 69,226 — 217, 54 434, 36 55 843 2.3.41.227 — 95^53 236, 7 215, 81 55 849 8.3.13.179 45» 2 32 209, 78 19,^6 427, 39 55 871 2.5-37-151 — — — — 55 889 16.7.499 233, 4o 201, 88 — — 55 897 8.3-i7-i37 221, 84 85,156 205, 68 1, 9i 55 901 4-25-13-43 235> 26 — — — 55 903 2.3-7-1331 — — 206, 67 5> 9i 55 921 I 6.3-5- 2 33 15*236 T73, XI 4 161,100 i39, 87 55 927 2.9.13.239 — . — 202, 71 11, 9 1 55 931 2.5.7.17.47 — I47.I3 1 — — 55 933 4-3-59-79 123,202 — 119,118 235. 79 55 949 4.71. 197 205,118 — — — 55 967 2.27983 — — — — 'QUADRATIC PARTITIONS. 143 p p-1 a b c a A B L M 55 987 2-3-7-3I-43 — 113^47 200, 73 19, 9 1 55 997 4-13999 101,214 — — — 56 003 2.28001 — 15^67 — — 56 009 8.7001 235, 28 99^52 — — 56 039 2.28019 — — — 56 041 8.3.5,467 229, 60 221, 60 83,128 467, 15 56 053 4.81. 173 233> 42 — 211, 62 25, 9i 56 081 16.5. 701 191,140 93,154 — — 56 087 2.29.967 — — — — 56 093 4-37-379 203,122 — — — 56 099 2.7.4007 — 231, 37 — — 56 101 4.3.25.11.17 225, 74 — 107,122 473, 5 56 113 16.3.7. 167 167,168 121,144 25,136 433, 37 56 123 2. 11. 2551 — 189,101 — — 56131 2.3.5.1871 — 41,165 88,127 4691 13 56 149 4.3.4679 57,230 — I3MI4 262, 76 56167 2.3.11.23.37 — — 230, 33 460, 22 56171 2.5.41. 137 — 237, 1 — — 56 179 29.3121 — 161,123 152,105 3°4, 7° 56197 4.9.7.223 161,174 — 235, 18 470, 12 56 207 2. 157.179 — — — — 56 209 16.3. 1171 65,228 61,162 169, 96 338, 64 56 237 4.17827 221, 86 — — ■ — 56 239 2. 3.7. 13.103 — 214, 59 37, 9i 56 249 8.79.89 2 35> 32 231, 38 — — 56 263 2-3-9377 — _ i34,u3 473, 7 56 267 2.7.4019 — 237, 7 ■ — — 56 269 4.27.521 237, 10 — 49^34 353, 61 56 299 2.3.11.853 — 43>i65 164, 99 328, 66 56 311 2.3.5.1877 — ■ — 2,i37 413, 45 56 333 4.14083 157,178 — — 56 359 2.9.31. 101 — 194, 79 43, 9 1 56 369 16. 13. 271 145,188 237, 10 — ; — 56 377 8.243.29 i79,!5 6 235> 24 85,128 299, 71 56 383 2-3-9397 — — 70,131 323, 67 56 393 8.7-19-53 107,212 5 x > l6 4 — — 56 401 16.3.25.47 225, 76 157,126 137,112 199, 83 56 417 32.4I-43 79,224 I i77,ii2 — — - 56 431 2.27.5.11.19 — — 58,i33 457, 25 56 437 ,4-3-4703 41,234 173, 94 109, 89 144 QUADRATIC PARTITIONS. p p-1 a b c d ! A B L M. 56 443 2.3.23.409 — 115,147124,117 248, 78 56 453 4. 1 1 1283 223, 82 — — 56 467 2 -9-3 I 37 — 233, 33112,121 475, 3 56 473 8.3.13.181 67,228 5,168155,104 467, 17 56 477 4.7.2017 181,154 — — — 56 479 2-3-94*3 — — 98,125 473, 9 56 489 8.23.307 115,208 81,158 — — 56 501 4.125.113 199,130 — — — 56 503 2-9-43-73 — — i4,i37 425, 4i 56 509 4.3.17.277 85,222 — . 151,106 469, 15 56 519 2. 7. 11. 367 — — — — 56 527 2.3.9421 — — 178, 91 45 1 , 29 56 531 2-5-5653 — . 159,125 — — 56 533 4-3-7-673 I53.I82 — 109,122 257, 77 56 543 2.17. 1663 — — — — 56 569 8.3-2357 237, 20 11, 168 163,100 463, 21 56 591 2-5-5659 — — — — 56 597 4.I4I49 119,206 — — — 56 599 2-3-9433 — — 218, 55 53, 91 56 611 2.9-5- I 7.37 — 217, 69 44,i35 88, 90 56 629 4.9.121.13 215,102 — 77,13° 3i3, 69 56 633 8.7079 53,232 39,166 — — 56 659 2.3-7-i9-7i — 47,165 *72, 95 XI 3, 89 56 663 2. 41. 691 — — — — 56 671 2.3.5.1889 — — 238, 3:476, 2 56 681 8.5.13.109 91,220 237, 16 — — 56 687 2.7.4049 — — — — 56 701 4.81.25.7 75.226 — 167, 98461, 23 56 711 2-553- io 7 — — 56 713 8. 3.17. 139 227, 72 65,162 35,i36 373, 57 56 731 2.3.5.31. 61 — 227, 5 1 208, 67 409, 47 56 737 32.9.197 81,224 17,168 103,124 475, 7 56 747 2. 17. 1669 — 237, 17 — — 56 767 2.39461 — — 190, 83 59, 9i 56 773 4.9.19.83 207,118 — 229, 38 115, 89 56 779 2.3-9463 ■ — 221, 63 236, 19 i79, 85 56 783 2. 11. 29.89 — — — — 56 807 2.28403 — — — — 56 809 8.27.263 165,172 19,168 211, 64 403, 49 56 813 4.7.2029 13,238 — — — QUADRATIC PARTITIONS. 145 p p-l a bio d A B J L M 56 821 4.3-5-947 105,214 — 227, 42454, 28 56 827; 2.9.7. ii. 41 — 163,123220, 53 61, 91 56 843; 2.97.293 — i95* 97 — 56 857 8.3.23.103 101,216 137^38 37^36445* 33 56 873 8.7109 187,148 141,136 5689112.5.5689 — 237, 19 i 56 893J4-3-H-43I 133^98 — 55**34347, 63 56 897 64.7.127 161,176 225, 56 — — 56 909 4-41-347 205,122 — — — ■ 56 911 2.3.5.7.271 — — 62,133337, 65 56921:8.5.1423 35*236213, 76 — — 56 923| 2.3.53.179 — 131,141 J 76, 93352, 62 56 929 32.3.593 177,160223, 60 199, 76427, 41 56 941 4 - 3-5-13-73 221, 90; — 79^30469, 17 56 951 2.25.17.67 — — — — 56 957; 4.29.491 i39>i94 — — — 56 963i 2.19. 1499 ■ — ■ 201, 91 — ; 56 983| 2.3.9497 — — 26,137437, 37 56 989| 4-9-1583 235> 42 — 233* 3 466, 20 56 993 32.13.137 233, 52 165,122 ! 56 999 2.28499 — — 57 03714.3.49.97 189,146 — 97,126194, 84 57 041 16.5. 23.31 215,104 57,164 57 047: 2. 11. 2593 — — 57 059: 2.47.607 — 231, 43 57 073 16.3.29.41 57,232 25,168 89,128473, 13 57 077 4.19:751 121,206 57 089 256.223 217,100 171,118 57 097|8.9.i3.6i 181,156 125,144 157,104155, 87 57 107 2.7.4079 — 63,163 57119 2.28559 — — 57 131 2.5.29.197 — 3, l6 9 57 139 2.3.89.107 — 239, 3 I96, 79 433, 39 57 143 2.28571 — — — 57 149 4-7-i3- I 57 155^82 — — 57 163 2.3.7. 1361 — 205, 87 64,133 463, 23 57 173 4.14293 23*238 — • — 57 179 2.1 1. 23. 113 — 123,145 — 57 191s 2.5.7.19.43 — — — 57193 8.3.2383 237> 32 239, 6 149,108 298, 72 146 QUADRATIC PARTITIONS. p p-1 a b c (1 A B i L M 57 203 2-37-773 — 9,169: — — 57 221 4.5.2861 239, 10 — ' — — 57 223 2.9.11.17.17 — — 94,127 475, " 57 241 8.27.5.53 125,204 197, 96 229, 40 349, 63 57 251 2.125.229 — 183,109 — 57 259 2.9.3181 — 53,i65 76,131 3i7, 69 57 269 4.103.139 25,238 — — — 57 271 2-3-5- 2 3-83 — — 218, 57 436, 38 57 283 2.3.9547 — 239, 9 236, 23 305, 7i 57 287 2.28643 — — 57 301 4.3.25.191 201,130 — 13,138 26, 92 57 329 16.3583 185,152 201, 92 — — 57 331 2.9.5.49.13 — 233, 39 32,137 443, 35 57 347 2-53-541 — i5,!69 — — 57 349 4.243.59 225, 82 — 59,i34 461, 25 57 367 2.9.3187 122,119 479, 1 57 373 4.3.7.683 27,238} 169, 98 125, 89 57 383 2.13.2207 — — — 57 389 4.14347 67,230 — — — 57 397 4.3.4783 151,186 — 125,118 229, 81 57 413 4-3M63 193,142 — — _ 57 427 2.3« I 7-5 6 3 — ,103,153 160,103 469, 19 57 457 16.27.7. 19 231, 64217, 72 185, 88 79, 9i 57 467 2.59.487 — 75,i6i — 57 487 2.3.11.13.67 110,123 220, 82 57 493 4.9.1597 217,102 — 19^38 38, 92 57 503 2.28751 — — — 57 527 2.49.587 — — — — 57 529 8.9.17.47 235, 48 71,162 131,116 479, 5 57 557 4.14389 i99,i34 57 559 2.3-53.181 — 206, 71 4i9» 45 57 571 2.3.5.19.101 — 239, 15 236, 25 161, 87 57 587 2.28793 — 225, 59 — — 57 593 8.23.313 203,128 231, 46 — — 57 601 256.9.25 1,240 127,144 73,i32 146, 88 57 637 4.9.1601 81,226 203, 74 425, 43 57 641 8.5.11.131 179,160 207, 86 — — 57 649 16.3. 1201 7,240 I5i»i3* 191, 84 382, 56 57 653 4.7.29.71 233, 58 — — — 57 667 2.3.7.I373 223, 63 88,129 176, 86 QUADRATIC PARTITIONS. 147 p p-l a be d A B L M 57 679 2.3.9613 — J202, 75U04, 50 57 689 8.7211 133,200 183,110, 57 6971 32.3.601 239, 24 95,*5 6 | 47,1361361, 61 57 709 4.9.7.229 147,190 — 239, 14281, 75 57 713 16.3607 113,212 5 I , I 66; — 57 719 2.28859 . 57 727 2.27.1069 — 238, 19295, 73 57 731 2.5.23 251 ^s,^ 1 — 57 737 8.7.1031 139,196 237, 28 57 75l! 2. 3.125. 7. n — 1 38,137 449, 33 57 773| 4.11.13.101 157,182 — — 57 781 4.27.5.107 55,234 — 163,102326, 68 57 787 2.3.9631 85,159200, 7743 1 , 4i 57 791 2.5.5779 57 793; 64.3.7.43 63,232 209, 84151,108302, 72 57 803 2.28901 45, l6 7 57 809 ! 16.3613 97,220 3,!7° — — 57 829 4.3.61.79 223, 90 — 101,126202, 84 57 839 2. 121. 239 — - __ — — 57 847 3.3.31.3 u — — :ii8,i2H48i, 1 57 853 4.9.1607 I97>138 — 199, 78398, 52 57 859 2.3.9643 121,147 124,119233, 81 57 881 8.5.1447 I55JI84 9,i7o — — 57 899j 2.28949 69,163 — — 57 901 4.3.25.193 205,126 — 127,118481, 3 57 917 4.14479 229, 74 — — — 57 923 2.28961 111,151 — — 57 943 2.27.29.37 J230, 41353, 63 57 947 2.7.4139 93,i57! 57 973 4-3-483I i37,T98 29,138 58, 92 57 977! 8.7247 211,116 165,124 57 991 2 -3-5- I 933 — — ' 98,127283, 75 58 013 4-i45°3 37,238 — — — 58 027 2.3.19.509 — 227, 57 8,139409, 49 58 031 2.5.7.829 — — — — 58 043 2.29021 — 219, 71 — 58 049 64.907 65,232 159,128 58057:8.3.41.59 221, 96 193,102133,116215, 83 58 061! 4.5.2903 125,206 — , — — 58 067 2.29033 — 225, 61 — — 148 QUADRATIC PARTITIONS. p-1 A B L M 58073,8.7.17.61 187,152 58 099 2.3.23.421 58109 4.73.199 58 111 2.3.5.13.149 58129,16.3.7.173 58 147| 58 151! 58 153 ! 58 169! 58 171| 58 189 58 193 58 199 58 207 58 211 58 217 58 229 58 231 58 237 58 243 58 271 58 309! 58 313 58 321| 58 337! 58 363; 58 367i 58 369 58 379 58 391! 58 393' 08 403 58 411' 58 417 58 427 58 439 58 441 58 451 58 453 58 477 2.3.11.881 2. 25.1163 8.3.2423 8.11.661 2.3-5-7-277 4-3-I3-373 16.3637 2.7.4157 2.3.89.109 2.5.5821 8.19.383 4-14557 2.9.5.647 4.3.23.211 2.3-17.571 2.5.5827 4.3-43.ii3 8.37.197 16.729.5 32.1823 201, 94 — 241, 3196, 81 203,130 23,240' 41,168 — 167,123 106,125 241, 4 392, 54 269, 77 253, 79 220, 57440, 38 173,168241, 6 181, 92 95, 91 115,212213, 80 — — 61,165 195,142 — 223, 92 189,106 136,115481, 7 241, 6 82,131 33^69 — 229, 76237, 32 73,230 — 59,234 — 24 95,222 ■ 4 82 : 3", 7i 238, 23 169, 87 103,126206, 84 44,i37j455> 3 1 139,114278, 76 67,232225, 62 — 161,180163,126239, 20299, 73 241, 16207, 88] — — 221, 69! 20,139397, 53 241, 12 16 r, 104 473, 19 51.167 2-3.71.137 ! 2-7.11.379 1 1024.3. 19 225, 2.1 7.17.101 2-5-5839 8.9.811 423,208215, 78 211, 68 7, 93 2.29201 81,161 2.9.5.11.59 i — 197, 99212, 67 11, 93 6.3.1217 1239, 36 77,162193, 84386, 56 2.131.223 2.61.479 8.3.5.487 2.25.7.167 4.3.4871 4.3. 1 1.443 '95, 29,240223, 66227, 48454, 32 — 201, 95 183,158 «— 205, 74 17, 93 61,234 — 223, 54446, 36 QUADRATIC PARTITIONS. 149 p-l A B L M 58 481, 58 511 58 537 58 543 58 549 58 567! 58 573 58 579 58 601 58 603 58 613 58 631 58 657, 58 661 58 679| 58 687| 58 693 58 699 58 711 58 727, 16.5.17.43 2.5.5851 8.27.271 2.3.11.887 4.3.7.17.41 2.3.43.227 4.9.1627 2.3-I3-75 1 8.25.293 2.3.9767 4.14653 2. 5. 11. 13. 4: 32.3.13.47 4.5.7.419 2.29339 2.3.9781 4-3.67.73 2.27.1087 2.3.5.19.103 2.29363 241, 20237, 34j — 109,216143,138203, 76 74,i33 105,218 179, 94 242, 239, 22 3,242 — — 239, 27236, 31 101,220147,136 — — j 11,171224, 5 7,242 — 241, 24 145^94 97,222 47,168145,112 — 1218, — ;235, jio9,i53|i84, 91 — I242, 58733.4.14683 : 13,242; 58 74l| 4.3.5. 1 1.89 |i2i,2io; 58 757 4.37.397 ' 241, 26 58 763 58 771 4-37-397 2. 11. 2671 2.9.5.653 58 787; 58 789 58 831] 58 889 58 897j 58 901 1 58 907! 58 909 58 913 58 921 58 937| 58 943 58 963 58 967 58 979 2.7.13.17.19 — 4.9.23.71 2-3.5.37.53 8.17.433 16.9.409 4.25. 19.31 2.29453 4.3.4909 32.7.263 8.3.5.491 8-53-139 2.13.2267 2.3-3 I -3i7 2.29483 2.37.797 15,242 75,^3 17,171 153,133 125,208 201,136 33,i7o 233, 48 151,190 165,178 233, 68 211,120 237, 37 219, 74 239, 30 179,164 123,148 — 241, 21 — 231, 53 64,135 229, 46 238, 27 113,124 71,134 11,140 236, 33 25, 325, 103, 239, i73, i43, 3^3, 57 481, 35, 93 337, 67 457, 3i 221, 83 r 73, 98467, 25 128, 90 367, 61 476, 18 259, 79 473, 21 43i, 43 472, 22 150 QUADRATIC PARTITIONS. P d I A B L M 58 991 58 997 59 009: 59 Oil 59 021 59 023! 59 029 59 051 59 053 59 063: 59 069; 59 077J 59 083: 59 093 ; 59 107| 59 113i 59 119 59 123 ! 59 141 1 59 149J 59 159| 59 1671 59 183 59 197; 59 207 59 209 59 219 59 221 59 233 59 239 59 243 59 263 59 273 59 281 59 333 59 341 59 351 59 357 59 359 59 369 2-5- I 7-347 4-343-43 128.461 2.3.5.7.281 4.5.13.227 2.27.1093 4.3.4919 2.25.1181 4-3-7-I9-37 2.29531 4.14767 4-27-547 2.3.43.229 4.11.17.79 2.3.9851 8.9.821 2.3.59.167 2.7.41. 103 4.5- 2 957 4-9 3T-53 2. n. 2689 2.9.19.173 I 2.127.233 ! 4.3.4933 i 2.7.4229 ,8.3.2467 1 2. 29.1021 4.9.5.7.47 32.3.617 2.27.1097 89,226 — — — 103,220171,122 — 23,171 52,137 359, 63 115,214 — — 134,117268, 78 135*202 — : 22 7, 50377, 59 243> 243> 1241, 18482, 12 2 35> 62 — 129,206 — ■ 107,126214, 84 — I39» I 4« 19 6 , 8 3 53, 93 23*242 — ; 25,171 188, 89455. 33 243, 8145,138235, 36470, 24 34,139451, 35 135^43 79,230 243, 10 219, 106 85, 228 221, 72 20I, 97 215* 114 207, 128 24T, 24 239* 26317, 71 238, 29 151, 89 73, J 343 2 9, 6 9 61,136469, 25 211, 70421, 47 209, 72418, 48 242, 15484, 10 2-i9- I 559 *95, io 3 — : — 2.3.7. !7.83 — — 214, 67,415, 49 8.31.239 227, 88129,146 16.3.5. 13.19 41,240103,156241, 20181, 87 4.7.13.163 223, 98 4.3.5-23.43 195^46 , 47,138 2.25.1187 4.11. 19.71 91,226 — 2.3.13.761 — 1154,109 8.41.181 155,1882-37, 40 — 94, 92 481, 15 QUADRATIC PARTITIONS. 151 V p-1 a bio d A B L M 59 377 16.3.1237 241, 36! 83,162 217, 64409, 51 59 387 2. 23.1291 — ! 243> 13 — i — 59 393 2048.29 127,208 15,172 — — 59 399 2.17. 1747 — — — 59 407 2.3.9901 — — 38,139379, 59 59 417 8.7.1061 61,236 75,164 59 419 2.9.3301 — 179,117 112,1251263, 79 59 441 i6.5-743 145,196243, 14I 59 443 2.3.9907 3M7i 56,137467, 27 59 447 2.29723 : l 59 453 4.89.167 53,238 — — — 59 467 2.3.11.17.53 — 227, 63! 80,133319, 71 59 471 2.5- I 9-3i3 i 59 473 16.9.7.59 233, 72 55,168239, 28^55, 89 59 497 8.3-37.67 229, 84157,132! 85,132170, 88 59 509 4.27.19.29 i S3j 1 9°\ — 109,126218, 84 59 513 8.43-J73 173,172219, 76 — 59 539 2.3.9923 — 241, 27244, 1 247, 81 59 557 43-7-709 209,126 — 235, 38 121, 91 59 561 8.5.1489 5,244243, i6| — 59 567 2.13.29.79 — _ 59 581 4-9-5-331 235, 66 — 233, 42466, 28 59 611 2.3.5.1987 — 187,111244, 5229, 83 59 617 32.81.23 9,244197,102185, 92461, 31 59 621 4.5.11.271 239, 5° — 59 627 2.7.4259 — 243, 17 — 59 629 4.3.4969 227, 90 — 161,106 r 57, 89 59 651 2. 25.1193 — T 77, TI 9 — 59 659 2.3.61. 163 — 211, 87 4,141 8, 94 59 663 2.23.1297 — 59 669 4.7.2131 55,238 — — 59 671 2.27.5- I 3 I 7 — — 58,137 353, 65 59 693 4.14923 163,182 — — — 59 699 2.19.1571 — 81,163 — — 59 707 2.9.31. 107 35,i7i 8,141 16, 94 59 723 2.13.2297 — 5 T , l6 9 — — 59 729 16.3733 223,100 99,i58 — — 59 743 2 .9.33i9 ■ — ■ — 10,141 20, 94 59 747 2.29873 — 63,167 59 753 8.7.11.97 77,232 m,i54 — - 1 152 QUADRATIC PARTITIONS. p p-1 a b c d A B L M 59 771 2.5-43-!39 — 243, 19 — 59 779 2.729.41 — 73, l6 5 244, 9488, 6 59 791 2-3-5-J993 — 82,133481, 17 59 797 4.9.11.151 71,234 — | 77,134479, 19 59 809 32.3.7.89 47,240191,108241, 24482, 16 59 833 8.27.277 243, 28235, 48149,112187, 87 59 863 2.3.11.907 — — 190, 89: 77, 93 59 879 2.49.13.47 — — — — 59 887 2. 27.1109 — — 242, 21 484, 14 59 921 16.5.7. 107 65,236189,110 — — 59 929 8.3.11.227 195,148 59,168173,100127, 91 59 951 2. 25. 11. 109 \ — 59 957 4.i3- IJ 53 119,214 — 59 971 2.3-5- J 999 — 97>l59l64,I05 328, 70 59 981 4.5.2999 205,134 — — 59 999 2. 131.229 ' — 60 013 4.9.1667 237, 62 — !i45>n4 290, 76 60 017 16.121.31 241, 44243, 22 — — 60 029 4-43-349 245, 2 — — 60 037 4-3-5 00 3 239, 54 — 245, 2 251, 81 60 041 8.5.19.79 245, 4237, 44 — — 60 077 4.23.653 221,106 — — — 60 083 2. 11. 2731 15,173 — — 60 089 8.7.29.37 245, 82 3i, 58 60 091 2.3.5.2003 — 221, 75196, 85451, 37 60101 4.25.601 95,226; — 60 103 2.81.7.53 — 230, 49 83, 93 60 107 2.41.733 — ;2 4 3, 23 — 60127 2. 3. 11. 911 22,141 44, 94 60 133 4.3.5011 223,102 245, 649O, 4 60139 2.9.13.257 181,117208, 75416, 50 60149 4.11.1367 2l5,Il8 — — — 60161 256.5-47 25,244 213, 86 — — 60167 2.67.449 — — — 60169 8.3.23.109 245, I2 61,168 60 209 16.53.71 175^72 141, 142 60 217 ZS'tS-W 171,176185,114245, 8269, 79 60 223 2.3.10037 — 206, 77 437, 43 60 251 2. I25.24I 147,139 — — 60 257 32.7.269 239, 56 33,i72 — QUADRATIC PARTITIONS. 153 p p — 1 a b c d A B L M 60 259 2.3. 121.83 — 241, 33 236, 39472, 26 60 271 2.3.5.49.41 — — 122,123244, 82 60 289 128.3. 157 167,180 149,138 119,124253, 81 60 293 4-*5°73 113,218 — — — 60 317 4.17.887 181,166 ' — 60 331 2.3.5.2011 • — 43^71 116,125491, 3 60 337 16. 9. 419 199,144 215, 84 167,1041479, 21 60 343 2.3-89.113 — — 194, 8 7 | 3 88, 58 60 353 64.23.41 »93» I 5 a 81,164 — — 60 373 4-27.13.43 2 33> 7? — 221, 62407, 53 6u 383 2.7.19.227 — — — 60 397 4.3.7-719 211,126 — 113,126 226, 84 60 413 4-H.I373 43,242 — — — 60 427 2.81.373 — 235> 5 1 28,141 5 6 , 94 60 443 2.47.643 — 219, 79 — — 60 449 32.1889 143,200 129,148 — — 60 457 8. 3. 11. 229 69,236 205, 96 245, 12 49°, 8 60 493 4.3.71. 71 243> 38 — . 1,142 427, 47 60 497 16. 19.199 3^244 195,106 — — 60 509 4.7.2161 245, 22 — — — 60 521 8.5.17.89 205,136 207, 94 — — 60 527 2.53.571 — — — — 60 539 2.30269 — 69,167 — — 60 589 4.81. 11. 17 45,242 — 239, 34 137, 9i 60 601 8.3.25. 101 245, 24 7,i74 107,128 49 1 , 7 60 607 2.9-7. 13-37 — — 158,109 169, 89 60 611 2. 5. 11. 19.29 — 177,121 — — 60 617 8.7577 149,196 243, 28 — — 60 623 2.17. 1783 — — — — 60 631 2.3.5.43.47 — — 166,105 332, 70 60 637 4-3-3 I -i63 11,246 — 233 ? 46 95, 93 60 647 2.30323 — — — — 60 649 8.3.7. 19.19 243, 40239, 42 43,140 377, 61 60 659| 2.13.2333 — 159^33 — — 60 661 4.9.5-337 135,206! — 13^42 439, 43 60 6791 2.9.3371 — — 154,111 308, 74 60 689 16.3793 233> 80 39,172 — — 60 703 2.3.67. 151 — — 230, 5 1 460, 34 60 719 2.7.4337 — — — — 60 727 j 2.3.29.349 — — 170,103 139, 9 1 154 QUADRATIC PARTITIONS. p p-i a b c d A B L M 60 733 4.9.7.241 107,222 — !85, 94 97, 93 60 737 64-I3-73 71,236 75,166 — — 60 757 4.3.61.83 86,231 — 83,134485, 17 60 761 8.5.49.31 35,244219, 80 — — 60 763 2.3.13.19.41 — 101,159 124,123248, 82 60 773 4.I5I93 47>242 — 60 779 2.30389 — HM43 — — 60 793 8.3.17.149 237, 68139,144 245, J 6i97, 87 60 811 2.3.5.2027 — 203, 99 88,133487, 15 60 821 4-5-304I 89,230 — — — 60 859 2.27.49.23 — 197,105 244, 21488, 14 60 869 4-15217 65,238 — — — 60 887 2.7.4349 — — — — 60 889 8-3-43-59 I 55, I 92i5 I , I 38 133,120,266, 80 60 899 2.30449 — 207, 95 — — 60 901 4.3.25.7.29 175^74' — 1101,130289, 77 60 913 16.81.47 177,172 19,174161,108322, 72 60 917 4-97-157 199,146 — 60 919 2.3.11.13.71 - J214, 71] 1, 95 60 923 2.83.367 — ji95,i°7| — 60 937 8-3-2539 139,204, 67,168227, 56 395, 57 60 943 2.3.7.1451 190, 91 463, 33 60 953 8. 19.401 133,208105,158 — — 60 961 32.3.5- I2 7 169,180187,114217, 68 !3, 95 61001 8.125. 61 235, 76 99,i6o: 61007 2.11.47.59 — — — — 61027 2-3-7-1453 — 247, 3232, 49 379, 61 61031 2-5-I7-359 — — 61043 2.23.1327 — 129,149: — — 61051 2.3.25.11. 37 — 227, 69208, 77 23, 95 61057 128.9.53 39,244 235, 54 247, 4 259, 81 61091 2.5.41. 149 — 63,169! — — 61099 2.3- I 7-599 — 157,135 56,139 361, 65 61121 64.5.191 185,164 117,154 — — 61129 8.27.283 ^95^S 2 127,150221, 64 29, 95 61141 4.3.5.1019 25,246 — 173,102 346, 68 61151 2.25.1223 — — — — 61153 32-3-49-13 247, 12 229, 66 241, 32 145, 9i 61169 16.3823 113,220 237, 5° — — 61211 2.5.6121 — 213, 89 — — QUADRATIC PARTITIONS. 155 p p-l a b c d A B L M 61 223 2-7-4373 — — — — 61231 2.3-5- I 3-i57 — — 142,117 284, 78 61253 4-i53 r 3 143,202 — — — 61261 4.3.5. 1021 131,210 — 223, 62 37, 95 61283 2. i3- 2 357 225, 73 — — 61291 2.27.5.227 53 5 i7i 188, 93 376, 62 61297 16.3.1277 121,216 247, 12 95,!3 2 190, 88 61 331 2-5-6133 — 9,175 — — 61333 4.3.19.269 247, 18 — 29,142 397, 57 61339 2 3.10223 — 83,165 224, 61 4i, 95 61343 2.30671 — — — 61357 4-3-5ii3 29,246 — 65,138 130, 92 61363 2.9.7.487 — 215, 87 4,i43 425, 49 61379 2.30689 39, J 73 — — 6138L 4.9.5.11.31 159,190 — 203, 82 43, 95 61403 2. 11. 2791 — 75, l6 7 — — 61409 32.19.101 247, 20 219, 82 — — 61417 8.9853 219,116 163,132 77,i36 33 1 , 7i 61441 4096.3-5 225,104 n^S 6 247, I2 494, 8 61463 2.79.389 — — — — 61469 4.121.127 245> 38 — — — 61471 2.9.5.683 — — 202, 83 47, 95 61483 2.3.10247 — 245, 27 100,131 293, 77 61487 2-71-433 — — — — 61 493 4.15373 247, 22 — — — 61507 2.27.17.67 — 35.17* 248, 1 245, 83 61511 2.5-6151 — ..._ — — 61519 2.3.10253 — — 226, 59 49, 95 61543 2.9.13.263 — — i4,M3 443, 43 61547 2.30773 — 165,13! — — 61553 16.3847 7,248 231, 64 — — 61559 2.7.4397 — — — — 61561 8.81.5.19 45> 2 44 181,120 163,108 326, 72 61583 2.41. 751 — — — — 61603 2.3.10267 — 185,117 16,143 4i3, 53 61609 8.3.17.151 147,200 241, 42 53,MC 473, 29 61 613 4.73-2ii 173,178 — — — 61627 2.3.10271 — 205, 99 232, 5 1 464, 34 61 631 2.5.6163 — — — - 61637 4.19.811 1209,134 — — 1 - 1 156 QUADRATIC PARTITIONS. V p-l a b | c d A B L M 61643 2.49.17.37 — 99,161 — — 61651 2.9.25.137 — 199,105 248, 7227, 85 61657 8.3-7.367 229, 96 247, 18 155,112181, 89 61667 2. 11. 2803 — 207, 97 61 67.3 8.13-593 13,248 81,166 61681 16.3.5.257 241, 60 173,126 97,132194, 88 61687 2.9.23.149 — — 238, 41115, 93 61 703 2.30851 — — — — 61717 4.3.37.I39 201,146 — 35,142391, 59 61723 2.243.127 — 235, 57244. 27488, 18 61729 32.3.643 15,248 239, 48 79,136487, 19 61751 2. 125.13.19 — — — . — 61757 4.15439 139,206 — — — 61781 4.5.3089 185,166 — — 61813 4.9.17.101 57>242 — 131,122497, 3 61819 2.3.10303 — 211, 93 212, 75424, 5° 61837 4.3.5153 221,114 — 175,102 35o, 68 61843 2.3.ii.937 — 169,129 116,127 265, 81 61861 4.3-5. io 3* 225,106 — 37,i42 463, 35 61871 2.5.23.269 — — 61879 2.3.10313 — 134,121 229, 85 61909 4.3.7.11-67 247, 30 221, 66442, 44 61927 2.3.10321 — 158,111 3*6, 74 61 933 4-3- I 3-397 227,102 209, 78 418, 52 61 949 4.17. 911 235, 82 — — — 61961 8.51549 245» 44 3,176 — — 61967 2.30983 — — — 61979 2.7.19.233 — 27,175 — — 61981 4.3-5- io 33 85,234 — 247, 18 494, 12 619»7 2.3.10331 — J 37,i47 208, 79 445, 43 61991 2.5.6199 — — — — 62 003 2.29.1069 — 249, 1 — — 62 011 2.9-5. T 3-53 — io7,i59 248, 13 209, 87 62 017 64.3.17. 19 249, 4 203,102 223, 64 4i5, 53 62 039 2.31019 — — — — 62 047 2.81.383 — — J 9°, 93 380, 62 62 053 4-3-5 z 7i 113,222 — 245, 26 323, 73 62 057 8.7757 109,224 207, 98 — — 62 071 2.3.5.2069 — — 86,135 172, 90 62 081 128.5.97 191,160 177,124 — ~~ QUADRATIC PARTITIONS. 157 p *-l a b c d A B L M 62 099 2.61.509 1 _ 249, 7 62 119 2.9.7.17.29 — 206, 81 412, 54 62 129 16.11.353 1 25,248 249, 8 — — 62 131 2. 3.5. 19.109 — 241, 45 28,143401, 57 62 137 8.9.863 5M44 197,108 235, 48470, 32 62 141 4-5- I 3- 2 39 245, 46 — — — 62 143 2-3- io 357 — 50,141 100, 94 62171 2.5.6217 — 1189,115 — — 62189 4.7.2221 205,142! — — — 62191 2.9.5.691 — — 238, 43 367, 65 62 201 8.25.311 149,200249, 10 — — 62 207 2. 19.1637 — — — — 62 213 4.103.151 I 93 > 1 5 8 — — 62 219 2 - T 3- 2 393 — 237, 55 — 62 233 8-3-2593 27,248 4i,i74 5, J 44 10, 96 62 273 64.7.139 223,112 159,136 — — 62 297 8.13.599 221,116213, 92 — — 62 299 2.9.3461 — I*79»"3 104,131 497, 9 62 303 2-3 II 5 I — — — — 62 311 2-3.5-31.67 — — 118,127 499, 3 62 323 2.3.13.17.47 — 239, 51 236, 47 377, ^3 62 327; 2.11.2833 — 62 347; 2.3.10391 — 187,117 52,141 104, 94 62 351 2.25.29.43 — — — — 62 383 2.3.37.281 146,117 292, 78 62 401! 64.3-25.13 249, 20 43,174 233, 52 77, 95 62 417: 16.47.83 169,184 57,172 — — 62 423 2.23.23.59 — — — — 62 459 2. n. 17. 167 51,173 — — 62 467 2.3.29.359 — 247, 27 112,129 224, 86 62 473 8.3.19.137 93,232191,114 101,132 202, 88 62 477 4.15619 211,134 - — — 62 483 2.7.4463 — 225, 77 — — 62 497 32.9.7.3 1 111,224145,144 i7,i44 34, 96 62 501 4.15625 1,250 — — — 62 507 2.31253 — 147,143 — — 62 533 4-81.193 63,242 — 229, 58 403, 57 62 539 2.3.7.1489 — i39,i47 164,109 163, 91 62 549 4.19.823 7,250 — — — 62 563 2.3.10427 I5 X » Z 4* 160,111 329, 74 3^S> 158 QUADRATIC PARTITION'S, p p — 1 | a b c d A B L M 62 581 4.3.5.7.149 9r25o — 109,130 499, 7 62 591 2. 5. 11. 569 — — — — 62 597 4.15649 239, 74 — — — 62 603 2.113-277 — l6 5>i33: — — 62 617 8.3.2609 189,164 245, 36 187, 96 374, 64 62 627 2.173.181 — I 35, 1 49 — — 62 633 8.7829 133,212 189,116 — — 62 639 2.31319 — — — — 62 653 4.3.23.227 I23 y 2l8 • — 215, 74 437, 47 62 659 2-9-59-59 — - M77 172,105 344, 70 62 683 2-3-3 I -337 — 5**77 220, 69440, 46 62 687 2.13.2411 — ■ — — 62 701 4.3.25. 11. 19 99,230 47,142 379, 63 62 723 2. 11. 2851 — 249, 19 — — 62 731 2.9.5.17. 41 — 9 1 > l6 5 212, 77443, 45 62 743 2.3-io457 250, 95°°, 6 62 753 32.37-53 233, 92219, 86 — — 62 761 8.3-5-523 205,144 47,174 181,100481, 27 62 773 4 3-523 1 247> 42 — 211, 78422, 52 62 791 2.3.5.7.13.23 — — 38,143467, 35 62 8<>1 16.25.157 151,200249, 20 — — 62 819 2.49.641 — 159,137 — — 62 827 2-3-37-283 13,177 248, 21 496, 14 62 851 2.3.25.419 — 223, 81 224, 65419, 53 62 861 4-5-7-449 19^50! — — — 62 869 4»3- x 3*i-3-5* 137,210 — 163,110 167, 91 62 873 8.29.271 37,248201,106 — — 62 897 16.3931 239, 76237, 58 — — 62 903 2.7.4493 — — 62 921 8.5-121.13 85,236243, 44 — — 62 927 2-73-43 1 — — — — 62 929 16.9.19.23 73,240199,108 239, 44 37i, 65 62 939 2.31469 — ! 99,163 — — 62 969 8.17.463 235, 88249, 22 — — 62 971 2.3.5.2099 — ! 67,171 148,117 296, 78 62 981 4.5.47.67 241, 70 s — — — 62 983 2.9.3499 — — 226, 63452, 4 62 987 2. 7. 11. 409 — H7,i57 — — 62 989 4.3-29-181 I95>*58 191, 94 9h 95 63 029 4.7.2251 23,25c — — — QUADRATIC PARTITIONS. 159 p p-1 a b c d A B L M 63 031 2.3.5.11.191 — — 82,137329, 73 63 059 2.41.769 — 249, 23 — — 63 067 2-3- 2 3-457 — 245, 39 100,133499, 11 63 073 32.27.73 183,172251, 6 i75, 1 °4 I 37, 93 63 079 2.3 io 5 t 3 2,i45433, 49 63 097 8.3.11.239 171,184:103,162 245, 32 341, 7i 63 103 2.3.13.809 — — 206, 83455, 41 63 113 8.343- 2 3 203,148195,112 — 63 127 2.27.7.167 — — 242, 39 484, 26 63 131 2.5.59.107 — 237, 59 — — 63149 4-I5787 125,218 — — 63 179 2.31. 1019 — 123,155 — — 63 197 4.7.37.61 251, J 4 — — - 63 199 2.9.3511 — — 166,109 493, 19 63 211 2.3.5.49.43 — 173,129 244, 35 139, 93 63 241 8-3-5-I7-3I 221,120 i93,n4 229, 60 458, 40 63 247 2.3.83.127 — — 170,107 49T, 21 63 277 4-3-5273 189,166 — 97,i34 305, 77 63 281 16.5.7. 113 209,140 243, 46 — — 63 299 2.31649 — 201,107 — — 63 311 2 5-J3-487 — — — — 63 313 16.3.1319 247, 48 121,1561119,128 503, 3 63 317 4.11.1439 199^54 — — — 63 331 2.3.5.2111 — 113,159! 16,145 45 1 , 43 63 337 83.7.13.29 219,124 83,168^35, 52 39 1 , 6l 63 347 2. 19. 1667 — 87,167 — — 63 353 8.7919 43,248 249, 26 — — 63 361 128.9.5. 11 231,100 53^74247, 28 33i, 73 63 367 2-3-59 J 79 — — I250, 17 199, 89 63 377 16.17.233 191,164 3,178, — 63 389 4-I3-23-53 245> 58 — — — 63 391 2.3-5-2113 — — i54,i?3 499, 13 63 397 4.27.587 111,226 — 203, 86 461, 39 63 409 16.3.1321 153,200 169,132 89,136 3i9, 75 63 419 2-37-857 — 213, 95 — — 63 421 4-3-5-7-I5 1 139,210 — 137,122 5°3, 5 63 439 2.3.97.109 — 74,i39 343, 7i 63 443 2.31721 — 231, 7i — — 63 463 2.3.7. 1511 — 46,143 3 8 3, 63 63 467 2. 13.2441 — 243, 47 — — 160 QUADRATIC PARTITIONS. p p-l a be d A B 1 L M 63 473 16.3967 217,128 39,5 76 63 487 2-9-3527 — 62,141 124, 94 63 493 4-3 II - I 3-37 193,162 245, 34143* 93 63 499 2.3.19.557 — 29,177236, 51472, 34 63 521 3 2 -5-397 239, 80 III,l6o — — 63 527 2. 23.1381 — 63 533 4.7.2269 83,238 — — 63 541 4-9-5-353 55^46, 221, 70 11, 97 63 559 2. 27. 11. 107 — — 22,145457, 4i 63 577 8.9.883 2 5 T > 2 4 55ri74 37,144; 74, 96 63 587 2.3 J 793 — 177,127 — — 63 589 4-3-7-757 33^5°! — 251, 14293, 79 63 599 2.31799 — — — — 63 601 16.3. 25-53 249, 40247, 36 223, 68 19, 97 63 607 2.3.10601 — — 242, 41365, 67 63 611 2.5.6361 — 237, 61 — — 63 617 1 2 8. 7. 7 1 89,236117,158 — — 63 629 4.15907 227 T IIO — — 63 647 2. 121. 263 — — 63 649 32.9.13.17 2i5> I 3225i, 18 143,120286, 80 63 659 2-7-4547 — 147,145 — 63 667 2.243. 131 — 143^47 212, 79 25, 97 63 671! 2.5.6367 — — — 63 689 8.19.419 235r 92 141,148 — — 63 691 2.3.5. 11. 193 229, 75 248, 27496, 18 63 697 16.3.1327 159,196 227, 78 233t 5 6 j4oi, 59 63 703!2. 9 .3539 — — 86,137 497, 17 63 709 4.3-5309 203,150 — 247, 3° 494, 20 63 719 2.31859 — — — 63727,2.3.13.19.43 — 182,101 485, 27 63 7371 8.31.257 l8l,I76l53,I42 — — 63 743 2.7.29.157 — — 63 761 16.5.797 65,244! 93,l66 — — 63 773 4.107. 149 *97>I58 — — — 63 781 4.3-5- *°6 3 95,234 187, 98 107, 95 63 793 16.9.443 17,252 179,126 121,128 263, 83 63 799 2.3.343.31 — 146,119 5°3, 9 63 803 2.19.23.73 219, 89 — — 63 809 64.997 185,172 21,178 — — 63 823 2.3.11.967 — 250, 21 500, 14 QUADRATIC PARTITIONS. 161 p p-1 a be d A B L M 63 839 2-59-54 1 — — — 63 841 32-3-5-7-I9 79,240 223, 84 71,140 49 1 , 23 63 853 ±$-i7-$*3 157,198 — 209, 82 37, 97 63 857 16.13.307 241, 76 237, 62 — — 63 863 2.37.863 — — — — 63 901 4.9.25.71 251, 3° — 199, 90 398, 60 63 907 2.3.10651 — i75, I2 9 160,113 179, 9i 63 913 8.3.2663 237, 88 241, 54 245, 3 6 490, 24 63 929 8.61. 131 205,148 69,172 — — 63 949 4.3-73-73 243, 7o — 1,146 437, 49 63 977 8.11.727 91,236 45^76 — — 63 997 4.3.5333 59,246 — 7,!4o 43i, 5 1 64 007 2.32003 — — — — 64 013 4.13.1231 253, 2 — — — 64 019 2.32009 23 1 , 73 — — 64 033 32.3.23.29 23,252 59,i74 239, 48 478, 32 64 037 4.7.2287 191,166 — — — 64 063 2-9-3559 — — 230, 61 47, 97 64 067 2.103.311 — 207,103 — — 64 081 16.9.5.89 225,116 253, 6 247, 32 151, 93 64 091 2.5.13.17.29 — 3,179 — — 64109 4.11.31.47 253, 10 — — — 64123 2.3.10687 — 211, 99 236, 53 395, 61 64151 2.25.1283 — — — — 64153 8.729.11 253, 12 251, 24 109,132 218, 88 64157 4-43-373 251, 34 — — — 64171 2.9.5.23.31 — 253, 9 152,117 3°4, 78 64187 2.67.479 — 213, 97 — — 64189 4.9.1783 75,242 — 167,110 497, 19 64 217 8.23.349 221,124 165,136 — — 64 223 2.163.197 — — — — 64 231 2.3.5.2141 — — 34,i45 469, 37 64 237 4-3-53.IOI 61,246 — 17,146 455, 43 64 271 2.5.6427 — — — — 64 279 2-9-3571 — — 98,135 196, 90 64 283 2.32141 — 141,149 — — 64 301 4.25.643 115,226 — — — 64 303 2-3-7-I53 1 — — 106,133 5o5, 9 64 319 2.32159 — — — — 64 327 2.3.71. 151 — — 190, 97 481, 31 162 QUADRATIC PARTITIONS. ,-i a b o d A B L M 64833 4.9-1787 64 373 4.7. 121. 19 64381 4-3-5- 2 9-37 64 399 2.3.10733 64 403 2.13.2477 64 433 16.4027 64 439 2.1 1.29.101 64 451 2.25.1289 64 453 4.3.41. 131 64483 2. 3. 11. 977 64 489 8.3.2687 64 499 2.7. 17. 271 64 513 1024.9.7 64 553 8.8069 64 567 2. 9.17. 211 64 577 : 64.1009 64 579 2.3.47.229 64 591 2.3.5.2153 64 601 8.25.17.19 64 609| 32.3.673 64 613; 4.29.557 64 621 -4.9-5.3S9 hi 6:27 2.3.10771 64 633 8.3. 269 ^ 64 661) 4.5.53.61 64 663 2.3.13.829 64 667J 2.7.31. 149 64 679 2.73.443 64 603 4.27.599 64 709 4.7.231 1 253. 18 247, 58 245, 66 175,106493, 23 233, 58 59, 97 218, 75 436, 5° 225, 83 103,232 135,152 249, 35 185,123 177,182 83,240 209,102 57,i75 217,1321181,126 187,172; 51,176 71,244213, 98 — 241, 57 251, 22 185, 91 56,143485, 29 179,104491, 25 95,!363i3, 77 251, 40 J247, 60 223,122 189,170 237, 92 169,190 233,102 47,250 221,126 64 717 4.3.5393 64 747 2. 27. 11. 109 J 64 763 2.32381 64 7S1 4.5.41.79 109,2^0 64 783 2.9.59.61 64 793 8.7.13.89 64 811 2.5.6481 64 817: 16.4051 64 849 10.3.7. 193 64 853! 4.31.523 253, 2 8 121, 2 24 I05, 232 247, 62 201,110 229, 78 193,117 245, 48 243, 53 235, 69 165,137 75, J 72 27,179 105,164 7,180 202, 89 244, 41 65, 97 121, 95 254, 5269, 83 49,144 98, 96 239, 50389, 63 212, 81424, 54 235, S 6 67, 97 254, 7 233, 87 211, 82 65,142 457, 43 361, 69 188, 99376, 66 [7308, 78 209, 84 418, 56 QUADRATIC PARTITIONS. 163 p P -l a b c d A B L M 64 871 2.5.13.499 — — — — 64 877 4-49-331 19,254 — — — 64 879 2.3.11.983 — 254, 11 287, 81 64 891 2.9.5.7.103 — 253, 21 8,147 16, 98 64 901 4.25.11.59 49,250 — — 64 919 2.7.4637 — — — 64 921 8.3-5-541 195,164 II,l8o 173,108 346, 72 64 927 2.9.3607 — 10,147 20, 98 64 937 8.8117 251, 44 I95,Il6 — — 64 951 2-3-25-433 — 182,103 127, 95 64 969 8.3.2707 213,140 I3,l8o 187,100 487, 29 64 997 4.16249 209,146 — — 65 003 2.7.4643 — l89,I2I — — 65 Oil 2.3.5.11.197 — 169,135 44,i45 39i, 63 65 027 2. 13. 41. 61 — 255, I — — 65 029 4-3-5419 255, 2 251, 26 329, 75 65 033 8.11.739 253, 32 255, 2 — — 65 053 4-9- J 3-i39 197,162 89,138 178, 92 65 063 232531 — — — 65 071 2.27.5.241 — 238, 53 79, 97 65 089 64.9. 1 13 255, 8 17,180 233, 60 466, 40 65 099 2. 121. 269 — 243, 55 — — 65101 4-3-25.7-3I 51,250 — 143,122 5°9, 7 65 111 2-5- I 7-383 — — — 65 119 2.3.10853 — — 74,141 148, 94 65 123 2.32561 — 255, 7 — — 65129 8.7.1163 205,152 177,130 — — 65 141 4.5-3257 25,254 — — — 65147 2.32573 — 237, 67 — — 65 167 2.3.10861 — — 110,133 289, 81 65 171 2-5-343- I 9 — 33,179 — — 65 173 4-3-5431 183,178 — 35,i46 473, 37 65 179 2. 27. 17. 71 — *$h 33 248, 35 353, 7i 65 183 2. 13. 23.109 — — — — 65 203 2.3.10867 — 121,159 164,113 503, i7 65 213 4-7- I 7-i37 133,218 — — — 65 239 2.3.83.131 — — 146,121 217, 89 65 257 8.3.2719 211,144 113,162 205, 88 469, 39 65 267 2.32633 — 255, *i — — 65 269 4.9-49-37 215,138 221, 74 443, 49 164 QUADRATIC PARTITIONS. p p-1 a b c d A B L M 65 287 2. 8i. 13.31 — — 130,127 5«i « 65 293 4-3-5441 93,238 191, 98 485, 31 65 309 4.29.563 53,250 — — 65 323 2. 9.19. 191 — 179,129 176,107 497, 23 65 327 2.89.367 — — — — 65 353 8.3-7-389 43,252 205,108 251, 28 167, 93 65 357 4-16339 29,254 — — — 65 371 2.3.5.2179 — 83,171 136,125 239, 87 65 381 4.5.7.467 191,170 — — — 65 393 16.61.67 143,212 45,178 — — 65 407 2.3.11.991 — — 118,131 275, 83 65 413 4.9.23.79 127,222 — 9M38 182, 92 65 419 2.3.10903 — 149,147 76,141 152, 94 65 423 2.7.4673 — — — — 65 437 4.3.7.19.41 229,114 — 185,102 37o, 68 65 447 2.43.761 — — — — 65 449 8.81. 101 243, 80 143**5° 139,124 5". 5 65 479 2-3-7-1559 — — 214, 81 428, 54 65 497 8.3.2729 99,236 i55, J 44 "5>*3 a 230, 88 65 519 2.17. 41.47 — — — — 65 521 16.9.5. 7.13 89,240 217, 96 167,112 169, 93 65 537 256.256 1,256 255, l6 — — 65 539 2.9.11.331 — 233, 75 256, 1 259, 85 65 543 2.32771 — — — — 65 551 2.3.25.19.23 — — 142,123 284, 82 65 557 4.27.607 71,246 — 163,114 326, 76 65 563 2.3.49.223 — 229, 81 256, 3 512, 2 65 579 2.32789 — 99,167 — — 65 581 4.3-5-I093 195,166 — |24i, 5° 9*i 97 65 587 2.3.17.643 — I37ii53 *5*»"9 509, 11 65 599 2.3.13.29.29 — — 254, 19 197, 91 65 609 8.59-I39 253, 40 159,142 — — 65 617 16.3.1367 9,256 247, 48 175,108 35o, 72 65 629 4.9.1823 235,102 — 41,146 479, 35 65 633 32.7.293 247, 68 219, 94 — — 65 647 2.9.7.521 — — 202, 91 475, 37 65 651 2.25.13.101 — «77» I 3 I — — 65 657 8.29.283 11,256 i35,i54 — — 65 677 4.3.13.421 141,214 — I45,T22 221, 89 65 687 2.32843 — — QUADRATIC PARTITIONS. 165 p p-1 a b c d A B L M 65 699 2.107.307 — 249. 43 — — 65 701 4-9- 2 5-73 255> 26 — 251, 3° 502, 20 65 707 2. 3-47-233 — 85,171 88,139 5o5, i7 65 713 i6.3-37-37 47.252 115,162 1,148 445, 49 65 717 4-7-2347 121,226 — — — 65 719 2.27. 1217 — — 238, 55 403, 61 65 729 64.13.79 65,248 81,172 — — 65 731 2-3-5-7-3I3 — 209,105 232, 63 464, 42 65 761 3 2 -3-5- I 37 15*256 31,180 7,i48 45*i 47 65 777 16.4111 79,244 243, 58 — — 65 789 4.16447 85,242 — — — 65 809 16.9.457 255. 28 253, 3o 247, 40 367, 69 65 827 2.27-23-53 — 215, 99 148,121 5". 9 65 831 2.5.29.227 — — — — 65 837 4.109.151 211,146 — — — 65 839 2.3.10973 — — 254, 21 508, 14 65 843 2.7.4703 — *$h 79 — — 65 851 2.3.25.439 — 203,111 32,147 64, 98 65 867 2.32933 165,139 — — 65 881 8.27.5.61 91,240 73^74 13,148 457, 45 65 899 2.9-7-523 107,165 256, 11 223, 89 65 921 128.5. 103 161,200 63,176 — — 65 927 2.7.17.277 — — — — 65 929 8.3.41.67 227,120 223, 90 61,144 122, 96 65 951 2.25.1319 — — — — 65 957 4.11.1499 239. 94 — — — 65 963 2.13-43-59 — | 21,181 — — 65 981 4-5-3299 59,250 — — 65 983J2. 3 . 7 .i57i — — 34,H7 68, 98 65 993 8. 73. 1 13 67,248 255, 22 — — 66 029 4. 17.97 1 173,190 — — — 66 037 4-3-55°3 39,254 — 253, 26 175, 93 66 041 8.5.13.127 235> io 4 153^46 — — 66 047 2.33023 — — — — 66 067 2.3.7. 121. 13 — 257, 3 248, 39 496, 26 66 071 2.5.6607 — — — — 66 083 2.19.37.47 — 255, 23 — — 66 089 8.11.751 133,220 141,152 — — 66103 2.3.23.479 — — 254, 23 323, 77 66107 2-33°53 — 45^79 — — 166 QUADRATIC PARTITIONS. p p — 1 a b c d A B L M 66 109 4.3.7.787 245, 78 — 199, 94 481, 35 66 137 8.7.1181 251, 56 105,166 — 66 161 16.5827 25.256 231, 80 — — 66 169 8.9.-919 237,100 37>i8o 221, 76 7, 99 66173 4.7I.233 203,158 — — 66179 2.7.29.163 — I 59 > 1 43 — — 66 191 2.5.6619 — — — — 66 221 4.5.7.II.43 61,250 — — — 66 239 2.33119 — — — — 66 271 2.3.5.47.47 — — 38,147 76, 98 66 293 4.16573 137,218 — — — 66 301 4.3.25.13.17 149,210 — 247, 42 494, 28 66 337 32.3.691 239, 96 257, J 2 25,148 469, 4i 66 343 2.3.11057 — 134,127 247, 87 66 347 2.49.677 — i95> IX 9 — — 66 359 2-33*79 — — — — 66 361 8.3.5.7.79 205,156 133^56 253, 28 337, 75 66 373 4-3-553 1 257> 18 — 245, 46 107, 97 66 377 8.8297 29,256 255> 26 — — 66 383 2.33191 — — — — 66 403 2.9.7.17. 31 — 89,171 256, 17 205, 91 66 413 4.16603 227,122 — — — 66 431 2.5.7.13.73 — — — — 66 449 16.4153 257, 20 93,170 — — 66 457 8.9-13.71 219,136 233, 78 197, 96 394, 64 66 463 2.3.11. 19.53 — — 214, 83 35, 99 66 467 2. 167. 199 — 225, 89 — — 66 491 2.5.61. 109 — 243, 61 — — 66 499 2.3.11083 — 257, 15 232, 65 37, 99 66 509 413.1279 253,50 — — 66 523 2.3.11087 245, 57 ^16,133 283, 83 66 529 32.27.7. 11 J 55,252 251, 42 239, 56 407, 61 66 533 4.16633 (257, 22 — — — 66 541 4.3-5- iio 9 45, 2 54J 97,138194, 92 66 553 8.3-47.59 ;I47>2I2,229, 84 29,148415, 59 66 569 8-53- J 57 163,200129,158 — — 66 571 2.3-5-7.3 I 7 — 211,105 164,115181, 93 66 587 2.13.13.197 1 — 213,103 — — 66 593 32.2081 113,232255, 28 — 66 601 8.9.25.37 251, 60 253, 36 203, 92 479, 37 QUADRATIC PARTITIONS. 167 P p-1 a a b L M 66 617 66 629 66 643 66 653 66 683 66 697 66 701 66 713 66 721 66 733 66 739 66 749 66 751 66 763 66 79l| 66 797; 66 809! 66 8211 66 841 66 851 1 66 853 66 863! 66 877i 66 883! 66 889 66 919 66 923 66 931 66 943 66 947 66 949 66 959 66 973 66 977 67 003 67 021 67 033 67 043 67 049 67 057 8.II.757 181,184 57,i78 4.16657 223,130 — 2. 3-29.383 — 239, 69 4.19.877 187,178 — 2-7 n-433 — 5 I , I 79 837.397 189,176 257, 18 4.25.23.29 125,226 — 8.31.269 253. 52 69,176 323-5- 1 39 105,236 187,126 4.3.67.83 13,258 — 2.3.49.227 191,123 4.11. 37.41 245, 82 — 2.3.125.89 — — 2.9.3709 — 91,171 2.5.6679 — — 4.16699 221,134 — 8.7.1193 203,160 231, 82 4-5- I 3-257 145,214 — 8-3-5-557 229,120 247, 54 2. 25. 7. 191 — 201,115 4.27.619 17,258 — 2.101.331 — — 4-3-5573 171,194 — 2-3-7 I - I 57 — 65,177 8.9.929 235,108 179,132 2.3.19.587 — — 2.33461 — 99,169 2.3.5-23-97 — 257, 21 2.9.3719 — — 2. 11. 17. 179 — 255, 3i 4-3-7-797 257, 30 — 2-33479 — — 4.3.558i 133,222 — 32-7- I 3-23 169,196 27,182 2 -3- I 3-859 — 5,183 4-3-5- III 7 211,150 — 8.9.49.19 197,168 215,102 2.33521 — 39, J 8i 8.17. 17. 29 115,232 207,110 16. 3. 11. 127 39,256 103,168 196, 97487, 33 67,i44i34, 96 89,140509, 17 79,i42 5 5, 21 244, 49 39 1 , 65 202, 93404, 62 44,147 88, 98 133,128251, 87 149,122515, 9 167,114334, 76 136,127517, 3 251, 36502, 24 62,145 373, 69 184,105368, 70 46,147 92, 98 139,126 55,^6 20,149 257, 18 179,108 223, 76 278, 84 383, 67 467, 43 5*4, 12 358, 72 45*i 49 168 QUADRATIC PARTITIONS. p p-l a b c d A B L M 67 061 4-5-7-479 119,230 — — — 67 073 512.131 257. 32 255. 32 — — 67 079 2. 11. 3049 — — — — 67 103; 2-7-4793 — — — — 67 1211 16.5.839 239,100 237. 74 — — 67 129) 8.3.2797 75.248 121,162 259. 4 271. 85 67 139 2-335 6 9 — 23 1 . 83 — — 67 141 4-9-5-373 255i 46 — 229, 70 439.' 53 67 153 16.3.1399 223,132 259. 6 145,124 $*y 7 67 157 4. 103. 1 63 199,166 — — — 67 169 32.2099 137,220 219, 98 — — 67181 4-5-3359 259, 10 — — — 67187 2.7.4799 — 225, 91 — — 67 189 4.3.11.509 25.258 — 259. 6 518, 4 67 211 2.5.11.13.47 — I47.J5 1 — — 67 213 4.9.1867 93,242 — 239. 58 65. 99 67 217 16.4201 41,256 153^48 — — 67 219 2.3.17.659 — H3> l6 5 112,135 224, 90 67 231 2.81.5.83 — — 166,115 51*1 x 7 67 247 2.33623 — — — — 67 261 4-3-5- 1 9-59 69,250 — 217, 82 463, 45 67 271 2-5-7-3 I -3 I — — — — 67 273 8.3.2803 213,148 221, 96 259. 8 235. 89 67 289 8.13.647 155,208 183,13° — — 67 307 2.73.461 — 195,121 — — 67 339 2.27.29.43 — 19.183 244. 5 1 488, 34 67 343 2. 11. 3061 — — — — 67 349 4.113.149 185,182 — — — 67 369 8.3.7.401 187,180 259, 12 109,136 5 J 7. 9 67 391 2.5-23-293 — — — — 67 399 2.3-47-239 — — 254. 31 161, 95 67 409 16.11.383 247, 80 249. 52 — — 67 411 2.9.5.7.107 — 233. 81 256, 25 33i. 77 67 421 4-5-3371 245, 86 — — — 67 427 2.33713 — 87.173 — — 67 429 4.9.1873 177,190 59.!4° 497. 29 67 433 8.8429 77,248 111,166 — 67 447 2.27.1249 — — 158,119 5i5. 13 67 453 4.3-7-II-73 203,162 — 151,122 215. 9i 67 477 4-3-5 62 3 249, 74 253, 34 355. 73 QUADRATIC PARTITIONS. 169 p P -\ a b c d A B L M 67 481 8.5.7.241 259, 20 117,164 _ — 67 489 32.3.I9-37 i75, x 92 239, 72 241, 56 73, 99 67 493| 4-47-359 257, 38 — — — 67 499 2.33749 — 243, 65 — — 67 511 2.5-43-I57 — — — — 67 523 2-49-I3-53 — i35,!57 — — 67 531 2.3.5.2251 — 259, *5 52,i47 104, 98 67 537 16.9.7.67 161,204 253, 42 73,i44 146, 96 67 547 2.33773 — 45, lSl — — 67 559 2. 17. 1987 — — — — 67 567 2.3.11261 — — 98,139 3i9, 79 67 577 8.8447 109,236 75,i76 — — 67 579 2.3.7.1609 — 229, 87 248, 45 496, 30 67 589 4.61.277 95,242 — — — 67 601 16.25.13.13 1,260 99,170 — — 67 607 2.7.11.439 — — — — 67 619 2.33809 — 249, 53 — — 67 631 2.5.6763 — — — 67 651 2. 3.25. 11. 41 — 167,141 212, 87 424, 58 67 679 2.13.19.137 — — — — 67 699 2.9.3761 — 7i,i77 68,145 367, 7i 67 709 4.16927 197,170 — 67 723 2.3.11287 — 131,159256, 27 512, 18 67 733 4.7.41.59 247, 82 — — 67 741 4.3.5.1129 85,246 103,138 206, 92 67 751 2. 125. 271 — — 67 757 4.i3- I 3°3 259, 26 — — — 67 759 2.3.23.491 — — 34,i49 4i3, 61 67 763 2.17.1993 — 255, 37 — 67 777 64.3-353 249, 76; 85,174 257, 24 5Mi 16 67 783 2.3.11. 13.79 — — 254, 33 508, 22 67 789 4.9.7.269 35,258 17,150 34,100 67 801 8.3.25.113 101,240 i5 I » I 5° 251, 40 I3 1 , 97 67 807 2.9.3767 — — 238, 61 421, 59 67 819 2.3.89.127 — 29,183 196, 99 392, 66 67 829 4-31-547 73,25o — — — 67 843 2.9.3769 — i45,!53 260, 9 520, 6 67 853 4.16963 253, 62 — — — 67 867 2.3.11311 — i57,i47 128,131 521, 1 67 883 2.33941 — I7M39 — — 170 QUADRATIC PARTITIONS. p j,-l a b c d A B L M 67 891 2-3-5-3I-73 97,i7i 172,113 167, 95 67 901 4.25.7.97 251, 70 — — — 67 927 2.3.11321 — — 190,103 499, 29 67 931 2.5-6793 — 141,155 — — 67 933 4.27.17.37 37,258 — 185,106 133, 97 67 939 2.3.13.13.67 — 31,183 176, 1 11 352, 74 67 943 2. 7. 23. 211 — — — — 67 957 4.3.7.809 201,166 — 227, 74 449, 5 1 67 961 8.5.1699 19,260 219,100 — 67 967 2.17.1999 — — — — 67 979 2.41.829 — 189,127 — — 67 987 2.27.1259 — 73, I 77l I 4o,i27 241, 89 67 993 8.3.2833 67,252 139,156229, 72 458, 48 68 023 2.9.3779 — — 230, 71 443, 53 68 041 8.243.5.7 21,260163,144221, 80 461, 47 68 053 4.3.53-io7 137,222 259, 18 518, 12 68 059 2.9.19.199 — 253, 45 256, 29 169, 95 68 071 2.3.5.2269 — — 1 82,143 347, 75 68 087 2.59.577 — — — — 68 099 2.79.431 — 111,167 — — 68111 2.5.49.139 — — — — 68113 16.9.11.43 127,228 125,162 49,148493, 33 68 141 4.5-3407 179,190 — i — — 68147 2. 13. 2621 — 105,169 — 68161 64.3.571 255, 56 223, 96233, 68437, 55 68171 2.5. 17.401 — 261, 5 — — 68 207 2.67.509 — — — — 68 209 16.3.49.29 103,240 247, 60 97,140323, 79 68 213 4-17053 233> II 8 — — — 68 219 2.23.1483 261, 7 — — 68 227 2.3.83.137 — 257, 33 200, 97 91, 99 68 239 2.9.17.223 — — 194,101497, 31 68 261 4.5.34I3 175^94 — — — 68 279 2.7.4877 — — — — 68 281 8.3.5569 141,220 59,180 259, 20199, 93 68 311 2. 27. 5. 11. 23 — — 242, 57 484, 38 68 329 8.9-I3-73 27,260 109,168 149,124 223, 91 68 351 2.25.1367 — — — — 68 371 2.3-5-43-53 — 239, 75 236, 65 43i, 57 68 389 4.3-4I.I39 255, 58 — i33,*3° 523, 1 QUADRATIC PARTITIONS. 171 p p-\ a b c d A B L M 68 399 1 2. II. 3IO9 — — — — 68 437 4.9.I9OI 89,246 — 67,146 37i, 7i 68 443 2. 3. 11. 17. 6l — 221, 99 124,133 523, 3 68 447 2.7.4889 — — — 68 449 32.3.23.3I 207,160 241, 72 79,!44 158, 96 68 473 8.27.317 213,152! 89,174 139,128 245, 89 68 477 4-I7-I9-53 251, 74 — — — 68 483 2.97.353 — 129,161 — — 68 489, 8.7.1223 245> 92 189,128 — — 68 491 2.9.5.761 — 179,135 152,123 304, 82 68 501 4.125-137 199,170 — — — 68 507 2.34253 — 93,173 — — 68 521 8.3.5.57I 261, 20 61,180 53,148 39i, 67 68 531 2.5. 7. 11. 89 — 9,185 — — 68 539 2.3.11423 — 259, 27 44,149 49i, 35 68 543 243.797 — — — — 68 567 2.34283 — — — — 68 581 4.27.5.127 225,134 — 107,138 214, 92 68 597 4-II.I5S9 15^214 — — — 68 611 2.3.5.2287 — 119,165 244, 55 409, 63 68 633 8.23.373 253, 68 261, 16 — — 68 639 2.34319 — — — — 68 659 2.3.11443 — 41,183 16,151 469, 45 68 669 4.17167 5,262 — — — 68 683 2.3. 1 1447 — 101,171 260, 19 203, 93 68 687 2.61.563 — — — — 68 699 2.49.701 — 261, 17 — — 68 711 2.5.6871 — ■ — — — 68 713 8.3.7.409 237,112 175^38 ns,^ 523, 7 68 729 8.121.71 85,248 249, 58 — — 68 737 128.3.179 231,124 245, 66 55,H8 499, 3 1 68 743 2.27.19.67 — — 86,143 5J5, 19 68 749 4.3.I7.337 157,210 — 257, 3° 514, 20 68 767 2-3-73-I57 — — 182,109 145, 97 68 771 2.5.13.23.23 57,i8i — — 68 777 8.8597 251, 76 195,124 — — 68 791 2.3.5.2293 — — 262, 7 283, 85 68 813 4.17203 13,262 — — — 68 819 2.19.1811 — 87,175 — — 68 821 4.3.5.3L37 185,186 211, 90 422, 60 172 QUADRATIC PARTITIONS. p P -l a b c d A B L M 68 863 2.3-23-499 — — 226, 77 5» IQI 68 879 2-34439 — — — — 68 881 16.3:5.7.41 191,180 259* 3° 241, 60 482, 40 68 891 2.5-83-83 — 21,185 — — 68 897 32.2153 241,104 255> 44 — — 68 899 2.3.11483 — 79>i77 224, 79 13,101 68 903 2-47-733 — — — 68 909 4.7.23.107 253> 7o — — 68 917 4-3-5743 * I 9> 2 34 — 173,114346, 76 68 927 2. 11. 13. 241 68 947 2.3.11491 — 247. 63 232, 71 19,101 68 963 2.29.29.41 — 249> 59 — — 68 993 1 28.49. 1 1 217,148; 75,178 — — 69 001 8.3.125.23 i95 ) I 76i93 ) I2 6 101,140521, 13 69 011 2.5.67.103 — I 53 > i5 I — — 69 019 2.3.11503 — |i49,i53 196,101 107, 99 69 029 4.17257 127,230 — — 69 031 2.9-5-!3-59 — — 202, 97 493, 35 69 061 4.3.5- II 5 1 81,250 — 181,110 i49, 97 69 067 2.27.1279 — 197,123 220, 83 29,101 69 073 16.3.1439 87,248 185,132 209, 92 485, 39 69109 4.3.13.443 247, 90 — 259, 26 181, 95 69119 2-7-4937 — — — — 69 127 2. 3. 41. 281 — — 250, 47 109, 99 69 143 2. 181. 191 — — — — 69149 4-59-293 235, IlS — — — 69151 2.3.25.461 — — 262, 13 3 QI , 83 69 163 2.3.11527 — 211,111 236, 67 35, IQ i 69 191 2. 5. 11. 17. 37 — — — — 69193 8.9.31. 31 253> 72 1,186 59,148 385, 69 69197 4.17299 259, 46 1 — 69 203 2-7-4943 — 231, 89 — 69 221 4.5-346i 239,110 — — — 69 233 16.4327 263, 8 39*184 — — 69 239 2.13.2663 — — — — 69 247 2.9.3847 ■ — — 98,141 196, 94 69 257 8.11.787 61,256 255> 46 — — 69 259 2.3.7.17.97 — 259, 33^72,115 5 J 7, i9 69 263 2.34631 — — — 69 313 64.3.19.19 263, 12 11,186 1,152 455, 5 1 QUADRATIC PARTITIONS. 173 p p-1 a b c d A B L M 69 317 4-I3-3M3 241,106 — — 69 337 8.81.107 99,244 235, 84 5,152 461, 49 69 341 4-5-3467 229,130 — — 69 371 2.5.7.991 — 261, 25 — — 69 379 2-3.3!-373 — 49,^3 164,119 521, 15 69 383 2. 113.307 — — — — 69 389 4. 1 1. 19.83 83,250 — — 69 401 8.25.347 251, 80 183,134 — — 69 403 2.3.43.269 — 205,117 200, 99 400, 66 69 427 2.9.7.19.29 — 233, 87 32,151 421, 61 69 431 2 -5-53- I 3i — — — — 69 439 2.3.71. 163 — — 134,131 527, 1 69 457 16.3.1447 151,216 263, 12 215, 88 49,101 69 463 2.9.17.227 — — 194,103 115, 99 69 467 2 -47-739 — 117,167 — — 69 473 32.13.167 247, 92 261, 26 — — 69 481 8.9.5.193 109,240 17,186 13,152 443, 55 69 491 2.5.6949 — 63,181 — — 69 493 4-3-5791 263, 18 — 125,134 527, 3 69 497 8.7.17.73 139,224 57,i82 — — 69 499 2.243.11.13 — 251, 57 184,109 5ii, 25 69 539 2.7.4967 — 33,i85 — — 69 557 4.17389 71,254 — — — 69 593 8.8699 157,212 219,104 — — 69 623 2-7-4973 — — — — 69 653 4.11.1583 263, 22 — — — 69 661 4.81.5.43 165,206 167,118 187, 95 69 677 4.17419 179,194 — 69 691 2. 3.5. 23.101 — i73, x 4i 188,107 5°9, 27 69 697 64.9.121 1,264 i45, x 5 6 193,104 119, 99 69 709 4-3-37-157 195,178 — 47,15° 94,100 69 737 8.23.379 101,244 45,^4 — — 69 739 2-3-59-197 — 229, 93 56,149 5°3, 3i 69 761 128.5. 109 65,256 207,116 — — 69 763 2.3.7.11.151 — 191,129 116,137 527, 7 69 767 2.34883 — — — — 69 779 2. 139.251 — 129,163 — ■ — 69 809 16.4363 47,260 141,158 — — 69 821 4.5.3491 155,214 — — — 69 827 2-349 r 3 — 255, 49 — — 174 QUADRATIC PARTITIONS. p-1 A B L M 69 829 69 833 69 847 69 857 69 859 69 877 69 899 69 911 69 929 69 931 69 941 69 959 69 991 69 997 70 001 70 003 70 009 70 019 70 039 70 051 70 061 70 067 70 079 70 099 70111 70117 70121 70 123 70139 70141 70157 70163 70177 70181 70183 70199 70 201 70 207 70 223 70 229 4.3.11. 23.23 8.7.29.43 2.3.7.1663 3 2 -37-59 2.9.3881 4.27.647 2.34949 2.5.6991 8.8741 2.27.5-7-37 175,198 — 149,1261298, 84 63,208225, 98 — — I 38,151415. 6 3 165,146 199,123 119,236 199,174 4.5.13.269 2.7.19.263 2.3-5-2333 4-3- I 9-3°7 16.625.7 2.9.3889 8.3.2917 2.13.2693 2.27.1297 2.3.25.467 4-53I-H3 2.53.661 2-37-947 2.3.7.1669 2.9.5. 19.41 4-3-5843 8-5-1753 2.3.13.29.31 2.35069 4-3-5-7-!67 4.17539 2.35081 32.3-!7-43 4.5. 121. 29 2.9-7-557 2-35°99 8.27.25.13 2.3.11701 2.35m 4.97. 181 173,200 215^54 259, 54 49,260 147,220 131,230 239,114 211,160 93^75 81,178 107,171 243> 74 55» l8 3 203,120 9,187 263, 21 135. 161 257, 45 111,170 259> 39 I7M43 224, 81 77ii46 248, 53 178,113 127,134 448, 54 515. 23 407> 6 5 161, 97 275. 87 40, 15 1 493. 37 221, 84 166,119 124,135 75.254 221,146 169,204 241,110 51,260 265, 2 1 5^87 133,162 442, 5 6 191. 95 248, 90 256, 39 238, 67 245. 58 260, 29 263, 18 145,128 94,H3 512, 26 439, 57 71,101 347. 77 526, 12 239. 9i 335, 79 251, 60 67,148 202, 99 5 11 , 2 7 404, 66 QUADRATIC PARTITIONS. 175 p p-1 a b c d A B L M 70 237 4.9.1951 261, 46 — 265, 2S259, 89 70 241 32-5-439 265, 4 123,166 70 249 8.3.2927 205,168 241, 78 107,140527, 11 70 271 2.5.7027 — — — — 70 289 16. 23. 191 8,265 231, 92 — — 70 297 8.3.29. 101 69,256 265, 6 173,116 521, 19 70 309 4.81. 7. 31 145,222 — 53, I 5° 106,100 70 313 8.11.17.47 187,188 5 I , I 84 — 70 321 16.3.5.293 25,264 263, 24 217, 88 481, 43 70 327 2.9.3907 — — 10,153 20,102 70 351 2.3.25.7.67 — — 158,123 316, 82 70 373 4.73.241 193,182 — — — 70 379 2. 7. 11.457 — 21,187 — — 70 381 4.9.5.17.23 125,234 — 257, 38 37i, 73 70 393 8.3.7.419 83,252 245, 72 181,112 5*7, 23 70 423 2.3.121.97 — — i4,i53 28,102 70 429 4.3.5869 245,102 — 151,126 302, 84 70 439 2.41.859 — — — — 70 451 2.25.1409 — 249, 65 — — 70 457 8.8807 179,196 213,112 — — 70 459 2.3-i J 743 — 59,183 104,141 208, 94 70 481 16.5.881 265, 16 183,136 — — 70 487 2.13.2711 — — — — 70 489 8.9.11.89 165,208 233, 9o 91,144 182, 96 70 501 4-3- I2 5-47 255, 74 — 251, 5° 401, 67 70 507 2.9.3917 — 253, 57 112,139 529, 9 70 529 128.19.29 95,2481177,1/1 — — 70 537 8.3.2939 29,264 223,102 35,!5 2 49i, 39 70 549 4-3-5879 265, 18 — 259, 34 361, 75 70 571 2.5-7057 — 261, 35 — — 70 573 4.3.5881 227,138 — 161,122 527, 13 70 583 2.35291 — — — 70 589 4.7.2521 133,230 — — 70 607 2.43.821 — — — — 70 619 2. 17. 31. 67 — 237, 85 — — 70 621 4.3.5. 11. 107 261, 50 — 263, 22 i97, 95 70 627 2.3.79.149 — 263, 27 20,153 40,102 70 639 2.3.61. 193 — — 214, 91 487, 41 70 657 1024.3.23 31,264 257, 48 265, 12 53o, 8 70 663 2.3.11777 — — 206, 97 85,101 176 QUADRATIC PARTITIONS. v- A B L M 70 667 70 687 70 709 70 717 70 729 70 753 70 769 70 783 70 793 70 823 70 841 70 843 70 849 70 853 70 867 70 877 70 879 70 891 70 901 70 913 70 919 70 921 70 937 70 949 70 951 70 957 70 969 70 979 70 981 70 991 70 997 70 999 71011 71 023 71039 71059 71069 71081 71089 71119 2.89.397 2. 27. 7. 11. 17 4.11.1607 4-3-7I-83 8.3.7.421 32.3.11.67 16.4423 2.3.47.251 8.8849 2.17.2083 8.5.7. 11. 23 2.3.11807 64.27.41 4-I77I3 2.9.31. 127 4.13.29.47 2.3.11813 2-3-5- I 7- I 39 4.25.709 256.277 2.59.601 8.9.5.197 8.8867 4-17737 2.3.25. 11. 43 4-243-73 8-3-2957 2.23.1543 4-3-5-7-I3-I3 2.5.31.229 4.17749 2-3- Il8 33 2.27.5.263 2.3.7.19.89 2. 11. 3229 2.3.13.911 4.109.163 8.5-1777 16.3. 1481 2.81.439 265, 22 101,246 85,252 137,228 263, 40 203,172 245,104 57,260 47,262 11,266 265, 26 97,248 27,187 77,180 101,174 9,188 195,128 153^54 i55> 1 53 181,138 215,111 221,105 15,188 230, 77 233, 74 227, 80 71,148 461, 5 1 455, 467, 53 49 266, 3 373, 73 532, 2 224, 83473, 47 257, 4oi37, 99 260, 33520, 22 106,141:212, 94 212, 93I424, 62 35,2641161,150 229,1361 87,178 257, 7° 141,226 213,160 15,266 169,206 187,190 59,260 185,192 263, 30 249, 6 7 143,159 209,117 141,160 121,168 253, 48 98,143 193,106 259, 36 59,i5o 266, 9 28,153 134,133 128,135 167,120 266, 11 5° 6 > 32 527, 15 511, 29 518, 24 118,100 532, 6 56,102 265, 89 256, 90 334, 299, 80 85 QUADRATIC PARTITIONS. 177 p- A B L M 71129 71143 71 147 71153 71161 71167 71171 71191 71209 71233 71237 71249 71257 71261 71263 71287 71293 71317 71 327 71329 71 333 71339 71341 71347 71353 71359 71363 71387 71 389 71399 71411 71413 71419 71429 71 437 71443 71453 71471 71473 71479 8.17.523 2. 3.71. 167 2-35573 16.4447 S-3-5-593 2.3.29.409 2. 5. 11. 647 2.9.5.7. 113 8.9.23.43 64.3.7-53 4.11.1619 16.61.73 8.3.2969 4-5-7-5°9 2.9.37.107 227,140 21,188 — — '254, 47 — i 75,181 — 167,208 201,124 75,256103,174' — 207,119 197^80253, 60 257> 72,239, 84 209,166 — 265, 32249, 68 261, 56137,162 245,106 2.3. 109.109 — 4-3-13-457 267, 4.9.7.283 2. 19.1877 32.3.743 123" , 2 ,134 177,200 4.17.1049 1113,242 2.53-673 4.3.5.29.41 221,150 2.3.11. 23.47 8.9.991 2.3.7.1699 2.31.1151 2.7.5099 4.27.661 2. 29.1231 2 .5.37.i93 4.3.11.541 2.3.11903 4-7-255 1 4-3-5953 2.729.49 4.17863 2.5.7.1021 16.3.1489 2. 9. 11. 19. 19 267, 8 267, 10 247,102 175,202 259, 66 ; 53>262 263, 48 2a 191,132 267, 5 263, 33 199,126 135,163 267, 7 231, 95 187,135 1,189 151,156 43,*5 2 262, 29 122,137 203,100 95,!44 197,104 266, 13 218, 89 119,138 13,154 209, 96 257, 42 100,143 149,128 178,115 217, 90 259, 38 116,139 395, 69 413, 175, 533, 5 97,101 190, 96 509, 3i 227, 93 485, 43 238, 92 475, 47 418, 64 244, 63 191,108 166,121 5 J 4, 329, 28 . 81 533, 7 5 2 3* 21 434, 60 145, 3 QI , 17,154445, 57 488, 42 382, 72 529, 15 178 QUADRATIC PARTITIONS. p p-1 a be d A B L M 71483 2.103347 — 261, 41 — — 71503 2.3.17. 701 — — 70,149 377, 73 71527 2.3.7. 13.131 — — 262, 31 355, 77 71537 16.17.263 241,116 147,158 — — 71549 4-31-577 155,218 — — — 71 551 2-27-25.53 — — 82,147 164, 98 71563 2.3.11927 — 11,189 136,133 535, 1 71569 16.9.7.71 63,260 163,150 113,140 533, 9 71 593 8.3.19.157 243,112 49,186 139,132 278, 88 71597 4.7.2557 29,266 — -— — 71633 16.121.37 223,148 189,134 — — 71647 2.3.1 1941 — — 142,131 251, 9i 71663 2.35 8 3 r — — — — 71671 2.3.5.2389 — — 38,153 76,102 71 693 4.17923 227,142 — — — 71699 2. 11. 3259 — 57,i85 — — 71707 2. 3.17. 19.37 — **S>*1* 260, 37 149, 99 71711 2.5.71.101 — — — — 71713 32.27.83 233^32 251, 66 49,152 407, 67 71719 2.3-1*953 — — 254, 49 107,101 71741 4.5.17.211 85,254 — — — 71761 16.3.5. 13.23 119,240 263, 36 169,120 338, 80 71777 32.2243 79,256 33,i88 — — 71789 4.i3!-i37 115,242 — — — 71807 2.7.23.223 — — — 71809 128.3.11.17 153,220 139,162 247, 60 494, 40 71821 4.27.5.7.19 189,190 — 239, 7° 29,103 71837 4.17959 251, 94 — — — 71 843 2. 17. 2113 — 225,103 — — 71849 8.7.1283 5,268 243, 80 — — 71 861 4-5-3593 185,194 — — — 71867 2.35933 — 267, 17 — 71879 2.83.433 — — — 71881 8.3.5.599 195,184 257, 54 259, 40 379, 73 71887 2.3.11981 — — 118,139 535, 7 71899 2.3.23.521 : — 211,117 268, 5 253, 9 1 71909 4.17977 97,250 — — — 71917 4.3.13.461 i3!, 2 34 223, 86 35, IQ 3 71933 4.49.367 197,182 — — — 71941 4.3.5.11.109 225,146 — 107,142 3i9, 83 QUADRATIC PARTITIONS 179 p p-1 a b c d A B L M 71947 2.97.571 — 253, 63 248, 59 425, 63 71963 2. n. 3271 — 45, l8 7 — — 71971 2-3-5- 2 399 — 23,189 268, 7 289, 87 71983 2.27.31.43 — — 194,107 5*5, 29 71987 2 -35993 — 255, 59 — — 71993 8.8999 13,268 261, 44 — — 71999 2.35999 — — — — 72 019 2.9.4001 — 71,183 212, 95 497, 39 72 031 2.3.5.2401 — — 242, 67 41,103 72 043 2.3.12007 — 229, 99 176,117 352, 78 72 047 2.13.17.163 — — — — 72 053 4.18013 217,158 — — — 72 073 8.9.7.11.13 267, 28 125,168 221, 88 43, io 3 72 077 4-37-487 211,166 — — — 72 089 8.901 1 67,260 267, 20 — — 72 091 2.81.5.89 — 197,129 4,i55 461, 53 72 101 72103 4.25.7.103 145,226 — — — 2.3.61. 197 — — 154,127 535, 9 72 109 4.9.2003 253, 9° — 3i,i54 493, 4i 72 139 2.3.11. 1093 — !33> l6 5 8,i55 473, 49 72 161 32.5.11.41 265, 44 219,110 — — 72 167 2.36083 — — — — 72 169 8.3-31-97 165,212 221,108 aii, 96 422, 64 72173 4.18043 157,218 — — — 72 211 2.3.5.29.83 — 263, 39 244, 65 49, io 3 72 221 4-5- 2 3-!57 i39. 2 3 — — — 72 223 2.3.12037 — — 86,147 172, 98 72 227 2. 49.11. 67 — i77,i43 — — 72 229 4.3- I 3-463 223,150 91,146 347, 79 72 251 2.125. 17.17 — 123,169 — — 72 253 4.81.223 117,242 — 265, 26 187, 97 72 269 4.7.29.89 125,238 — — — 72 271 2.95.11.73 — — 14,155 479, 47 72 277 4-3- I 9-3 I 7 39,266 157,126 3 r 4> 84 72 287 2.47.769 — — — — 72 307 2.27. 13.103 — 73,183 188,111 376, 74 72 31c 1 8.3.23.131 267, 32 185,138 245, 6 4 53,i°3 72 33^ ' 16.3.11.137 129,23^ • 227,102 55,!52 401, 69 72 341 ■ 4-5-36i7 265, At — 72 35^ * 32.7-I7-I9 23,26* 5 26l, At — 180 QUADRATIC PARTITIONS. p p-1 a b c d A B [ L M 72 367 2.3.7.1723 — — 218, 91 55,103 72 379 2.9.4021 — 269, 3 76,149371, 75 72 383 2.36191 — — — — 72 421 4.3.5.17.71 255> 86 — 203,102406, 68 72 431 2.5.7243 — — — — 72 461 4-5-3 62 3 269, 10 — — — 72 467 2. 19.1907 — 255, 6l — — 72 469 4. 27. 11. 61 215,162 — 269, 6538, 4 72 481 3S8.3.5.X51 241,120 209,120 217, 92! 59,io3 72 493 4.3.7.863 77,258 — 209, 98503, 37 72 497 16.23.197 239,124 243, 82 — — 72 503 2.36251 — — — — 72 533 4-18133 263, 58 — — — 72 547 2.3.107. 113 — 257, 57 232, 79;4 6 9, 5 1 72 551 2. 25.1451 — — — — 72 559 2.9.29.139 — — 22,155443, 59 72 577 128.81. 7 161,216 127,168 265, 28349, 79 72 613 4.9.2017 63,262 — 229, 82 475, 49 72 617 8.29.313 269, 16 207,122 — — 72 623 2. 11. 3301 — — — — 72 643 2.3.12107 — 119,171 260, 41 383, 73 72 647 2.7.5189 — — — 72 649 8.9.1009 235^32 269, 12 I3M36 277, 89 72 661 4 3-5.7.I73 169,210 — 269, 10 239, 93 72 671 2.5.13.13.43 — — — — 72 673 32.3.757 247,108 59,186 239, 72 478, 48 72 679 2.3.12113 — — 98,145 337, 81 72 689 16.7.11.59 217,160 183,140 — — 72 701 4.25.727 101,250 — — 72 707 2-36353 — 153,157 — — 72 719 2 io3-353 — — — — 72 727 2 -3- I 7-23-3 I — — 5o,i53 100,102 72 733 4.3.11. 19.29 267, 38 — 215, 94 67,103 72 739 2.81.449 — 161,153 256, 49 403, 69 72 763 2.3.67. 181 — 149,159 196,107 125,101 72 767 2.36383 - — — — — 72 797 4.18199 91,254 — — — 72 817 16.3.37.41 249,104265, 36 103,144 206, 96 72 823 2.3-53-229 ■ 170,121 193, 97 72 859 2.3.12143 101,177 28,155 437, 61 QUADRATIC PARTITIONS. 181 V p-1 a b c d A B L M 72 869 4-18217 65,262 1 — 72 871 2.3.5.7.347 — 214, 95 71,103 72 883 2.9.4049 — (199,129 224, 87448, 58 72 889; 8.3.3037 267, 40 ^67,150 259, 44127,101 72 893 4.18223 203,178 — — 72 901 4.729.25 1,270 149,130241, 93 72 907 2.3.29.419 ■ — 77 5 i83 268, 19325, 83 72 911 2.5.23.317 — — — — 72 923; 2.19.19.101 — 261, 49 — — 72 931I2.3.5.11. 13.17 — I9M35 52,153 104,102 72 937 18.9.1013 269, 24 143,162 85,148 529, 21 72 949 4-3-6079 7,270 — 269, 143 11 , 85 72 953 8.11. 829 107,248 249, 74 — — 72 959 2.36479 — — 72 973 4.9.2027 243,118 — 95^46 533, 17 72 9771 16.4561 151,224 105,176 — — 72 997| 4.3.7. 11-79 239,126 — 43,154 505, 37 73 009 16.27. 13.13 145,228 269, 18 1,156 2,104 73 013 4.18253 263, 62 — — 73 019 2.11.3319 — 141,163 — — 73 037 4.19.31. 31 269, 26 — — — 73 039 2.3.7.37.47 — — 206,101 509, 35 73 043 2.59.619 — 9,191 — — 73 061 4.5.13.281 175,206 — — 73 063 2.81. 11. 41 — — 190,111 380, 74 73 079 2.61.599 — — — — 73 091 2.5-7309 — 87,181 — — 73 121 32.5.457 215,164 261, 50 — — 73 127 2.36563 — — — — 73133 4.47.389 67,262 — — — 73 141 4.3-5.23.53 265, 54 — 221, 90 442, 60 73 181 4-53659 235^34 — — — 73 189 4-9.i9« I o7 17,270 — 139,134 263, 91 73 237 4.3.I7.359 249,106 — 205,102 410, 68 73 243 2.9-i3-3 I 3 — 269, 21 220, 91 493, 43 73 259 2.36629 — 189,137 — — 73 277 4.7.2617 149,226 — — — 73 291 2.3.5.7.349 — 43,189 92,147 184, 98 73 303 2.3.19.643 — 70,151 5 2 3, 27 73 309 4.3.41. 149 155,222 199,106 5i7, 31 182 QUADRATIC PARTITIONS. p p-l a b c d A B L M 73 327 2.3.121.101 — — 82,149 365, 77 73 331 2-5-7333 — 159,155 — — 73 351 2.9.25.163 — — 158,127 223, 95 73 361 16.5.7. 131 265, 56 231,100 — — 73 '463 2.3.12227 — I5M59 56,153112,102 73 369 8.9.1019 195,188 251, 72 ^S 6 38,104 73 379 2.19.1931 — 177,145 — 73 387 2.243.151 — 163,153 148,1311245, 93 73 417 8.3.7.19.23 61,264 65,186 253, 56 85,103 73 421 4-5-3 6 7i 211,170 — — — 73 433 8.67.137 227,148 165,152 t 73 453 4.3.6121 83,258 — 271, 2^65, 91 73 459 2.9.7. n. 53 — 271, 3 i76,n9533, !9 73 471 2-3-5-3 I -79 — — 218, 93436, 62 73 477 4.9-i3-i57 271, 6 — 235, 78470, 52 73 483 2-3-37-331 — 221,111 236, 77 467, 53 73 517 4.18379 269, 34 — — — 73 523 2.36761 — 225,107 — — 73 529 8.7.13.101 77,260 261, 52 — — 73 547 2.11.3343 — n7,!73 — — 73 553 16.4597 247,112 249, 76 — — 73 561 8.3-5-613 219,160 169,150 269, 20329, 83 73 571 2.5.7. 1051 — iu,i75 — — 73 583 2.36791 — — — — 73 589 4.18397 265, 58 — — — 73 597 4-3- 6l 33 261, 74 — 217, 94 499, 4i 73 607 2.13.19.149 — — — — 73 609 8.3.3067 203,180 131,168 229, 84 458, 56 73 613 4.7.11.239 253, 98 — — — 73 637 4.41.449 271, 14 — — — 73 643 2.36821 — 171,149 — — 73 651 2.3.25.491 — 47,189 188,113 527, 25 73 673 8.9209 43,268 141,164 — 73 679 2. 11. 17. 197 — — — — 73 681 i6.3-5-3°7 159,220 67,186 209,100 9!, io 3 73 693 4.9.23.89 123,242 265, 34 367, 77 73 699 2.3.71. 173 — 193^35 268, 25 343, 81 73 709 4.18427 205,178 — — 73 721 8.5.19.97 235> I 3 6 39, I 9 C — — 73 727 2. 191. 193 — — — — QUADRATIC PARTITIONS. 183 p p-1 a b c d A B L M 73 751 2.625.59 — — — — 73 757 4.18439 229,146 — — — 73 771 2. 3-5- 2 459 — 139.165 164,125 539, J 3 73 783 2.9.4099 — — 226, 87 452, 5 8 73 819 2.27.1367 — 269, 27 244, 69 488, 46 73 823 2.7-5273 — — — — 73 847 2.36923 — — — — 73 849 8.3.17.181 45,268 11,192 29,156 58,104 73 859 2.36929 — 249. 77 — — 73 867 2-3-13947 — 83,183 208,101 95, IQ 3 73 877 4-H-23-73 151,226 — — — 73 883 2.I7-4I-53 — 99, J 79 — — 73 897 8-3-3°79 261, 76 13,192 245, 68 449, 59 73 907 2.7.5279 — 63,187 — — 73 939 2.3.12323 — 209,123 224, 89 49 1 , 45 73 943 2.11.3361 — — — — 73 951 2.3.25.17.29 — — 2,i57 469, 53 73 961 8.5-43-43 269, 40 177,146 — — 73 973 4.18493 73,262 — — — 73 999 2.9.4111 — — 86,149 533, 21 74 017 32.9-257 271, 24 17,192 167,124 205, 97 74 021 4.5-37oi 239 5 i3 — — 74 027 2.37013 — 267, 37 — 74 047 2.3.7.41.43 — — io,i57 481, 49 74 051 2. 25.1481 — Sb^ 1 — — 74 071 2.9.5.823 — — 62,153 124,102 74 077 4-3- 6l 73 i39 5 234 — 247, 66 494, 44 74 093 4.18523 163,218 — — — 74 099 2.37049 — 207,125 — — 74101 4.3.25.13.19 249,110 — 253, 58 427, 65 74131 2-3-5-7-353 _ 247, 81 272, 7 25 1 , 93 74143 2.27.1373 — — i4,i57 457, 57 74149 4-3-37-i°7 2 57. 9° — 101,146 539, i5 74159 2.7.5297 — — — 74161 16.9.5. 103 81,260 269, 30 257, 52 101,103 74167 2.3.47.263 — — 178,119 179, 99 74177 64.19.61 121,244 '267, 38 — — 74188 4.17. 1091 125,242 — — — 74197 4.81.229 199,186 163,126 326, 84 74 201 8.25.7.53 155.224 201,130 ! — 184 QUADRATIC PARTITIONS. B L M 74 203 74 209 74 219 74 231 74 257 74 279 74 287 74 293 74 297 74 311 74 317 74 323 74 353 74 357 74 363 74 377 74 381 74 383 74 411 74 413 74 419 74 441 74 449 74 453 74 471 74 489 74 507 74 509 74 521 74 527 74 531 74 551 74 561 74 567 74 573 74 587 74 597 74 609 74 611 74 623 2.3-83-149 32-3-773 2.43.863 2.5i3-57i 16.3.7. 13.17 2.37139 2.9.4127 4.3.41. 151 8-37-251 2-3-5-2477 4-3- II -5 6 3 2.9.4129 16.3.1549 4.29.641 2.37181 8.9.1033 4.5-37I9 2.3.49.11.23 2.5.7.1063 4.27-I3-53 2-3-79-J57 8.5.1861 16.9.11.47 4.7.2659 2.5.11.677 8.9311 2.37253 4.3.7.887 8.81.5.23 2.3.12421 2.5.29.257 2.3.25.7.71 64-5-233 2.23. 1621 4.103.181 2.3.31.401 4.17.1097 16.4663 2.9.5.829 2.3.12437 15,272 201,184 183,202 269, 44 99, 2 54 263, 72 169,214 181,204 109,250 253,102 221,160 215,168 233,142 83,260 147,230 261, 80 95,256 77,262 271, 34 25,272 97,180 237, 95 23,192 85,183 16,157487, 47 123,172 271, 21 25,192 189,139 253, 72 219,115 239, 93 129,170 199,132 271, 16319, 85 137,136271, 91 170,123340, 82 131,138262, 92 106,145541, 13 i43, I 34j545, 3 64,153128,102 71,1521527, 27 37,i56 146,133 271, 18 236, 79 239, 76 267, 40 3,i93 — 241, 74 73,186 211,100 — 1122,141 273, i j — — 242, 73 273, 4 I 55, I 59i5 2 ,i3 I i53, l6 o — 127,1711256, 55 — I 26,157 74,104 253, 93 542, 12 1,105 11,105 19,105 5«i 37 244, 94 23, IQ 5 545, 421, 67 445, 61 QUADRATIC PARTITIONS. 185 V P -\ a b c d A B L M 74 653 4.3.6221 267, 58 — 119,142 307, 87 74 687 2.107.349 — — — — 74 699 2.13.13.13.17 — 69,187 — — 74 707 2.3.12451 — 167,153 268, 31 361, 79 74713 8.3.11.283 27,272 119,174 269, 28 185, 99 74 717 4.18679 101,254 — — — 74 719 2.9-7-593 — — 262, 45 524, 3° 74 729 8.9341 115,248 273, 10 — — 74 731 2.3.5.47-53 — 187,141 28,157 499, 43 74 747 2.7. 19.281 — 147,163 — — 74 759 2.37379 — — — — 74 761 8.3.5.7.89 131,240 257, 66 227, 88 37,io5 74 771 2-5-7477 — 273, 11 — — 74 779 2. 3. 121. 103 — 211,123 52,155 4i3, 69 74 797 4.3.23.271 211,174 — 257, 54 514, 36 74 821 4-3-5- 2 9-43 111,250 — 133,138 266, 92 74 827 2.9.4157 — 235, 99 100,147 200, 98 74 831 2.5.7.1069 — — — — 74 843 2.23.1627 171,151 — — 74 857 8.3.3119 219,164 227,108 43,i56 86,104 74 861 4.5 19.197 269, 50 — — — 74 869 4-3- I 7-367 i35>238 — 6i,i54 523, 3i 74 873 8. 49.191 173,212 219,116 — 74 887 2.3.7.1783 — — 158,129 316, 86 74 891 2.5.7489 243, 89 — 74 897 16.31. 151 191,196 93,182 — — 74 903 2.17.2203 — — — — 74 923 2.3.12487 — 59,i89 184,117 368, 78 74 929 16.3.7.223 273, 20 i73,i5 127,140 293, 89 74 933 4.11.13.131 247,118 — — — 74 941 4.3.5.1249 229,150 — 7,i58 467, 55 74 959 2 -3-i3-3 I -3 I — — 254, 59 43i, 65 75 Oil 2-5-13-577 — 81,185 — — 75 013 4.3.7.19.47 273, 22 — 11,158 485, 49 75 017 8-9377 139*236 195,136 — — 75 029 4.18757 185,202 — — — 75 037 4.3-!3-i3-37 171,214 — 215, 98 5°9, 39 75 041 32.5-7-67 271, 40 273, 16 — — 75 079 2.9.43.97 — 274, 1 277, 91 75 083 2.7.31. 173 261, 59 — — 2 b 186 QUADRATIC PARTITIONS. p-1 A B L M 75109 75 133 75 149 75 161 75 167 75169 75181 75193 75 209 75 211 75 217 75 223 75 227 75 239 75 253 75 269 75 277 75 289 75 307 75 323 75 329 75 337 75 347 75 353 75 367 75 377 75 389 75 391 75 401 75 403 75 407 75 431 75 437 75 479 75 503 75 511 75 521 75 527 75 533 75 539 4.3.11.569 4.9.2087 4.18787 8.5.1879 2.49.13.59 32.81.29 4-3-5-7-I79 8.3.13.241 8.7.17.79 2.3.5.23.109 16.3.1567 2.27.7.199 2.29.1297 2.37619 4.3.6271 4.31.607 4.27.17.41 8.3.3137 2. 3.7. 11. 163 2.13.2897 64.11. 107 8.3-43-73 2.101.373 8.9419 2.9-53-79 16.7.673 4.47.401 2-3-5-7-359 8.25.13.29 2.9.59.71 2.37.1019 2-5- I 9-397 4.18859 2.13.2903 2-7-5393 2.9.5.839 256.5-59 2.II-3433 4.23.821 2.179.211 47,270 267, 62 205,182 125,244 267, 44 87,260251, 78 259, 9° — 117,248 121,174 35,272159,158 — i57»i59 169,216 137,168 27,193 263, 78 1 — 113,250 269, 54 133,240 223,160 99,256 37,272 151,162 205,129 99,181 197,110 121,142 271, 24 17,158 259, S 2 56,155 47,156 274, 7 19,158 175,122 251, 64 272, 21 527 ; 547. 542, 16 49i, 47 4i5, 69 521, 33 94,104 295, 89 455, 59 191, 99 59,io5 544, 14 271, 235, 273, 20 — I93,'38|i87,n6i< i35, l6 9i — 9, J 94! — — 238, 79|475, 53 237, 98! — 1245,124 19*274; 89,260 83,262 147,164 269, 39 38,i57 433, 65 260, 51 520, 34 — 206,105 267, 46 — 412, 70 183,145 QUADRATIC PARTITIONS. 187 p p—1 a b c d A B L M 75 541 4-3-5-I259 105,254 — 253, 62 67,105 75 553 32-3-737 273, 32 239, 96 79,i52 377, 77 75 557 4.I3.I453 271, 46 — — — 75 571 2.3.5.11.229 — 257, 69 272, 23 34i, 83 75 577 8.3.47.67 141,236 43,^2 245, 72 490, 48 75 583 2.9.13.17.19 — — 274, 13 3i3, 87 75 611 2.5-756i — 243, 9i — — 75 617 32.17.139 239^36 207,128 — — 75 619 2.9.4201 — 27*, 33 112,145 547, " 75 629 4.7.37.73 275, 2 — — — 75 641 8.5.31.61 275, 4 117,176 — — 75 653 4.18913 257, 98 — — — 75 659 2.11.19.181 — 141,167! — — 75 679 2.3-12613 — 254, 61 7M°5 75 683 2.79.479 — |255, 73 — — 75 689 8.9461 ! 275, 8111,178 — — 75 703 2.3.11.31.37) — 74,i53 148,102 75 707 2.37853 — 267, 47 — — 75 709 4.27.701 53,270 — 247, 7° 457, 59 75 721 8.3.5.631 189,200 223,114 163,128 221, 97 75 731 2-5-7573 — 177,149 — — 75 743 2.37871 — — — — 75 767 2.43.881 — — — — 75 773 4.19.997 187,202 — — — 75 781 4.9.5.421 145,234 91,150 182,100 75 787 2.3- I 7-743 — 275, 9 248, 69 496, 46 75 793 16.3.1579 63,268 259, 66 271, 28 355, 81 75 797 4.7.2707 71,266 — j — 75 821 4.5.17.223 275, J 4 — — i - 75 833 8.9479 43,272 231,106 75 853 4.9.49.43 163,222 — 1 31,158 ;443, 63 75 869 4.i3-!459 | 85,262 — — — 75 883 2.3.12647 — 115,177 44,i57 427, 67 75 913 8.3.3163 267, 68 275, i2 101,148 i343, 83 75 931 2.3.5.2531 — 67,189 268, 37 1379, 77 75 935 ' 32.3.7-H3 79,264 47,*9 2 i43,i3^ 265, 93 75 94] - 4-5-3797 271, 5 C — — — 75 96*5 7 2.3.11.1151 — — 250, 6) 45 1 , 6t 75 97< ) 2.81.7.67 — 181,14; '256, 5c ) 79, IQ 5 75 98: 5 2.37991 1 "~~ — — — 188 QUADRATIC PARTITIONS. p p-l a b c d A B L M 75 989 4.121.157 217,170 — — — 75 991 2.3.5.17.149 — — 146,135292, 90 75 997 4.9.2111 251,114 — 185,118 169,101 76 001 32.125.19 265, 76 27,194 ! 76 003 2.3-53- 2 39 — 95>i83 76,153152,102 76 031 2.5.7603 — — — — 76 039 2.3.19.23.29 — — 14,159 28,106 76 079 2.38039 — — — — 76 081 16.3.5.317 209,180 83,186 263, 48 526, 32 76 091 2.5.7.1087 — 267, 49 — — 76 099 2.3.11.1153 — 7,195 16,159 32,106 76103 2.13.2927 — — — — 76123 2.9.4229 — 251, 81 224, 93 448, 62 76 129 32.3.13.61 273> 4o 49,192 209,104 521, 35 76147 2.3-343-37 — 247, 87 88,151 54i, 21 76157 4.79.241 229,154 — — — 76159 2.9.4231 — — 274, 19 33i, 85 76163 2.H3-337 — 225,113 — — 76 207 2-3-I3-977 — — 98,149 545, 17 76 213 4.9.29.73 87,262 — 275, 14 3i7, 87 76 231 2.9.5.7.121 — — 122,143 55i, 7 76 243 2.3.97.131 — 191,141 20,159 40,106 76 249 8.27.353 , 93> 26 ° 107,180 269, 36 538, 24 76 253 4.11.1733 1133,242 — — — 76 259 2.7-I3-4I9 | 231,107 — — 76 261 4-3-5-3 I -4i !255) 106 — 37,J5S 437, 65 76 283 2.43.887 219,119 — — 76 289 512.149 1167,220 267, 50 — — 76 303 2.243.157 — 266, 43 137,103 76 333 4.3.6361 1237,142 — 241, 78 482, 52 76 343 2.49.19.41 — — — — 76 367 2.38183 — — — 76 369 I6.3-37-43 137,240 263, 60 119,144 238, 96 76 379 2.38189 — 123,175 — — 76 387 2.3-29-439 — 97,183 268, 39 536, 26 76 403 2.38201 — 111,179 — — 76 421 4.5.3821 175*214 — — — 76 423 2.3.47.271 — — 254, 63 508, 42 76 441 8-3-5-49-I3 195,196 187,144 197,112 139,103 76 463 2.38231 1 — — — QUADRATIC PARTITIONS. 189 p F--1 a b c d A B L M 76 471 2.3.5.2549 — j _ 142,1371269, 93 76 481 64.5.239 |l9I,200 159,160; 76 487 2.167.229 — 76 493 4.13.1471 227,158 — i — i — 76 507 2.3.41. 311 — 275> 21272, 29359, 81 1 76 511 2.5.7.1093 — 76 519 2.27. 13.109 — • — 26,159 52,106 76 537 8.9.1063 19,276 53^92 85,152 37i, 79 76 541 4-5-43-89 235^46 — — — 76 543 2.3.12757 — 130,141260, 94 76 561 16.3.5.11.29 105,256 167,156 247, 72494, 48 76 579 2.3.12763 — 23»i95 148,135296, 90 76 597 4.3.13.491 39,274 — 275, 181550, 12 76 603 2.3-17-751 — 259, 69 100,149347, 83 76 607 2.38303 — — — 76 631 2.5.79.97 — — — 76 649 8.11. 13.67 275> 32 207,130 — — 76 651 2.3.25-7-73 — 149,165 52,i57 523, 35 76 667 2.38333 — r 95>i39 — — 76 673 128.599 217,172 I7i>i54 — ~~ 76 679 2-7-5477 — — — 76 697 8.9587 131,244 267, 52 — — 76 717 4.9.2131 269, 66 — 113,146 55i, 11 76 733 4.19183 277, 2 — — 76 753 16.9.13.41 183,208 55^92 i75, I2 4 547, 17 76 757 4.31.619 41,274 — — — 76 771 2.9-5-853 73,189 212,103 97,io5 76 777 8-3-7-457 229,156 275, 2 4 277, 4 289, 91 76 781 4-5-H-349 275. 34 — — — 76 801 1024.3.25 25,276 277, 6 1,160 481, 53 76 819 2-3-7-3!-59 — 119,177 164,129 328, 86 76 829 4.19207 277, 10 — — — 76 831 2-3-5- r 3-i97 — 266, 45 532, 30 76 837 4-3- 19.337 111,254 — 277, 6 554, 4 76 847 2.7.11.499 — — — — 76 871 2.5.7687 — — — — 76 873 8.3-3203 277, 12 205,132 251, 68 455, 6i 76 883 2.13.2957 255, 77 — — 76 907 2.38453 — 267, 531 — — 76 913 16.11. 19.23 263, 88 9,196 — ~ 190 QUADRATIC PARTITIONS. p p-l a b c d A B L M 76 919 2.38459 — — — — 76 943 •.17.31.73 — — — — 76 949 4.19237 265, 82 — — — 76 961 32.5-I3-37 169,220 69,190 — — 76 963 2.3.101.127 209,129 200,111 400, 74 76 991 2.5.7699 — — — — 77 003 2.38501 — 141,169 — — 77 017 8.3.3209 29,276 277, 12 205,108 410, 72 77 023 2.9.11.389 — — 226, 93 452, 62 77 029 4-3-49- I 3 I 273> 5° — 277, 10 307, 89 77 041 16.9.5.107 271, 60 179,15° 167,128 551, n 77 047 2.3.12841 — — 182,1211 181,101 77 069 4.19267 *75> 38 — — — 77 081 8.5.41.47 259,100 123,176 — — 77 093 4.19273 143.238 ~~ — — 77 101 4.3.25.257 45.274 47,158 521, 37 77137 16.3.1607 31,276 157,162 265, 48 530, 32 77 141 4.5.7.19.29 121,250 — — — 77153 32.2411 73,268 165,158 — — 77167 2.27.1429 — — 190,117 380, 78 77171 2.5.7717 — 207,131 — — 77191 2-3-5-3I-83 — — 254, 65 449, 63 77 201 16.25.193 215,176 i53> l6 4 — — 77 213 4.97.199 277, 22 — — — 77 237 4.19309 199,194 — ■ — — 77 239 2.9.7.613 — — : 94,15! 547, 19 77 243 2.11.3511 — 219,121 ; — 77 249 64.17.71 193,200 81,188 — 77 261 4.5.3863 269, 70 — — — 77 263 2.3-79- l6 3 — — 274, 27 548, 18 77 267 2.7.55 L 9 — 273, 37 — 77 269 4.3.47.137 263, 90 163,13c 553, ll 77 279 2.38639 — — — — 77 291 2.5.59.131 — I7I.I55 — 77 317 4.3- I 7-379 81,266 277, M ^35, 97 77 323 2.3.49.263 — 245, 9: ;244, i) i3, IQ 7 77 33S 2.38669 ' — 267, 51 — 77 345 2.9.4297 — 217,12; 5260, 5' ^520, 38 77 351 2.25.7.13.1' J — ; — 1 77 35S \ 2.3-12893 1 — ; — 278, . 5|293, 9i QUADRATIC PARTITIONS. 191 V P -l a b c d A B L M 77 369 8.19.509 205,188 261, 68 — 77 377| 64.3.13.31 249,124 277, 18 223, 96 446, 64 77 383! 2.27.1433 — — 266, 47 407, 73 77 417 8.9677 109,256 273, 38 — — 77 419 2. 9. 11. 17. 23 — 37,195 104,149 55i, i5 77 431 2.3.5.29.89 — — 278, 7 257, 95 77 447 2.38723 — — — — 77 471 2.5.61. 127 — — — — 77 477 4.7.2767 49,274 — — — 77 479 2.3-37-349 — — 166,129 332, 86 77 489 16.29.167 185,208 249, 88 — — 77 491 2.27.5.7.41 — 271, 45 248, 73 29,107 77 509 4.92153 15,278 — 203,110 533, 31 77 513 8.9689 277, 28 99,184 — — 77 521 16.3.5.17.19 225,164 227,114 233, 88 3M<>7 77 527 2.9-59-73 — 278, 9 556, 6 77 543 2.137.283 — — — 77 549 4.19387 230,157 — — — 77 551 2.3.25.11.47 — 74,155 539, 27 77 557 4.3.23.281 15^234 — 173,126 346, 84 77 563 2.9.31. 139 269, 51 140,139 277, 93 77 569 256.3.101 255,112 113,180)137,140557, 1 77 573 4.11. 41.43 17,278 — ! — 77 587 2.3.67.193 — :io3,i83 ! 232, 89 35, io 7 77 591 2-5-7759 — — 77 611 2.3.5.13.199 277, 21 208,107 h3, io 5 77 617 16.9.49. 1 1 89,264 233,108193,116 i55, io 3 77 621 4.5.3881 265, 86 — 77 641 8.3.5-647 171,220221,120 29,160 45 1 , 63 77 647 2.3-12941 278, 11 311, 89 77 659 2.3-7-43-43 — ^03,135 272, 35 377, 79 77 681 16.5.971 241,140 141,170 — — 77 687 2.7.31. 179 — — — 77 689 8.9.13.83 267, 80:199,138149,136 259, 95 77 699 2-53-733 — 244 227,162 271, 66 101,260 23,278 155,232 — 230, 91 57,193 — 181,150 31,160 — 271, 38 237,104 279, 243, 9 273, 58 43,i95 275, 48239,102 253,118 265, 88 91,264 199,196 229,160 143,240 55,274 261,100 269, 76 189,206 277, 38 207,188 279, 8 215,126 267, 58 279, 10 271, 48 21,197 253, 84 213,128 251, 87 265, 63 279, 13 269, 54 261, 71 ;I97,H4 106,149 10,161 !55,i34 268, 45 277, 20 275, 28 254, 67 98,15! 158,133 7M56 206,109 139,140 136,141 145^38 20,161 161,132 43,^7 5ii, 43 i57,io3 394, 76 34i, 85 473, 57 557, 7 536, 30 217, 99 191,101 53,io7 355, 83 241, 97 142,104 121,105 281, 93 272, 94 290, 92 5°3, 47 322, QUADRATIC PARTITIONS. 193 p p-1 a b c d A B L M 78 229 4- 9-41-53 73,270 211,106 529, 35 78 233 8. 7. n. 127 187,208 279, 14 — 78 241 32-3-5 163 279, 20 133^74 271, 40 39i, 77 78 259 2-3- I 3°43 — 47,195 244, 79 481, 55 78 277 4-3-H-593 209,186 — 245, 78 490, 52 78 283 2.9.4349 — 125,177 116,147 232, 98 78 301 4.27.25.29 165,226 — 217,102 434, 68 78 307 2.3.31. 421 — 247, 93 200,113 539, 29 78 311 2.5.41. 191 — — — 78 317 4.7.2797 259,106 — — — 78 341 4-5-39I7 271, 70 — — — 78 347 2.43.91 1 — 27,197 — — , 78 367 2.3-37-353 — — 278, 19 221, 99 78 401 64.25.49 1,280 273, 44 — — 78 427 2-9-4357 — 107,183 280, 3 560, 2 78 437 4.19609 239,146 — — — 78 439 2.3.17.769 — . — 26,161 509, 45 78 467 2-39233 — 6 3,i93 — — 78 479 2.39239 , — — — — 78 487 2.3.103.127 — — 25°, 73 469, 59 78 497 32.11.223 15^236 123,178 — — 78 509 4.19.1033 35»278 — — — 78 511 2.3.5.2617 — — 182,123 364, 82 78 517 4.27.727 279, 26 — 157,134 245, 97 78 539 2.107.367 — I7i,i57 — 78 541 4.3.5.7.11.17 275> 54 — 223, 98 71,107 78 553 8.9.1091 163,228 235,108 251, 72 502, 48 78 569 8.7.23.61 13,280 111,182 78 571 2.81.5.97 197,141 68,157 403, 75 78 577 16.3.1637 49,276 i3,!98 263, 56 43i, 69 78 583 2.3.7. 1871 — — 190,119 167,103 78 593 256.307 257,112 129,176 — — 78 607 2.9.11.397 — — 278, 21 556, 14 78 623 2.19.2069 — — — — 78 643 2.9.17.257 — 271, 5 1 280, 9 560, 6 78 649 8.3.29.113 243,140 149,168 43,160 523, 39 78 653 4-7-53-53 37,278 — — — 78 691 2.3.5.43.61 — 263, 69 92,i53 184,102 78 697 89.1093 179,216 17,198 275, 32 37i, 81 78 707 2.23.29.59 — 33,i97 — — 2c 194 QUADRATIC PARTITIONS. V p-1 a b c d A B L M 78 713 8.9839 83,268 219,124 — — 78 721 128 3.5.41 95,264 193,144 97*i5 2 359, 83 78 737 16.7. 19.37 169,224 105,184 — — 78 779 a.7-17-33* — 261, 73 — — 78 781 4.3.5.13.101 I55>234 — 7,162 14,108 78 787 2.27.1459 — 127,177 32,161 5!5* 43 78 791 2.5.7879 — — — 78 797 4.19699 61,274 — — 78 803 2.31. 31.41' — 255* 83 — — 78 809 8.9851 197,200 279, 22 — — 78 823 2.9.29.151 — 170,129 340, 86 78 839 2.39419 — — — — 78 853 4-3-6571 177,218 — 11,162 22,108 78 857 8.9857 i39>244 45*^6 — — 78 877 4-9-7.3I3 251,126 — 185,122 55i, 21 78 887 2-39443 — — — — 78 889 8.3.19.173 205,192 241,102 181,124 553, 19 78 893 4.121.163 253,122 — — — 78 901 4.3.25.263 249,130 . — 13,162 26,108 78 919 2.3.7.1879 — — 34,i6i 449, 65 78 929 16.4933 23,280 249* 9 2 — — 78 941 4-5-3947 235^54 — — — 78 977 128.617 281, 4 267, 62 — — 78 979 2.3.13163 — 281, 3 56,159 112,106 78 989 4.49.13.31 275* 58 — — — 79 031 2.5.7.1129 — — — — 79 039 2.9.4391 — — 166,131 227, 99 79 043 2.39521 — 201,139 — — 79 063 2.3.13177 — — 94,153 188,102 79 087 2.3.49.269 — — 262, 59 85,107 79103 2-3955 1 — — — — 79111 2.27.5.293 — — 202,113 137,105 79133 4.73.271 43*278 — — — 79 139 2.39569 — 39,197 — — 79147 2.9.4397 — 253, 87 112,149 335, 87 79151 2.25.1583 ■ — — — — 79 153 16.3-17-97 273, 68 275* 42 281, 8 305, 9 1 79 159 2.3.79.167 — — 278, 25 203,101 79181 4-5-37-107 1259,110 — — 79187 2.17.17.137 — 153*167 — QUADRATIC PARTITIONS. 195 p p-\ a b c d A B L M 79193 8.19.521 1 j 133.248279, 26 — 79 201 32. 9.25. 11 55,276251, 90, 49,160 529, 37 79 229 4.29.683 277, 5° — 79 231 2 -3-5- I 9-i39 — — 1242, 83 49i, 53 79 241 8.5.7.283 29,280 63,i94 — 79 259 2.23.1723 — 69,193 — — 79 273 8.27.367 237,152 271, 54 269, 48 538, 32 79 279 2.3.73.181 — — 146,139 27 1 , 95 79 283 2.49.809 — 9,i99 — 79 301 4.25.13.61 65,274 — — 79 309 4.9.2203 45,278 — 239, 86 497, 5 1 79 319 2 -39659 — — — 79 333 4.3. 11. 601 113,258 — 149,138 298, 92 79 337 8.47. 211 229,164 93,188 — — 79 349 4.83.239 215,182 — — 79 357 4-3-17.389 261,106 — 25,162 50,108 79 367 2.7.5669 — — — 79 379 2.I3-43-7I — 177,155 — — 79 393 32.3.827 87,268 101,186 281, 12 562, 8 79 397 4.23.863 241,146 — — 79 399 2.9.11.401 — — 206,111 412, 74 79 411 2.3.5.2647 — 281, 15 152,137 563, 5 79 423 2. 3.7. 31. 61 — — 74,157 397, 77 79 427 2. 151. 263 — I 5, I 99 — 79 433 8.9929 277, 52 51,196 — — 79 451 2.25.7.227 — 243,101 ■ 79 481 8.5.1987 109,260 267, 64 — — 79 493 4.7.17.167 47,278 — — — 79 531 2.3.5. 11. 241 — 59,i95 272, 43 143,105 79 537 16.3.1657 281, 24 263, 72 217,104 95, io 7 79 549 4.3.7.947 5,282 — 281, 14 323, 89 79 559 2.39779 — — — — 79 561 8.9.5.13.17 235, J 5 6 269, 60 253, 72 506, 48 79 579 2.9.4421 — 181,153 224, 99 448, 66 79 589 4.101.197 145,242 — — 79 601 16.25.199 199,200 201,140 — — 79 609 8.3.31. 107 272, 75 281, 18 53,i6o 427, 71 79 613 4.13-1531 197,202 — — 79 621 4.3-5.1327 239,15° — 187,122 179,103 79 627 2-3.23.577 — 245, 99 268, 51 536, 34 196 QUADRATIC PARTITIONS. p p-l a b c d A B L M 79 631 2-5-7963 _ — — — 79 633 16.9.7.79 127,252 35,198 265, 56 97,107 79 657 8-3-33 x 9 59,276 77,192205,112541, 31 79 669 4.9.2213 105,262 — 179,126358, 84 79 687 2.9.19.233 — — 62,159 124,106 79 691 2.5. 13.613 — 213^31 — — 79 693 4.3-29-229 13,282 — 31,162 62,108 79 697 16.17.293 119,256 183,152 — — 79 699 2-3-37-359 — 191,147 44,161 527, 39 79 757 4-I27-I57 269, 86 — — — 79 769 8.I3-I3.59 37,280 87,190 — — 79 777 32.9.277 279, 44 37,198 175,128 209,IOT 79 801 8.3.25.7.19 149,240 103,186 277, 32 l8l,I03 79 811 2.5.23-347 — 23MI5 — 79 813 4.27.739 17,282 — 139,142 565, I 79 817 8.11.907 221,176 255, 86 — 79 823 2.107.373 — — — 79 829 4.7.2851 265, 98 — — 79 841 32-5-499 271, 80 207,136 — 79 843 2.3.7. 1901 — 281, 21 136,143 293, 93 79 847 2-13.37-83 — — — — 79 861 4-3-5- I 33i 281, 30 — 269, 50 4i9, 73 79 867 2.81. 17.29 — 235, 111 148,139 565, 3 79 873 2048.3.13 167,228 139*174 119,148 325, 89 79 889 16.4993 233,160 279, 3 2 — — 79 901 4.25.17.47 251,130 — — — 79 903 2.9.23.193 — — 14,163 475, 59 79 907 2-39953 — 225,121 — — 79 939 2.9.4441 — 271, 57 64,i59 128,106 79 943 2.39971 — — — — 79 967 2.39983 — — — — 79 973 4.19993 257,118 — — — 79 979 2.39989 — 261, 77 — — 79 987 2-3-13331 — 223,123 280, 23 211,101 79 997 4.7.2857 229,166 — — — 79 999 2.3.67.199 . — — 182,125 557, 19 80 021 4.5.4001 185,214 — — — 80 039 2.7.5717 — — — — 80 051 2.25. 1601 — 249, 95 — — 80 071 2-3-5- I 7.i57 — — 178,127 559, 17 QUADRATIC PARTITIONS. 197 V p-1 a b d A B L M 80 077 4.36673 259,114 — 127,1461311, 91 80107 2.3-i3- I 3-79 — 283, 3 20,163^69, 61 80111 2.5.8011 — . — — 80141 4.5.4007 125,254 — — — 80147 2.11.3643 — 273, 53 — 80149 4.3.6679 25,282 — 259, 66518, 44 80153 8-43-233 283, 8 279, 34 80167 2-3-3 I -43 I — — 278, 3 1 185,103 80 173 4.9.17. 131 147,242 — 95, r 54 367, 83 80177 16.5011 121,256 i35«!76 — — 80191 2.729.5.11 — — 22,163 367, 47 80 207 2.7.I7.337 — — — — 80 209 16.9.557 225,172 2 53, 90 247, 80 7,109 80 221 4.3.5-7.I9I 261,110 — 73,i58 401, 77 80 231 2. 5.71. 113 — — — — 80 233 8-3-3343 283, 12 275, 48 85,156 170,104 80 239 2-3-43-3 11 — — 242, 85 *3, io 9 80 251 2.3.125.107 — 283, 9 268, 53 109,107 80 263 2-9-343-J3 — — 50,161 533, 37 80 273 16.29.173 137,248 231,116 — — 80 279 2.1 1. 41. 89 — — — — 80 287 2.3- r 33 81 — — 250, 77 19,109 80 309 4.17. 1181 55^78 — — — 80 317 4.9.23.97 171,226 — 265, 58 439, 69 80 329 8-3-3347 277, 60 227,120 25 1 , 76 23,109 80 341 4.3.5. 13.103 279, 5° — 227, 98 521, 43 80 347 2.3.7. 1913 — 133,177 80,157 39i, 79 80 363 2.23.1747 — 165,163 — — 80 369 16.5023 113,260 237,110 — — 80 387 2.40193 — 207,137 — — 80 407 2.27.1489 — — 238, 89 29,109 80 429 4.20107 227,170 — — — 80 447 2.19.29.73 — — — 80 449 64.3.419 257,120 239,108 193,120 386, 80 80 471 2.5. 13.619 — — — — 80 473 8.3.7.479 93,268 i55> l6 8 269, 52 113,107 80 489 8. 1 006 r 283, 20 99,188 — — 80 491 2.3.5.2683 — I73»i59 28,163 5i7, 45 80 513 128.17.37 193,208 255, 88 — — 80 527 2.3.13421 — — 118,149 329, 89 OF THE 198 QUADRATIC PARTITIONS. p p-i a b c d A B L M 80 537 8.10067 259,116 267, 68 80 557 4-3-49-I37 99,266 — 97,i54 559. 19 80 567 2.40283 — — 80 599 2.3.7. 19.101 — — 218,105 436, 70 80 603 2. 191. 211 — 261, 79 ' 80 611 2.3.5.2687 — 247, 99 272, 47 4i3, 75 80 621 4-5- 2 9-i39 211,190 — — — 80 627 2-7- I 3-443 — 177,157 — — 80 629 4-3- 6 7i9 265,102 — 173.13° 217,101 80 651 2.25. 1613 — 123,181 — 80 657 16.71. 71 .1,284 195,146 — — 80 669 4.7.43.67 155.238 — — — 80 671 2.3.5.2689 — 82,157 553, 25 80 677 4.243.83 161,234 — 283, 14 241, 99 80 681 8.5.2017 5.284 243,104 — 80 683 2.3.7. 17.113 — 149,171 284, 3 568, 2 80 687 2.40343 — — — — 80 701 4.3.25.269 75.274 — 263, 62 449. 67 80 713 8.9.19.59 213,188 J 79.!5 6 5> l6 4 497. 53 80 737 32.3.29.29 9,284 283, 18 7,164 485, 57 80 747 2.47.859 — 2I3.J33 — — 80 749 4.9.2243 35.282 — 257, 7o 47,109 80 761 8.3-5-673 245. r 44 281, 30 107,152 563. i5 80 777 8.23.439 11,284 147,172 — — 80 779 2.3-J3463 — 277. 45 224,101 527. 4i 80 783 2. 13.13.239 — — 80 789 4.19.1063 167,230 — — — 80 803 2.9.67.67 — 1,201 284, 7 263, 97 80 809 8.3.7.13.37 72,275 49,198 11,164 5°3. 5 1 80 819 2.17.2377 — 249, 97 — 80 831 2.5-59- I 37 — — — — 80 833 64.3.421 263,108245,102 169,132338, 88 80 849 16.31. 163 95,268 93,190 80 863 2-3- J 3477 — — 34,163523, 43 80 897 1024.79 281, 44 75^94 — — 80 909 4.113.179 253^30 — — — 80 911 2.9.5.29.31 — — 94>i55!37i, 83 80 917 4.3.11.613 231,166 — 275. 4255°. 28 80 923 2.3-J3487 — 11,201 280, 29193,103 80 929 32.9.281 273. 80 127,180 89,156 178,104 QUADRATIC PARTITIONS. 199 p p-1 a b c d A B L M 80 933 4.20233 257,122 — 80 953| 8.3.3373 243,148 85,192 259, 68 55, IQ 9 80 9631 2.7.5783 105,187 — — 80 989 4-3-I7-397 283, 30 — 281, 26 359< 85 81001 8.81. 125 51,280 143^74 149,140 569, 3 81013 4-3-43-157 183,218 — 205,114 410, 76 81017 8.13.19.41 19,284 165,164 — — 81019 2.9.7.643 — 163,165 284, 11 3i7, 91 81023 2.17.2383 — — — 81031 2 -3-5-37-73 — — 134,145 3°h 93 81041 16.5.1013 265,104 279, 40 — — 81 043 2.3.13.1039 — 185,153 io4,i53 208,102 81047 2.49.827 — — — 81049 8.3. 1 1.307 165,232 169,162 19,164 473, 61 81071 2. 5. 121. 67 — — — — 81077 4.20269 281, 46 — 81083 2.71.571 — 171,161 — — 81097 8.3.31. 109 21,284 157,168 187,124 559, 21 81101 4.25.811 275> 74 — — 81119 2-40559 — — — — 81131 2.5.7.19.61 — i4i,i75 — — 81157 4-3- 6 763 129,254 — 155,138 310, 92 81163 2.243.167 — 19,201 284, 13 245, 99 81173 4.7.13.223 247,142 — — — 81181 4.9.5. 11. 41 91,270 — 247, 82 493, 55 81197 4-53-383 269, 94 — — — 81199 2-9- I 3-347 — — 266, 59 443, 69 81203 2. 11. 3691 . — 279, 4i — — 81223 2.3 13537 — — 250, 79 487, 57 81233 16.5077 97,268 285, 2 — — 81239 2. 151. 269 — — — — 81281 128.5.127 25,284 2i3, x 34 — — 81283 2-3-I9-23-3 1 — I5M7I 280, 31 373, 83 81 293 4.20323 157,238 — — — 81299 2.7.5807 201,143 — — 81307 2.9.4517 — 253, 93 40,163 529, 4i 81 331 2.3.5.2711 — 23,201 284, 15 568, 10 81343 2.9.4519 — — 86,157 385, 81 81 349 4.3-6779 193,210 — 101,154 361, 85 81353 8.10160 277, 68 285, 8 — — 200 QUADRATIC PARTITIONS. p p-l a b c d A B L M 81359 2.19.2141 — — 81 371 2.5.79.103 — 267, 71 — — 81 373 4.3.6781 43,282 — 199,118553, 27 81401 8.25.11.37 275, 76 117,184 — — 81409 512.3.53 255,128 241,108 161,136247, 99 81421 4-3-5- 2 3-59 285, 14 — 239, 90478, 60 81439 2.3.49.277 — — 214,109 54i, 35 81 457 16.3.1697 239,156 275, 54 263, 64 71,109 81463 2-3-13577 — — 106,153 212,102 81 509 4.7.41. 71 65,278 — — 81517 4-3-6793 189,214 — 145,142 57i, 1 81527 2.40763 — — — — 81533 4.11.17.109 283, 38 — — — 81547 2.3-i359i — 283, 27 148,141 296, 94 81551 2.25.7.233 — — — — 81 553 16.3.1699 87,272 281, 36 271, 52 427, 73 81559 2.9.23.197 — — 194,121 169,105 81563 2.I3-3I37 — 285, 13 — — 81569 32.2549 215,188 261, 82 — — 81611 2.5.8161 — 93, T 9i — — 81619 2.3.61.223 — 121,183 76,159 152,106 81629 4.20407 277, 7o — — — 81637 4.3.6803 81,274 — i33, J 46 305, 93 81647 2.40823 — — — — 81649 16.729.7 57,280 89,192 3^164 461, 65 81667 2.9.13.349 — 233,117 280, 33 560, 22 81671 2.5.8167 — — — — 81677 4.7.2917 131,254 — — — 81689 8.10211 283, 40 9,202 — — 81701 4.25.19.43 175,226 — — — 81703 2.27.17.89 — — 274, 47 133,107 81707 2.40853 — 237,H3 — — 81727 2-3-53- 2 57 — — 130,147 260, 98 81737 8.17. 601 149,244 285, 16 — — 81749 4.107. 191 185,218 — — — 81761 32.5.7-73 119,260 219,130 — — 81769 8.3.3407 237,160 209,138 269, 56 437, 7i 81773 4.20443 67,278 — — — 81799 2.3-13633 — — 286, 1 289, 95 81817 8.3.7.487 219,184 247,102 283, 24 566, 16 QUADRATIC PARTITIONS. 201 P p-l A B L M 81839 81847 81853 81869 81883 81899 81901 81919 81929 81931 81937 81 943 81953 81967 81971 81 973 82 003 82 007 82 009 82 013 82 021 82 031 82 037 82 039 82 051 82 067 82 073 82 129 82139 82 141 82 153 82163 82 171 82183 82189 82 193 82 207 82 217 82 219 82 223 2.17.29.83 2.9.4547 4-3-'9-359 4.97.211 2.9.4549 2.40949 4.9.25.7.13 2.27.37.41 8.49.11.19 2-3-5- 2 73i 16.9.569 2.3.7. 1951 32.13.197 2.3.19.719 2.5.7.1171 4.81. 11. 23 2-3-79-I73 2.131-313 8.9.17.67 4.7.29. 101 4.3-S-I367 2.5. 13.631 4.20509 2. 3. 121. 113 2.3.25-547 2. 37.1109 8.10259 16.3.29.59 2.7.5867 4.3.5.37.37 8.9.7.163 2.41081 2. 9.5. 11. 83 2.3.13697 4.27.761 16.1 1.467 2.9.4567 8.43.239 2.3.71. 193 2.49.839 283, 42 115,262 285, 26 245,148 279, 64 143,248 153*242 285, 28 203,202 15,286 199,206 197,208 223,180 269, 69 261, 83 189,152 277, 5 1 217,132 255, 92 273, 61 281, 39 91,192 103,189 87,193 279, 46 61,198 117,185 171,230 243,152271, 66 — 129,181 37,201 125,258 193,212 179,224 285, 22 273, 62 259, 87 278, 39 185,126 260, 69 193,122 266, 61 16,165 33, 96 286, 7 170,133 556, 26 37o, 84 520, 46 i73»i°5 83,109 32,110 233, 9 6 466, 64 307, 93 275, 46 224,103 197,120 229,101 137,107 85,109 394, 80 277, 42|554, 28 286, 9:572, 6 232, 971523, 45 73,160 121,150 211,112 248, S3 250, 81 271, 54 5°, l6 3 188,125 553, 29 242,100 547, 33 497, 55 5o°, 54 542, 36 439, 7i 563, 21 2d 202 QUADRATIC PARTITIONS. p P -l a be d A B L M 82 231 2.3.5.2741 — — 166,135 332, 90 82 237 4.3.7.11.89 21,286 — 263, 66 526, 44 82 241 64-5- 2 57 121,260 267, 74 — 82 261 4-9-5-457 231,170 — J253, 78 5°6, 52 82 267 2.3.13711 — 283, 33268, 59 91,109 82 279 2-9-7-653 — — 274, 49 421, 75 82 301 4.25.823 85,274 — — — 82 307 2.7.5879 — 135^79 — 82 339 2-3- I 37 2 3 — 167,165 196,121 559, 25 82 349 4.7-I7.I73 275, 82 — — — 82 351 2.27.25.61 — — 26,165 52,110 82 361 8.5.29.71 269,100 2i3, r 36| — 82 373 4-20593 287, 2 — — — 82 387 2.9.23.199 — 287, 3 68,161 55 1 , 3i 82 393 8-3-3433 283, 48 265, 78 205,116 i43> 10 7 82 421 4.5^3.3i7 25,286 — — — 82 457 8.11.937 259,124 75,^6 — — 82 463 2.41231 — — — — 82 469 4.53.389 287, 10 — — — 82 471 2.3-5-2749 — — 286, 15 572, 10 82 483 2.3-59-233 — 41,201 200,119 557, 27 82 487 2.41243 — — — — 82 493 4-4i. 5°3 187,218 — — — 82 499 2.13.19.167 — 9,203 — — 82 507 2-3- I 375 I — I55,i7i 280, 37 39i, 81 82 529 32.2579 145,248 177,160 — — 82 531 2.9.5.7.131 — 287, 9 284, 25 209,103 82 549 4.9.2293 55,282 — 221,106 97,109 82 559 2.7.5897 — — — — 82 561 128.3.5.43 281, 60 277, 54 287, 8 3*Ij 93 82 567 2. 27. 11. 139 — — 82,159 164,106 82 571 2.5-23-359 — 261, 85 — — 82 591 2.3-5-2753 — — 238, 93 476, 62 82 601 8.25.7-59 251,140 51,200 — — 82 609 16.3. 1721 175,228 211,138 191,124 181,105 82 613 4.19.1087 73,278 — — — 82 619 2. 101.409 — 237,u5 — — 82 633 8.3.11.313 93,272 65,198 259, 72 518, 48 82 651 2.3.25.19.29 — 43,201 172,133 57i, 13 82 657 32.9.7.41 271, 96 287, 12 i43,i44 ! 286, 96 1 QUADRATIC PARTITIONS. 203 p p-1 a b c d A B L M 82 699 2. 3.7. 11. I79 — 229,123 32,165 64,110 82 721 32.5.II.47 239,160273, 64 — — 82 723 2. 3.I7. 8ll — 241,111 260, 71 473, 63 82 727 2.7.I9.3II — — — — 82 729 8.27.383 123,260 269, 72 77,160 403, 79 82 757 4 I7.I217 31,286 — — — 82 759 2.3.I3.I061 — — 214,111 428, 74 82 763 2.41381 — 99,191 — — 82 781 4.5-4I39 235,166 — — — 82 787 2.11. 53.7I — 183,157 — — 82 793 8.79.I3I 283, 52 285, 28 — — 82 799 2.41399 — — — — 82 811 2.5.49.I3.I3 — 243,109 — — 82 813 4.3.67.IO3 277, 78 — 89,158 563, 23 82 837 4.27-I3-59 201,206 — 13,166 5", 5i 82 847 2. 23.1801 — — — — ' "" ■ 82 883 2.29.I429 — 225,127 — — -- • 82 889 8.I3.797 67,280 129,182 — — 82 891 2.27.5.307 — 107,189 io4,i55 569, 17 82 903 2-3-4I-337 — — 226,103 535, 4i 82 913 32.2591 247,148 261, 86 — — 82 939 2.3.23.60I — 83,195 208,115 553, 3i 82 963 2.9.II.419 — 271, 69 280, 39 560, 26 82 981 4.9.5.461 255>i34 — 203,118 i5 r , I0 7 82 997 4.20749 89,274 — — — 83 003 2.47.883 — 165,167 — — 83 009 64.I297 95*272 111,188 — — 83 023 2.3.IOI. I37 — — 194,123 388, 82 83 047 2.3.I3841 — — 182,129 364, 86 83 059 2.3. IO9.I27 — 247,105 272, 55 107,109 83 063 2.7.17.349 — — — — 83 071 2.9.5.I3.7I — — 58,163 547, 35 83 077 4.3.7.23.43 111,266 277, 46 415, 77 1 : 83 089 16.9.577 215,192 233,120 49,164 443, 7i 1 83 093 4.20773 263,118 — — 83101 4.3.25.277 101,270 233, 98 527, 45 83117 4.II.1889 179,226 — — — 83 137 64.3.433 191,216 97,192 287, 16 239,101 83 177 8.37.281 269,104 207,142 — — 83 203 2.3.49.283 — 49,201 164,137 575, 9 204 QUADRATIC PARTITIONS. p p-l a b c d A B L M 83 207 2.41603 — — — — 83 218 2.41609 — 249,103 — 83 221 4.3-S-*9-73 265,114 67,162 134,108 83 227 2.3.11.13.97 — 277, 57 232, 99464, 66 83 231 2.5.7.29.41 — — — — 83 233 32.9.17.17 17,288 1,204 145^44 290, 96 83 243 2.41621 — 75,197 — — 83 257 8.3.3469 51,284 5,204 245, 88 19,111 83 267 2.17. 31. 79 — 153.173 — — 83 269 4.81.257 287, 30 139,146 299, 95 83 273 8.7.1487 107,268 285, 32 — — 83 299 2-3-13883 — 191,153 244, 89 23,111 83 311 2.3-5-2777 — — 106,155 359, 87 83 339 2.41669 — 219,133 — — 83 341 4-9-5-463 285, 46 — 287, 18 574, 12 83 357 4.7.13.229 91,274 — — — 83 383 2.3.13.1069 — — 286, 23 217,103 83 389 4.3.6949 267,110 — 217,110 113,109 83 399 2.49-23-37 — — — — 83 401 8.3-25-139 85,276 13,204 133,148 577, 5 83 407 2.3.13901 — — 242, 91 $M« 83 417 8.10427 229,176 183,158 — — 83 423 2.53-787 — — — — 83 431 2.81. 5.103 — — 266, 65 461, 67 83 437 4.3.17.409 221,186 — 223,106 54i, 39 83 443 2.3.13907 — 209,141 280, 41 157,107 83 449 8.9.19.61 235,168 71,198 i57,i4o 263, 99 83 459 2.41729 — 279, 53 — — 83 471 2.5.17.491 — — — — 83 477 4.41.509 41,286 — — — 83 497 8.3.49.71 261,124 205,144 53,i64 545, 37 83 537 16.23.227 289, 4 285, 34 — — S3 557 4.9.11.211 289, 6 — 283, 34 385, 83 83 561 8.5.2089 155,244 147,176 — — 83 563 2-3- I 9-733 — 275, 6 3 160,139 577, 7 33 579 2. 1 1. 29.131 — 123,185 — — 83 591 2.5.13.643 — — — — 83 537 4.20899 269,106 — — — 83 609 8.7.1493 253^40 261, 88 — — 83 617 32.3.13.67 279, 76 283, 42 103,156 206,104 QUADRATIC PARTITIONS. 205 f p- A B L M 83 62l! 4 .5.37.ii3 83 639, 2.19.31.71 83 6411 8 3.5. 1 7.41 83 653 4.3.6971 83 663 2.59.709 83 689 83 701 83 717 83 719 83 737 83 773 83 777 83 791 83 813 83 833 83 843 83 857 83 869 83 873 83 891 83 903 83 911 83 921 83 933 83 939 83 969 83 983 83 987 84 011 84 017 84 047 84 053 84 059 84 061 84 067 84 089 84121 84127 84 131 8.3.11.317 4.27.25.31 4.20929 2.9.4651 8.9.1163 83 761 16.3.5.349 4.9-13-179 64.7.11.17 2.9.5.49.19 4.23.911 8.3.7.499 2.11. 37.103 16. 3.1747 4.3-29-241 32.2621 2.5.8389 2.7. 13.461 2-3-5-2797 16.5. 1049 4.20983 2.41969 2048.41 2-3-!3997 2.49.857 2.5.31. 271 16.59.89 2.42023 4.21013 2.13-53-61 4.9-5-467 2.3.14011 8.23-457 8.3.5.701 2.3.7.2003 2.5.47.179 289, 10 205,204187,156 207,202 — 283, 60221,132 199,210 — 289, 14 — 251,144 r 35>256 123,262 289, 16 287, 38 1267,112 119,264 165,238 233*172 289, 20 283, 62 287, 40 239,164 263,122 219,190 275> 92 189,220 73>i98 23,204 273, ^ 121,186 255, 97 25,204 219,134 279, 55 93,194 277, 48 229,102 83,160 163,138 2 38, 95 275, 52 281, 40 71,162 46,165 221,108 554, 32 458, 68 39,203 63,200 105,191 213,139 237,118 215,112 263, 70 278, 47 3,205 !93,i53 267, 80 139,180 9,205 286, 27 397, 81 326, 92 47,111 119,109 161,107 142,108 92,110 442, 72 121,109 53,ni 4i9, 77 572, 18 73,162 20,167 187,128 290, 3 146,108 521, 49 i97,io5 580, 2 206 QUADRATIC PARTITIONS. p P -i a b c d A B L M 84137 8.13.809 59,284 243,112 — — 84 143 2.42071 — — — — 84 163 2.3 i3- x 3' 8 3 — 281, 51 80,161 563, 27 84179 2.42089 — 81,197 — — 84181 4.3.5.23.61 9,290 — 253* 82 499, 57 84191 2.5.8419 — — — — 84199 2-3-14033 — — 254, 81 508, 54 84 211 2.3.5.7.401 — 113,189 248, 87 496, 58 84 221 4.5.4211 11,290 — — — 84 223 2.9.4679 — — 266, 67 65,111 84 229 4.3.7019 177,230 — 277, 5° 127,109 84 239 2.7. 11. 547 — — — — 84 247 2-3-I9-739 — — 290, 7 269, 99 84 263 2.42131 — — — — 84 299 2H3-373 — 99>!93 — — 84 307 2.3.14051 — 263, 87 92,i59 184,106 84 313 8.9.1 171 37,28821 179,132 358, 88 84 317 4.io7-i97 251,146 — — — 84 319 2.3.13.23.47 — — 286, 29 199,105 84 347 2. 181.233 — 165,169 — — 84 349 4.27. 11. 71 107,270 — 41,166 457, 69 84 377 8.53-I99 61,284 117,188 — — 84 389 4.I7.I7-73 17,290 — — — 84 391 2-3-5- 2 9-97 — — 146,145 289, 97 84 401 16.25. 211 185,224 87,196 — — 84 407 2.7.6029 — — — — 84 421 4.9.5.7.67 289, 30 — 283, 38 169,107 84 431 2-5-8443 — — — — 84 437 4.11.19.101 281, 74 — — — 84 443 2.42221 45*203 — — 84 449 32.7.13.29 175*232 159,172 — — 84 457 8.27.17.23 91,276 35,204 107,156 214,104 84 463 2.3.7.2011 — — 290, 11 323, 93 84 467 2.157.269 — 177,163 — — 84 481 512.3-5.11 225,184 257, 9 6 137,148 307, 95 84 499 2.3.14083 ■ — 239,117 268, 65 73, 111 84 503 2. 11. 23. 167 — — — — 84 509 4-37-57 1 85,278 — — — 84 521 8.5-2113 211,200 111,190 — — 84 523 2.3.14087 — 61,201 224,107 545, 39 QUADRATIC PARTITIONS. 207 p p-1 a b c d A B L M 84 532 84 551 4.7.3019 2.25.19.89 167,238 — — — 84 55S 84 588 84 629 2.3.17.829 4-3-7- I 9-53 4-2H57 285, 5* 23,29c i — — i34,i4S 241, 94 >58i, 5 •523, 49 84 631 84 649 84 653 2 -3-5-7.i3-3i 8-3.35 2 7 4.21163 243,16c 227,182 79,198 262, 73 269, 64 481, 63 77,111 84 659 84 673 2.7.6047 64.27.49 287, 48 153,175 289, 24 1,168 2,112 84 691 84 697 2.9.5.941 8.3-3529 291, 4 271, 75 283, 48 32,167 5,168 533, 45 10,112 84 701 84 713 84 719 4-25.7-121 8.10589 2-42359 149,250 283, 68 291, 4 — — 84 731 84 737 84 751 84 761 2.5.37.229 256.331 2.3.125.113 8.5.13.163 281, 76 131,260 291, 5 267, 82 69,200 178,133 577, 15 84 787 2.3.13.1087 — 185,159 128,151 325, 93 84 793 84 809 8-3-3533 8.10601 43,288 235^72 281, 54 291, 8 11,168 22,112 84 811 84 827 84 857 2.3.5.11.257 2.7.7383 8.10607 139,256 227,129 75, J 99 57,202 56,165 112,110 84 859 84 869 2-3- I 4i43 4-49-433 287, 50 149b 1 {7 164,139 253,101 84 871 84 913 84 919 2.9.5.23.41 16.3.29.61 2-3 -14153 153,248 41,204 23^, 97 65,164 206,119 529, 47 557, 33 563, 29 84 947 84 961 2.42473 32.9-5-59 81,280 225,13! 287, 36 17,168 34,n2 84 967 84 977 84 979 2. 3.49.17. 17 16.47.113 2.9.4721 241,164 147,178 289, 27 290, 17 148,145 34i, 91 583, 1 84 991 85 009 85 021 85 027 2 -3-5-2833 16. 3. 7. 11. 23 4.3-5- I 3-i°9 2-3-37-383 1 105,272 261,130 169,168 — 1 65,201 142,147 I5M44' 167,138 280, 47 284, 98 302, 96 334, 92 139,109 85 037 4-7-3037 259,134 — — — 208 QUADRATIC PARTITIONS. V p-1 a b c d A B L M 85 049 8.10631 115,268 261, 92 — — 85 061 4.5-4253 31,290 — — — 85 081 8.3.5.709 291, 20 43,204 91,160 57i, 23 85 087 2.9.29.163 — — 1278, 5 1 556, 34 85 091 2.5.67.127 — 129,185 — 85 093 4.3.7. 1013 257,138 — 101,158 575, 19 85 103 2.17.2503 — — — — 85109 4.21277 265,122 — — — 85121 128.5.7.19- 289, 40 177,164 — — 85 133 4.21283 163,242 — — — 85 147 2.3.23.617 — 275, 69272, 61 89,111 85159 2.27.19.83 — — 86,161 569, 25 85 193 8.23.463 277, 92 291, 16 — — 85 199 2.41. 1039 — — — — 85 201 16.3.25.71 95>276 i57,i74 23,168 46,112 85 213 4.81.263 267,118 — 215,114 43°, 76 85 223 2.42611 — — — — 85 229 4.11. 13.149 275> 98 — — — 85 237 4-3-7 io 3 279, 86 — 227,106 91,111 85 243 2.3.14207 — 205,147 160,141 320, 94 85 247 2.7.6089 — — — — 85 259 2.47.907 — 291, 17 — — 85 297 16.3.1777 209,204 83,198 25,168 50,112 85 303 2.9.7.677 — — 130,151 583, 7 85 313 &4.3M3 7,292 21,206 — — 85 331 2.5-7-23.53 — 183,161 — — 85 333 4.3- I 3-547 137,258 — 259, 78 518, 52 85 361 16.5.11.97 281, 80153,176 — — 85 363 2.3.41.347 — I265, 87 220,111 440, 74 85 369 8-3-3557 213,200263, 90 163,140257,101 85 381 4.3.5.1423 175,234' — 283, 42 566, 28 85 411 2.9-5' I 3-73 — 1287, 39 292, 7 3i3, 95 85 427 2. 121.353 — 255,101 — — 85 429 4.27.7.113 215,198 — 269, 66 538, 44 85 439 2.42719 — — 85 447 2.9.47. 101 . — — 98,159 196,106 85 451 2.25.1709 — 237,121 — — 85 453 4.3.7 121 77,282 — 209,118 145,109 85 469 4.23.929 37,290 — — — 85 487 2.42743 — — — — QUADRATIC PARTITIONS. p p-l a b c d A B L M 85 513 8.3.7.509 117,268 259, 96 29,168 58,112 85 517 4.21379 61,286 — — 85 523 2.61. 701 — io 5, j 93 — — 85 531 2.3.5.2851 — 187,159 116,155 581, 13 85 549 4.3.7129 195,218 — 289, 26 211,105 85 571 2.5.43.199 — 39,205 — — 85 577 8.19.563 259>i3 6 63,202 — — 85 597 4.3.7.1019 219,194 — 263, 74 485, 63 85 601 32.25.107 265,124 27,206 — — 85 607 2. 23.1861 — — — 85 619 2.13.37.89 231,127 — — 85 621 4-3-5- I 427 39,290 — 83,162 166,108 85 627 2.9.67.71 — 197,153 292, 11 259,101 85 639 2.3.7.2039 — — 242, 95 527, 49 85 643 2.42821 — 285, 47 — 85 661 4.5.4283 181,230 — — — 85 667 2. 7. 29.211 — 57,203 — — 85 669 4.3.121.59 113,270 — 187,130 577, 19 85 691 2.5. 11. 19.41 — 147,179 — — 85 703 2.73587 — — — — 85 711 2.3-5- 2 857 — — 278, 53 437, 75 85 717 4.9.2381 249>i54 — 275, 58 101,111 85 733 4-21433 287, 58 — — 85 751 2-125.343 — — — — 85 781 4.5.4289 41,290 — — — 85 793 32.7-383 23,292 261, 94 — — 85 817 8.17.631 269,116 123,188 — — 85 819 2-3-i43°3 — 11,207 224,109 103,111 85 829 4-43-499 223,190 — — — fc5 831 2.3.5.2861 — — 218,113 557, 35 85 837 4.3.23.311 291, 34 — 287, 34 185,107 85 843 2.9.19.251 — 71,201 100,159 200,106 85 847 2.42923 — — — 85 853 4.13.13.127 293, 2 — — — 85 889 128 11. 61 25,292 117,190 — — 85 903 2.3. 103. 139 — — 286, 37 397, 83 85 909 1 4-3-7159 153,250 — *79, J 34 581, 15 85 931 2.5.13.661 — 291, 25 — — 85 933 4.9.7.11. 31 93,278 — 239, 98 533, 47 85 991 2-5-8599 — — — 2e 210 QUADRATIC PARTITIONS. p P -l a b c d A B L M 85 999 2.3.11.1303 — — 118,155 347, 9 1 86 011 2.3.5.47.61 — 293> 9 212,117 424, 78 86 017 4096.3.7 281, 84 245,114 73^64 4i9, 79 86 027 2.43013 — 285, 49 — — 86 029 4.3.67.107 275,102 — 223,110 107,111 86 069 4.215x7 263,130 — — — 86 077 4.27.797 261,134! 217,114 434, 76 86 083 2.3.14347 — 121,189 20,169487, 63 86111 2.5.79.109 — — — — 86 113 32.913.23 207,208289, 36 i75^3 6 583, 13 86117 4.21529 209,206 — — — 86131 2. 27. 5. 11. 29 ; 73>2oi 292, 17 241,103 86137 8.3.37.97 211,204293, 12 277, 5 6 109,111 86 143 2.3.49.293 — — 146,147 292, 98 86 161 16.3.5.359 169,240281, 60 143,148 301, 97 86171 2.5.7. 1231 — 261, 95 — — 86179 2.3.53-271 — 223,135 152,145 283, 99 86 183 2.41.1051 — — — — 86197 4.3- II -653 201,214 — 253, 86 5,U3 86 201 8.25.431 235,176249,110 — — 86 209 64.3.449 185,228 203,150 97,160 577, 21 86 239 2.27.1597 — — 274, 61 457, 7i 86 243 2.13.31.107 — 255>i°3 — — 86 249 8.10781 293, 20 291, 28 — — 86 257 16.9.599 199,216 55.204 287, 36 574, 24 86 263 2.3.11.1307 — — 250, 89 I7,n3 86 269 4.3.7.I3.79 245,162 — i37,i5o|274,ioo 86 287 2.3-73.I97 — — 290, 271580, 18 86 291 2.5.8629 — 279, 65 — — 86 293 4.27.17.47 217,198 — 211,118565, 31 86 297 8.7.23.67 229,184 105,194 86 311 2.9.5.7.I37 — — 158,1431587, 5 86 323 2.3.M387 — 25,207 260, 79 23,113 86 341 4-3-5- I 439 255,146 — 107,158581, 17 86 351: 2.25. n. 157 — — — — 86 353 16.3.7.257 33> 2 92 131,186 41,168 82,112 86 357, 4-21589 281, 86 — — — 86 369 32.2699 137,260 69,202 — — 86 371! 2.3.5.2879 — 167,171 52,167449, 73 86 381 4.5.7.617 125,266 — ~ — QUADRATIC PARTITIONS. 211 p P -l a b c d A B L M 86 389; 4.3-23-3I3 183,230 61,166 559, 35 86 399 2.13.3323 — — — 86 413 i 4-3-I9-379 83,282 — 161,142 265,101 86 423J 2.7.6173 — — — — 86 441 8.5. 2161 275, IQ 4 177,166 — — 86 453 4-21613 167,242 — — — 86 461 !4.3-5-".i3i 5,294 — 281, 50 43i, 77 86 467 2.3.14411 — 263, 93 28,169 535, 47 86 477 4.13.1663 221,194 — — 86 491 2.9.5-3 I -3 I — I79,i65 112,157 583, 15 86 501 4-125.173 49,290 — — — 86 509 4.243.89 253 3 i5 — 271, 66 542, 44 86 531 2.5.17.509 — 159,175 — 86 533 4.3-7211 193,222 — 245, 94 37,U3 86 539 2.3.14423 — 29,207 164,141 328, 94 86 561 32.5.541 145,256 81,200 — — 86 573 4.23.941 173,238 — — — 86 579 2-73-593 — 129,187 — — 86 587 2.3.14431 — 283, 57 292, 21 584, 14 86 599 2.9.17.283 — — 94,161 389, 85 86 627 2.43313 — 183,163 — — 86 629 4.3.7219 273,110 — 181,134 221,105 86 677 4.3-3I-233 279, 94 — 205,122 161,109 86 689 32.9.7-43 233,180 91,198 167,140 587, 9 86 693 4.21673 97,278 — — 86 711 2.5.13.23.29 — — — — 86 719 2.3.97.149 — — 226,109 553, 39 86 729 8 -37-293 277,100 291, 32 — 86 743 2.9.61.79 — — 266, 73 47,n3 86 753 32.2711 113,272 15,208 — 86 767 2.3.14461 — — 142,149, 305, 97 86 771 2.5.8677 — 87,199 — 86 783 2.43391 — — — — 86 813 4.11.1973 283, 82 — — — 86 837 4-17-1277 71,286 — — — 86 843 2.7.6203 — 285, 53 — — 86 851 2.9.25 193 — 217,141 292, 23 223,105 86 857 8.3.7.11.47 131,264 257,102 157,144. 314, 96 86 861 4.5. 43.101 275,106 — — 86 869 4.9.19.127 135,262 — i3,!7o< *97, 61 212 QUADRATIC PARTITIONS. V p-1 d A B L M 86 923 86 927 86 929 86 939 86 951 86 959 86 969 86 981 86 993 87 011 87 013 87 037 87 041 87 049 87 071 87 083J 87 103| 87107 87 119 87121 87133 87149 87151 87179 87 181 87187 87 211 87 221 87 223 87 251 87 253 87 257 87 277 87 281 87 293 87 299 87 313 87 317 87 323 87 337 2.9.11.439 2.49.887 16.3. 1811 2.17-2557 2.25.37.47 2.9.4831 8-7-1553 4-5-4349 16.5437 2.5.7. 11. 113 4.9.2417 4-3-7253 1024.5. 17 8.27.13.31 2.5.8707 2.43541 2.27. 1613 2.97.449 2.43.1013 16.9.5. 121 4-3-53-I37 4.21787 2.3-25-7.83 2.7.13.479 4.3-5I4S3 2.3.11.1321 2.27.5.17.19 4.5.49.89 2-3-14537 2.125.349 4.3.11.661 8.13.839 4-3-7-i°39 16.5. 1091 4-i39-!57 2.43649 16.3.17.107 4.83.263 2.43661 8.9.1213 255,148 205,212 241,170 287, 68 143,258 229,186 295, 4 93,280 35,207 221,138 261, 97 21,208 184,133 79,164 122,155 583, 17 413, 81 587, 11 289, 60 277,102 157,250 291, 50 295, 14 247,162 221,196 29,294 295, 16 293, 3^ 183,232 151,254 251,156 291, 34 273, 79; — 91,162182,108 — 295, 2J289, 99 171,170 — — 289, 42293, 20353, 9i 165,173 — — , 86,163 177,167 — 163,174239,100 — 295, 6 J 74,i65 69,203 — — 191,130 295, 9208,121 181,165256, 85 207,149 27,208 183,164 57,205 295, 12 254, 87 259, 82 127,154 271, 68 i95,i57 253,108203,124 403, 83 61,113 59o, 4 148,110 i99,io7 57i, 29 5ii, 57 508, 58 505, 59 589, 9 67,113 169,109 QUADRATIC PARTITIONS. 218 P p-1 A B L M 87 359 87 383 87 403 87 407 87 421 87 427 87 433 87 443 87 473 87 481 87 491 87 509 87 511 87 517 87 523 87 539 87 541 87 547 87 553 87 557 87 559 87 583 87 587 87 589 87 613 87 623 87 629 87 631 87 641 87 643 87 649 87 671 87 679 87 683 87 691 87 697 87 701 87 719 87 721 87 739 2.31. 1409 2.43691 2.3.7.2081 2. 11. 29. 137 4-3-5-3I-47 2.27. 1619 8-3.3643 2.43721 16. 7. 11. 71 8.5.27.81 2.5.13.673 4.131.167 2.3.5.2917 4.9.11.13.17 2.3.29.503 2.11. 23.173 4.3.5.1459 2.3.14591 512.9.19 4.7.53.59 2-3-I4593 2.3.11.1327 2-43793 4.27. 811 4.3.49.149 2.193.227 4.i9.ii53 2.3.5.23.127 8.5-7.313 2.81. 541 32.3.11.83 2.5.11.797 2.9.4871 2.7.6263 2.3.5.37.79 16.27.7.29 4.25.877 2. 61. 719 8.3.5.I7.43 2.3.7.2089 75,286 67,288 47,292 141,260 j295, 22 181,234 121,270 287, 72 191,226 7116,157 263, 78 143,183212,119 95,198229,108 9,209 — 51,200 — 1 97 > i5 6 53,i68 153,179 — — I 62,167 — 247, 94 265, 93236,103 145,258 293, 42 227,190 5,296 265,132 249,H3 — I 29,170 43,207172,139 271, 84265, 76 355, 9i 526, 52 569, 31 458, 72 106,112 563, 35 529, 5 1 73,H3 15,209 9,296 295, 26 261,140 279, 70 251,111 293, 30 194,129 190,131 283, 50 295, 14 231,13! 83,201 215,144 67,204 211,147 266, 75 296, 3 121,156 202,125 296, 5 55,i68 539, 47 589, 11 493, 63 388, 86 203,107 i33,in 253,103 532, 50 592, 2 242,104 173,109 3ii, 97 110,112 211,120 4,171 422, 80 8,114 214 QUADRATIC PARTITIONS. p p—l a b c d A B L M 87 743 2.19.2309 — — — 87 751 2.27. 125.13 — — 274, 65 79,113 87 767 2.7.6269 — — — — 87 793 l6 -3-3i-59 207,212 275, 78 295, 16343, 93 87 797 4.47.467 281, 94 — 87 803 2. 11. 13.307 — 21,209 87 811 2.3.5.2927 — i93,i59 268, 73487, 65 87 833 8.10979 283, 88201,154 — — 87 853 4-3-7321 237,178; — 289, 38 175,109 87 869 4.11.1997 187,230, — — — 87 877 4.9.2441 289, 66 — 293, 26 37i, 89 87 881 8.5.13.13.13 85,284291, 40 — — 87 887 2.43943 — — — — 87 911 2.5.59.149 — — — — 87 917 4.31.709 131,266 — — 87 931 2.9.5.977 — 109,195 152,147 304, 98 87 943 2.3.14657 — — 110,159 220,106 87 959 2. 13.17. 199 — — — — 87 961 8.3.5.733 219,200 137,186 197,128 581, 23 87 973 4.3.7331 177,238 — 155,146)593, 3 87 977 8.7.1571 19,296 273, 82 — — 87 991 2.3.5.7.419 — — 178,137 233, io 5 88 001 64.125. 11 199,220 213,146 — — 88 003 2.9.4889 — 145,^3 140,151 3 r 3, 97 88 007 2.79-557 — — — — 88 019 2.7.6287 — 63,205 — — 88 037 4.13.1693 79,286 — — — 88 069 4.3.41. 179 63,290 — 37,i7o473, ^9 88 079 2-47-937 — — — — 88 093 4.9.2447 197,222 — 185,134587, 17 88117 4.3.7.1049 41,294 — H5,i58359, 9i 88129 64.81.17 255^52 289, 48 161,144 322, 96 88169 8. 103. 107 275,112 81,202 — — 88 177 16. 3. 11. 167 281, 96 295, 24 287, 44 419, 81 88 211 2.5.8821 — 297, 1 88 223 2.44111 . — — 88 237 427.19.43 269,126 — 257, 86515, 57 88 241 16.5.1103 25,296 297, 4 — — 88 259 2.44129 — 297, 5 — — 88 261 4-3-5- I 47i 225,194 — 277, 62 9i, JI 3 QUADRATIC PARTITIONS. 215 p ^-1 a b c d A B L M 88 289 32.31.89 55 5 2 9 2 219,142 — — 88 301 4.25.883 II5.274 — — — 88 321 256.3.5.23 295. 36 11,210 289, 4°'4°9. 83 88 327 2.9.7.701 — — 262, 81 524, 54 88 337 16.5521 15^256 297, 8 — — 88 339 2.3.14723 — 241,123 196,129392, 86 88 379 2.44189 — 291. 43 — — 88 397 4.49.11.41 259,146 — — — 88 411 2.3.5.7.421 — I73,i7i 188,133211,107 88 423 2-3-14737 — — 286, 47 I45, 111 88 427 2.13.19.179 — 237,127 — — 88 463J 2. ii. 4021 — — — — 88 469 4.17. 1301 295. 38 — — — 88 471 2.9.5.983 — 238,103547, 45 88 493 4.22123 173,242 — — — 88 499 2.44249 — 279. 73: — — 88 513 64.3.461 57.292 I39,!86 151,148 595. 1 88 523 2.7.6323 — 261,101 — — 88 547 2.44273 — 297, 13 — — 88 589| 4.22147 67,290 — — — 88 591 2.3.5.2953 • — — 218,1 17 436, 78 88 6071 2.7.6329 — — — — 88 609 32-3-I3-7 1 297, 20 101,198 89,164 581, 25 88 643 2.23.41.47 — !o5.!97 — — 88 651 2.9.25.197 — 253,111 208,123 416, 82 88 657 16.3.1847 279,104 265, 96247, 96 494. 64 8866ll4.5-n.13-3! 215,206 — — — 88 663 2.3.7.2111 — — 290, 39 580, 26 88 667 2.43. 1031 — 285, 61 — — 88 681 8.3.5.739 205,216 209, 150 109, 160 589. 17 88 721 16.5.1109 265,136297, 16 — — 88 729 8.3.3697 165,248 23,210173,140 593, 11 88 741; 4.9.5.17.29 255^54 — |22 9 ,IIO 101,113 88 747 2.3.7.2113 — 275, 8l 32,171 64,114 88 771 2. 3.5. 11. 269 — 263, 99236,105 472, 70 88 789 4-3-49- 15 1 295. 42 — 269, 74 49 1 , 65 88 793! 8. 1 1. 1009 187,232279, 74 — • — 88 799 2. 29.1531 — — ; — — 88801132.3.25.37 201,220283, 66 7,172 523, 55 88 807 2.3.19.19.41 — — 298, 1 3 QI , 99 216 QUADRATIC PARTITIONS. p P -l a b c d A B L M 88 811 2.5.83.107 — 69,205 — — 88 813 4.9.2467 3*298 — 289, 42 578, 28 88 817 16.7. 13.61 271,124 243,122 — — 88 819 2.3.113.131 — 113,195 56,169 45i, 75 88 843 2.3.13.17.67 — 205.153 280, 59 103,113 88 853 4.97.229 7,298 — — 88 861 4.3.5. 1481 69,290 — 217,118 57i, 33 88 867 2 -9 4937 — 287, 57 212,121 151,111 88 873 8.3.7.23.23 77,288 239,126 11,172505, 61 88 883 2.19.2339 — 39,209 88 897 64.3.463 249,164 277, 78 65,1681130,112 88 903 2.9. 1 1.449 — — 166,143263,103 88 919 2.23.1933 — — — — 88 937 8.1 1 1 17 91,284 237,128 — — 88 951 2-3.25.593 — — 298, 7 3i9, 97 88 969 8.3-II-337 285, 88 191,162 91,164 401, 85 88 993 32.27.103 297, 28 251,114 271, 72542, 48 88 997 4.19.1171 289, 74 — — — 89 003 2.44501 — 99,199 — — 89 009 16.5563 103,280 297, 20 — — 89 017 8.3.3709 139,264 103,198 277, 64 469, 71 89 021 4-5-445 1 85,286 — — — 89 041 163.5-7.53 225,196 29,210 17,172 499, 63 89 051 2.25.13.137 — 3,211 — — 89 057 32.121.23 241,176 207,152 — — 89 069 4.7.3181 163,250 — — — 89 071 2.3.5.2969 — — 86,165 172,110 89 083 2.9.49.101 — 91,201284, 53 443, 77 89 087 2-44543 — — — 89101 4.81. 25.11 195,226! — 49» I 7© 461, 73 89107 2.3.14851 — i75> T 7 I2 72, 71 485, 67 89113 8.3.47.79 123,2721169,174 19,172 535. 5i 89119 2.9.4951 — — 194,131 587, 21 89123 2. 11. 4051 9,211 — — 89137 16. 9. 619 39,296233,132127,156 254,104 89153 64.7.199 257»I5« 111,196 — — 89 189 4.11.2027 175,242 — — — 89 203 2.3.14867 — 295. 33296, 23 365. 9i 89 209 8.27.7.59 147,260 181,168 221, 116 569, 35 89 213 4.22303 293. 58 — — — QUADRATIC PARTITIONS. 217 p p-1 a b c d A B L M 89 227 2.9.4957 — 163,177 172,141344, 94 89 231! 2.5.8923 — — — 89 237i4.7-3i87 119,274 — — — 89 261 4-5-4463 269,130 — — 89 269 4.3.43-I73 265,138 — 259, 86j 1,115 89 273 8.11159 277,112 231,134 — — 89 293J4-3-7- io 63 237,182! 241,102 482, 68 89 303j 2.44651 — — — — 89 317 4-27-827 271,126 — 293, 34 191,109 89 329 16.3.1861 295, 48281, 72 289, 44 i57,in 89 363 2.7. 13.491 — 159,179 — — 89 371 2.27. 5-33 1 — 197,159 292, 37 403, 85 89 381 4.5.41. 109 191,230 — — 89 387 2. 11. 17.239 — 45,209 — — 89 393 16.37. 151 167,248 279, 76 — — 89 399 2.44699 — — — — 89 413 4-3-7451 273,122 — 299, 2305, 99 89 417 8. 1 1 177 299, 4 285, 64 — — 89 431, 2. 3.5. 11. 271 — — 182,137 593, 15 89 443 2.9.4969 — 2i5»i47 76,167 425, 81 89 449 1 8.3.3727 293, 60 157,180 299, 4 287,101 89 459 2.44729 — 297, 25 — — 89 477 4.22369 209,214 — — — 89 491 2.3.5.19.157 — 223,141 296, 25 221,107 89 501 4.125. 179 299, 10 — — — 89 513 8.67.167 133,268189,164 — — 89 519 2.11.13-313 — < — — 89 521 ^■3-5-373 239,180211,150 i 9 3,i32; 3 86, 88 89 527 2-3-43-347 — — 62,169445, 77 89 533 4.27.829 27,298 — i 121,158 353, 93 89 561 8.5.2239 155,256297, 26 — — 89 563 2.3.11.23:59 — |2 9 9, 9 280, 61 463, 73 89 567 2.19.2357 — - 89 591 2. 5. 17. 17. 31 — — — — 89 597 4.13.1723 299, 14 — — — 89 599 2.3.109.137 — — 286, 51 572, 34 89 603 2. 71. 631 — 129,191 — — 89 611 2.3.5.29.103 — 1283, 69 268, 77 37,n5 89 627 2.41. 1093 — 123,193 — — 89 633 32.2801 233,188 69,206 — — 2f 218 QUADRATIC PARTITIONS. p p-l a b c d A B L M 89 653 4.3.31. 241 297, 38 — 205,126 410, 84 89 657 8.7.1601 299, 16153,182 — — 89 659 2.9.17.293 — 1269, 93 44,171 88,114 89 669 4-29-773 145,262 — 89 671 2.3.5.49.61 — — 1298, 17 247,105 89 681 16.5. 19.59 95,284 2 9 J , 5° — — 89 689 8.3.37.101 285, 92 299, 12269, 76 4i,n5 89 753 8.13.863 67,292 261,104 — 89 759 2.44879 — — — — 89 767 2.9.4987 — — 118,159 236,106 89 779 2.3.13.1151 — 151,183 64,169 57i, 35 89 783 2.7. 121.53 — — — — 89 797 4.3.7.1069 159,254 — 277, 66 554, 44 89 809 16.3.1871 297, 40 247,120 209,124 163,111 89 819 2.44909 — 141,187 — — 89 821 4.9.5.499 235,186 — 247, 98 47,u5 89 833 8.3.19.197 83,288 241,126 299, 12 598, 8 89 839 2.9.7.23.31 — — 46,171 92,114 89 849 8.11.1021 107,280 249,118 — — 89 867 2-343-I3 1 — 195,161 — — 89 891 2.5.89. 101 — 297, 29 — — 89 897 8.17.661 251,164 3,212 — — 89 899 2.3.14983 — 293, 45 1I 9 6 , I 3i; I 97,i°9 89 909 4.7.13.13.19 247,170 — — — 89 917 4.3-59- I2 7 59,294 — i37,i54 325, 97 89 923 2.3.7.2141 — 65,207 200,129 400, 86 89 939 2.193.233 — 111,197 — — 89 959 2.3.11.29.47 — — 278, 65 473, 7i 89 963 2.31. 1451 — 51,209 — — 89 977 8.3.23.163 299, 24 263,102 35, J 72 481, 69 89 983 2.9.4999 — — i4,i73 533, 53 89 989 4-3-7499 255,i5S : 299, 14 34i, 95 90 001 16.9.625 i,3°° 2 53, I][ 4 73,i68 146,112 90 007 2.3.7.2143 — — 218,119 575, 33 90 011 2.5.9001 — 219,145 — — 90 017 32.29.97 49,296 273, 88 — — 90 019 2.27.1667 — 289, 57 188,135 376, 90 90 023 2. 19.23.103 — — — — 90 031 2.3.5.3001 — — ^34,155 599, 7 90 053 4.47.479 113,278 — — — QUADRATIC PARTITIONS. 219 p p-1 a b c d A B L M 90 059 2. 37.1217 147,185 90 067 2.3.I7.883 — 295, 39 80,167 581, 29 90 071 2.5.9OO7 — — . — — 90 073 8.8LI39 163,252 235^32 229,112 565, 39 90 089 8.II26I 283,100 291, 52 — 90107 2-45°53 — 267, 97 — — 90121 8.3.5-75I 11,300 83,204 37,i72 553, 45 90127 2.27.1669 — — 298, 21 59 6 , 14 90149 4.31.727 i93>23o — — — 90 163 2.9.5009 — 199,159 184,137 227,107 90173 4.22543 37»298 — — — 90187 2.3- I 5°3 I — 67,207 20,173 539, 5i 90191 2. 5. 29.311 — — — — 90197 4.22549 281,106 — — — 90199 2.9.5011 — — 274, 71 61,115 90 203 2.7.17.379 — 285, 67 — — 90 217 8.9.7.179 51,296 145,186 235,108 470, 72 90 227 2.197.229 — 105,199 — — 90 239 2.45119 — — — 90 247 2.3.13.13.89 — 170,143 599, 9 90 263 2.45!3i — — — — 90 271 2.9.5.17.59 — — 22,173 497, 65 90 281 8.5.37.61 109,280 207,154 — — 90 289 16. 27. 11. 19 17,300 109,198 217,120 434, 80 90 313 8.3-53.7I 213,212 221,144 259, 88 523, 57 90 353 16.5647 217,208 231,136 — — 90 359 2.45179 — — — — 90 371 2.5.7.1291 — 273, 89 — — 90 373 4-3-17-443 207,218 — 299, 18 598, 12 90 379 2.9.5021 — 251,117 256, 91 529, 55 90 397 4.729.31 219,206 — 265, 82 511, 61 90 401 32.25.113 151,260 123,194 — — 90 403 2.3.13.19.61 239,129 284, 57 568, 38 90 407 2.17.2659 — — — 90 437 4-23-983 161,954 — — — 90 439 2 -3-i5°73 1 _ — 266, 81 532, 54 90 469 4-9-7-359 I287, 90 — i39,i54 601, 5 90 473 8.43.263 293, 68 285, 68 — 90 481 16.3.5. 13.29 1241,180 *73, J 74 287, 52 i3!, I][ 3 90 49S 2-3-i5°83 ' — 209,153 296, 31 203,109 220 QUADRATIC PARTITIONS. P-i A B L M 90 511 90 523 90 527 90 529 90 533 90 547 90 583 90 599 90 617 90 619 90 631 90 641 90 647 90 659 90 677 90 679 90 697 90 703 90 709 90 731 90 749 90 787 90 793 90 803 90 821 90 823 90 833 90 841 90 847 90 863 90 887 90 901 90 907 90 911 90 917 90 931 90 947 90 971 90 977 90 989 2.3.5.7.431 2.9.47.107 2.45263 32.3.23.41 4.13.1741 2.3.15091 2.3.31.487 2.97.467 8.47.241 2.3.11.1373 2 -9-5-i9-53 16.5. 11. 103 2.61.743 2.45329 4.22669 2.3.7.17.127 8-3-3779 2-9-5°39 4-3-7559 2.5-43-2II 4.49.463 2-3-i5 I 3* 8.9.13.97 2.83.547 4.5-I9-239 2.3-15137 16.7.811 8-3-5-757 2.9.49.103 2. 181. 251 2.29.1567 4.9.25-101 2.3.109.139 2.5.9091 4.7.17.191 2 -3-5-7-433 2.37.1229 2.5.11.827 32.2843 4.23.23.43 23,300 223,202 179,171 229,138 167,177 301, 4 55,296 199,226 299, 36 297, 5° 293, 7o 197,228 95,286 287, 92 29,300277, 84 27,212 3°!, 3 279, 80 2 97 5 35 205,156 291, 55 94,165 188,110 104,163385, 89 241,104 268, 79 70,169 176,141 166,145 7i,n5 505, 63 577, 33 352, 94 601, 7 298, 25373, 91 133,156266,104 194,133205,109 301, 6602, 4 232,111 7,213 269, 963c 159,181 189,166 249,170 — 13,213 289, 86 239,184 83,290. 191,165 297, 37 2i3, I 5 I 33,212 206,127 179,140 130,157 301, 10 248, 99 172,143 464, 74 277,103 i75,in 599, 601, 33h 97 496, 66 257,105 QUADRATIC PARTITIONS. 221 V p — 1 a b c d A B L M 90 997 4.3-7583 231,194 — i3 5 i74 26,116 91009 128.9.79 153,260 53,2io 247,100 547, 49 91019 2.17.2677 — 261,107 — — 91033 8-3-3793 293, 72 265,102 301, 12 602, 8 91079 2-i3-3 I - II 3 — — — — 91081 8.9.5.11.23 291, 80 287, 66 197,132 394, 88 91097 8-59-193 59,296 297, 38 — — 91099 2.27.7.241 — 19,213 284, 59 461, 75 91121 16.5.17.67 295, 64 i53, l8 4 — — 91127 2.7.23.283 — — — — 91129 8-3-3797 277,120 281, 78 299, 24 598, 16 91139 2.455 6 9 — 129,193 — — 91141 4.3.5.49.31 175,246 — 293, 42 586, 28 91151 2.25.1823 — — — — 91153 16.27. 211 233» I 9 2 89,204 49,172 565, 4i 91159 2 -3-i5 I 93 74,169 433, 81 91 163 2.19.2399 — *95, l6 3 — — 91 183 2.3.7.13.167 — — 214,123 428, 82 91193 8.11399 77,292 171,176 — — 91199 2-45599 — — — — 91229 4.22807 5>3°2 — — — 91 237 4-3-7603 191,234 — 245,102 490, 68 91243 2.9-37-I37 — 181,171 224,117 448, 78 91249 16.3. 1901 207,220 301, 18 281, 64 89,115 91253 4.7.3259 7,302 — — — 91283 2.45641 — 249,121 — — 91291 2-3-5- I 7-i79 — 227,141 296, 35 401, 87 91297 32.9-317 279,116 197,162 103,164 389, 89 91303 2.3.15217 — — 290, 49 I43,H3 91309 4.3.7.1087 205,222 — 209,126 418, 84 91331 2.5-9I33 — 63,209 — — 91367 2.11.4153 — — — — 91369 8.243.47 37,3°° 163,180 301, 16 349, 95 91373 4.53.431 i3>3° 2 — • — — 91381 4-3.5-1523 295, 66 — 259, 90 518, 60 91387 2.9.5077 — 253>n7 40,173 479, 7i 91 393 256.3.7.17 167,252^ 149,186 265, 84 53o, 56 91 397 4-73-3I3 271, 134 1 — — 91411 2.3.5.11.277 — 103,201 88,167 413, 85 91423 2.27.1693 — — 266, S 3 5i5, 61 222 QUADRATIC PARTITIONS. p p-l a b c a A B L M 91433 8.11.1039 173,248 81,206 — — 91 453 4.3.7621 267,142 — 25>i74 50,116 91457 64.1429 161,256 273, 92 — — 91459 2.9.5081 — 289, 63 76,169 583, 3i 91463 2.7.47.139 — — — — 91493 4.89.257 17,302 — — — 91499 2.11.4159 — 189,167 — — 91513 8.9.31.41 237,188 91,204 149,152 605, 1 91529 8.17.673 227,200 159,182 — — 91541 4.5.23.199 265,146 — — — 91571 2.5-9I57 — 297, 41 — — 91 573 4-3-I3.587 297, 58 — 301, 18 602, 12 91577 8.1 1447 179,244 213^52 — « — 91583 2.29.1579 — — — — 91591 2-3-5-43-7I — — 254, 95 539, 53 91621 4.9-5-5°9 289, 90 — 283, 62 97,1*5 91631 2.5.49.11.17 — — — — 91639 2.27.1697 — — 242,105 484, 70 91 673 8.7.1637 133*272 9,214 — — 91691 2-5-53-173 — 267,101 — — 91703 2-I3-3527 — — — — 91711 2.9.5. 1019 — — 3°2, 13 263,105 91733 4.17.19.71 23,302 — — — 91753 8.3.3823 283,108 301, 24 299, 28 215,109 91757 4.7.29.113 3 QI , 34 — — — 91771 2.3.5.7.19.23 — 203,159 272, 77 503, 65 91781 4-5-J3-353 145,266 — — — 91801 8.27.25.17 125,276 251,120 301, 20 241,107 91807 2. 3.11. 13.107 — — 110,163 379, 9 1 91811 2.5.9181 — 3°3> 1 — 91 813 4.3.7.1093 3°3, 2 — 251, 98 545, 5i 91823 2.31. 1481 — — — 91837 4-9-255 1 261,154 — 167,146 605, 7 91841 64.5.7.41 65,296 3°3, 4 — — 91867 2. 3.61. 251 — 277, 87 280, 67 481, 71 91 873 32.9.11.29 303> 8 271, 96 199,132 398, 88 91909 4-27-23-37 3°3, I0 203,130 187,111 91921 16.3.5.383 255> l6 4 61,210 233,112 103,115 91939 2. 3.7. 11. 199 — 79,207 8,i75 5*7, 61 91 943 2.45971 — QUADRATIC PARTITIONS. 223 p p-1 a b c d A B L M 91951 2.3.25.613 — — 274, 75 548, 50 91 957 4-3-79-97 281,114 115,162 230,108 91961 8.5. 121. 19 269,140 123,196 — — 91967 2.7.6569 — — — — 91969 64.3.479 95,288 239^32 191,136 217,109 91997 4.109. 211 101,286 — — 92 003 2.157.293 — 23i»i39 — — 92 009 8.7-3I.53 275,128303, 10 — — 92 033 128.719 217,212 21,214 — — 92 041 8-3-5-I3-59 285,104 257,n4 221,120 442, 80 92 051 2.25.7.263 — 3°3, n — 92 077 4-3-7673 291, 86 — 97,166 595, 23 92 083 2.3.103.149 — 281, 81 80,169 427, S3 92 107 2.9.7.17.43 — 37,213 248,101 55i, 49 92 111 2.5.61. 151 — — — 92119 2.3.13.1181 — — 154,151 607, 1 92 143 2.9.5119 — — 226,117 452, 78 92 153 8.11519 83,292 75,208 — 92 173 4.3.7681 243,182 i45,i54 607, 3 92177 16.7.823 191,236 285, 74 92 179 2.81.569 — 127,195 296, 39 592, 26 92 189 4.13.1213 283,110 — — — 92 203 2.3.121.127 — 229,141 160,149 287,103 92 219 2.49.941 — 99,203 — 92 221 4.3-5-29-53 139,270 — 247,102 494, ^ 92 227 2.3.19.809 — 295, 5i 128,159 256,106 92 233 8.27.7.61 253,168 289, 66 59,i72 457, 77 92 237 4-23059 131,274 — — 92 243 2-17-2713 201,161 — 92 251 2. 9.125. 41 — 107,201 112,163 601, 17 92 269 4.9.11.233 237,190 — 289, 54 578, 36 92 297 8.83.139 181,244 147,188 92 311 2. 3.5. 17. 181 — — i94,i35 388, 90 92 317 4.3-49- 157 2 99, 54 — 295, 42: 590, 28 92 333 4-4i.5 6 3 227,202 — — 92 347 2-3-I539 1 — 293, 57 68,171 136,114 92 353 64-3-I3.37 97,288 209,156 215,124 i57,n3 92 357 4. 11. 2099 289, 94 — 92 363 2.46181 219,149 — 92 369 16.23.251 287,100 291, 62 — — 224 QUADRATIC PARTITIONS. p P -l a b c d A B L M 92 377 8.9.1283 69,296 I 233,138,283, 64475, 73 92 381 4-5-3 I - I 49 91,290 — — 1 — 92 383 2.3.89.173 — — 166,147332, 98 92 387 2.7.6599 — 3°3, 17 — — 92 399 2.46199 — . — 92 401 16.3.25. 7. 11 49,300 301, 30263, 88 1,117 92 413 4.9.17.151 123,278 — I265, 86 7,i<7 92 419 2.3.73.211 — 41,213304, 1 307,101 92 431 2.9.5.13.79 — — 266, 85 11,117 92 459 2.46229 — 3,215 — — 92 461 4-3-5- 2 3- 6 7 285,106 — 287, 58 113,115 92 467 2.9.11.467 — 145,189 292, 49 439, 81 92 479 2-3 I 54i3 — — 298, 35 i93,in 92 489 8.11.1051 85,292 51,212 — — 92 503 2. 81. 571 — — 94,167 407, 87 92 507 2. 23.2011 — 267,103 — — 92 551 2.3.25.617 — — 26,175 499, 67 92 557 4.27.857 179,246 — 257, 94 2 5, IX 7 92 567 2.31. 1493 — — — — 92 569 4.3.7.19.29 187,240 AV^ 1X09,164 383, 91 92 581 4-3-5-1543 255,166 — 133,158 34i, 97 92 593 16.9.643 3°3, 28 179,174 89,1681178,112 92 623 2.3-43-359 — — 7°, I 7 I 140,114 92 627 2.29.1597 — 297, 47 — — 92 639 2.7.13.509 — — — — 92 641 32-3-5- I 93 i5>3°4 97,204 271, 80 3M*7 92 647 2.9.5147 — — 122,161 605, 13 92 657 16.5791 71,296 183,172 — — 92 669 4.23167 155,262 — — — 92 671 2.3.5.3089 — — 214,125 161,113 92 681 8-5-7-33I 259,160 33>2i4 — — 92 683 2. 9. 19. 271 — 109,201 280, 69 560, 46 92693 4.23173 247,178 — — — 92 699 2.46349 — 93,205 — — 92 707 2.3-J545 1 — 185,17! 272, 79 35,n7 92 717 4-i3- I 783 301, 46 — — — 92 723 2.7.37.179 — >35> I 93 — — 92 737 64.9.7.23 289, 96 287, 72 i93,!36 601, 19 92 753 16.11. 17.31 137,272 249,124 — — 92 761 8.3-5-773 165,256 247,126 293, 48 586, 32 QUADRATIC PARTITIONS. 225 p p-1 a b c d A B L M 92 767 2.3.15461 — — 182,141 364, 94 92 779 2.3-7.47.47 — 3 OI > 33 3°4, 11 271,105 92 789 4.23197 185,242 — — 92 791 2.9.5.1031 — — 302, 23 37i, 93 92 801 128.25.29 295, 76 213,1541 — 92 809 8.9.1289 53>3°o 253,120^29,116 ii9,n5 92 821 4-3-5.7.I3.I7 105,286 - j 2 53, 98 4i,n7 92 831 2.5.9283 — 92 849 16.7.829 145,268 2 43, T 3° — — 92 857 8.3.53-73 21,304 2 95, 54!235,ii2 57i, 4i 92 861 4-5.4643 235>i94 — 92 863 2. 9.7. 11. 67 — — i 2 74, 77 43,H7 92 867 2.59.787 — 3°3, 23 — 92 893 4.3-774I 213,218 — 119,162 238,108 92 899 2.9-I3.397 — 161,183 3 2 >i75 493, 69 92 921 8.5. 23.101 211,220 267,104 92 927 2.97.479 — — — — 92 941 4.3-5-J549 221,210 — 79,170 43i, 83 92 951 2. 25. 11. 13.13 — — — 92 957 4.17.1367 149,266 — — — 92 959 2 .3.i5493 — — 286, 61 469, 75 92 987 2.19.2447 — 75, 2 °9 — — 92 993 64.I453 223,208 159,184 — — 93 001 8.3.125.31 299, 60 227,144 251,100 49,n7 93 047 2.46523 — — — 93 053 4-43-54I 43>3°2 — — — 93 059 2.7.17.17.23 — 303, 25 — — 93 077 4.23269 169,254 — — 93 083 2. 11. 4231 — 285, 77 — — 93 089 32.2909 305, 8 81,208 — — 93 097 8.27.431 269,144 3°5> 6 13,176 5i5, 63 93 103 2 -3-59-263 — — 250,101 53,n7 93 113 8.103.113 277,128 39>2i4 — 93131 2.5.67.139 — 291, 65 — — 93 133 4-9-i3-i99 163,258 305, 6 610, 4 93 139 2.3.19.19.43 — 49,213 124,161 359, 95 93 151 2.81.25.23 — — 58,i73 461, 77 93 169 16.9.647 3°5, 12 269,102 287, 60 574, 40 93179 2.46589 — 27,215 — — 93187 2.9.31. 167 — 305, 9 208,129 416, 86 2g 226 QUADRATIC PARTITIONS. p p-1 a b I c d A B 1 L M 93199 2.3-49-3!7 — — 74,i7i|i48,ii4 93 229 4-3-!7-457 45,3° 2 — 49,174 98,116 93 239 2.46619 — — — — 93 241 8-9-5-7-37 75>296 71,210 67,172583, 35 93 251 2-125-373 — 249,125 — — 93 253 4.3.19.409 303, 38 — 181,142607, 13 93 257 8,11657 29,304 225,146 — — 93 263 2. 13. 17. 211 — — — — 93 281 33.5.11.53 3°5, l6 177,176 — 93 283 2.3.7.2221 — 175^77 304, 17253,107 93 287 2.46643 — — — — 93 307 2 -3- I 555 r — 245,129 188,139229,109 93 319 2.3.103.151 — — 38,175:487, 7i 93 323 2.29.1609 — i7i,i79 93 329 16.19.307 265,152 279, 88 93 337 8.3.3889 131,276 5,216 i55» I 5 2 6n, 1 93 371 2.5.9337 — 243, 1 3 1 — — 93 377; 64.1459 3i 5 304 303, 2 8| — — 93 383 2.46691 — 93 407 2.46703 — — — — 93 419 2.13-3593 — 2i3,i55 — — 93 427 2.3.23.677 — 257,117: 88,i6q 595, 27 93 463 2.3.37.421 — — 266, 87 532, 58 93 479 2. 7. 11. 607 — — — 93 481 8.3.5.19.41 59,300 13,216 203,132 406, 88 93 487 2.3-15581 — — 262, 91 535, 57 93 491 2-5-9349 — 303, 29 — 93 493 4-9-49-53 233,198 221,122 587, 33 93 497 8.13.29.31 299, 64 I 35, I 94 — — 93 503 2.46751 — — 93 523 2.3.11. 13.109 — 295, 57 280, 71 67,117 93 529 8.27.433 123,280 73,2io 269, 84 538, 56 93 553 16.3.1949 103,288 265,108 25,176 5o3, 67 93 557 4.19.1231 151,266 — 93 559 2.3-3 I -5°3 — 226,119 i3i,n5 93 563 2.7.41. 163 — 219,151 — — 93 581 4.5-4679 275^34 — — 93 601 32-9-25-13 305, 24 17,216 167,148 277,105 93 607 2.3.15601 — — 238,111 476, 74 93 629 4.89.263 277,130 — — — QUADRATIC PARTITIONS. 227 p-l A B I L M 93 637 93 683 93 701 93 703 93 719 93 739 93 761 93 763 93 787 93 809 93 811 93 827 93 851 93 871 93 887 93 889 93 893 93 901 93 911 93 913 93 923 93 937 93 941 93 949 93 967 93 971 93 979 93 983 93 997 94 007 94 009 94 033 94 049 94 057; 94 063 94 079| 94 099 94 1091 94 111! 94 117 4.81. 17.17 2.31.1511 4.25.937 2.3.7.23.97 2.47.997 2.3.17. 919 64.5.293 2.9.5209 2.3.49.11.29 16.11.13.41 2.3.5.53.59 2.43.1091 2.25.1877 2.9.5.7.149 2.13.23.157 64.9.163 4.23473 4.3-25-3 I 3 2-5-939 1 8.3.7.I3.43 2.151.311 16.3.T9.103 4.5.7.11.61 4.3.7829 2.3.15661 2-5.9397 2.9.23.227 2.343.I37 4.9.7373 2.11.4273 8.3.3917 16.9.653 32.2939 8.3-39!9 2.3.61.257 2.17.2767 2.3.15683 4.7.336i 2.3-5-3 I 37 4.3.11. 23.31 1,306 3°5, 26 185,244 3°5, 28 225,208 193*238 99,290 93,292 39,304 265,154 293, 90 19,306 205,228 279, 89 i33>i95 267,106 55,213 293, 6 3 147,190 263,111 297, 53 99,205 289, 72 229,144 81,209 25,216 39,215 91,207 53,i74 286, 63 304, 21 256, 97 220,123 44,175 202,133 3^176 287, 62 115,164 295, 48 I5M54 230,117 148,155 305, 18 299, 48253,100 287,108125,198145,156 305, 32207,160; — 229,204275, 96277, 76 190,139 — 281, 87 203,230 — 111,286 — 224,121 142,157 107,166 106,116 572, 42 608, 14 547, 53 440, 82 481, 73 601, 23 497, 69 473, 75 377, 93 59o, 32 613, 460, 78 317,101 610, 12 553, 5i 290,104 505, 67 607, 17 i39,n5 613, 5 39i, 9 1 228 QUADRATIC PARTITIONS. A B L M 94121 94 151 94 153 94169 94 201 94 207 94 219 94 229 94 253 94 261 94 273 94 291 94 307 94 309 94 321 94 327 94 331 94 343 94 349 94 351 94 379 94 397 94 399 94 421 94 427 94 433 94 439 94 441 94 447 94 463 94 477 94 483 94 513 94 529 94 531 94 541 94 543 94 547 94 559 94 561 8.5.13.181 2.25.7.269 8.3-39 2 3 8.79.149 8.3-25-!57 2.3.7.2243 2.3-41-383 4.23557 4-23563 4-3-5- I 57i 64.3.491 2.3.5.7.449 2.61.773 4.3.29.271 16.9.5.131 2.3.79.199 2-5-9433 2.43.1097 4.103.229 2.3- 2 5- I 7-37 2.47189 4-23599 2.315733 4.5.4721 2-3 I - I 5 2 3 32.13.227 2.23.2053 8-3-5-787 2. 81. 11. 53 2.73.647 4-3-7873 2.9.29.181 16.3.11.179 64.7. 211 2-3.5- 2 3- I 37 4.5.29.163 2.3.7.2251 2.41. 1153 2.47279 32.3.5-I97 275^36 277,132 163,260 301, 60 55.302 3°7, 2 25>3° 6 257,168 303, 5° 3°5. 36 307, 10 139.274 295, 86 143,272 45.304 29,306 303. 52 127,280 179,250 265,156 3°3. 34 29,216 219,152 283, 84 59.213 31,216 247,129 255. 12 i 307. 6 123,199 141,193 243.*33 225,148 79,210 305. 27 205,162 273,100 241,135 303, 37 293. 66 35.176 299. 40 242,109 112,165 307. 2 169,148 3°4, 25 59.174 289, 60 250,103 298, 43 218,125 3o7. 8 82,171 3°5, 22 104,167 281, 72 268, 87 290, 59 263, 92 563, 47 I79.II3 85,n7 224,110 301,103 613, 379, 93 118,116 578, 40 559, 49 427, 85 593. 31 283,105 164,114 239,109 605, 21 562, 48 536, 58 467, 77 539, 57 QUADKATIC PAETITIONS. 229 p p-1 a b c d A B L M 94 573 4-9-37-7I 307, 18 — 175^46 263,107 94 583 2.19.19.131 — — 94 597 4-3-7883 S 1 ^ 06 293, 54 586, 36 94 603 2.3.15767 — 299, 5 1 3°4, 27 608, 18 94 613 4.7.31. 109 217,218 — — — 94 621 4-3-5-I9-83 245,186 — 89,170 599, 27 94 649 8.11831 307, 20 69,212 — — 94 651 2.3.25.631 3 OI > 45 272, 83 521, 63 94 687 2-3-43-3 6 7 — — 7o,i73 449, 81 94 693 4.3.13.607 273,142 299, 42 598, 28 94 709 4.23677 103,290 — — — 94 723 2.3.15787 95*207 196,137 215,111 94 727 2.473 6 3 — — — 94 747 2-3-I579 1 — 227,147 208,131 185,113 94 771 2.729.5.13 289, 75 28,177 56,118 94 777 83.11.359 171,256 185,174 43, J 7 6 485, 73 94 781 4.5.7.677 155,266 — — — 94 789 4.9.2633 3°5, 42 — 283, 70 493, 7i 94 793 8.17. 17.41 227,208 255,122 — — 94 811 2.5.19.499 — 237,139 — — 94 819 2.3.15803 — 137,195 296, 49 I49,n5 94 823 2.7. 13.521 — — — — 94 837 4.3.7.1129 281,126 — 307, 14 265,107 94 841 8.5.2371 85,296 57,2i4 — — 94 847 2.47.1009 — — — — 94 849 128.3. 13.19 193,240 257,120 119,164 611, 15 94 873 8.3.59-67 3.3o8 245,^2 101,168 202,112 94 889 8.29.409 5,3°8 189,172 — — 94 903 2.3.15817 — — 106,167 395, 9i 94 907 2.7.6779 — 27,217 — — 94 933 4.81.293 297, 82 — 301, 38 187,113 94 949 4.7-339* 257,170 — — — 94 951 2. 9.25. 211 — — 238,113 101,117 94 961 16.5.1187 305, 44 243,^34 — — 94 993 16.3.1979 183,248 41,216 79,172 595> 3i 94 999 2.3.71.223 — — 226,121 589, 35 95 003 2.47501 — 285, s 3 — — 95 009 32.2969 145,272 3°3, 4o — — 95 021 4-5-475I 115,286 — — — 95 027 2.475 J 3 — 225,149 — — 230 QUADRATIC PARTITIONS. V p — 1 a b c d A B L M 95 063 2. 11. 29. 149 95 071 2 -3-5-3 I 69 — — 278, 77 509, 67 95 083 2.3.13.23.53 — 211,159 124,163 613, 13 95 087 2 -47543 — — — — 95 089 16.3.7.283 15,308 83,210 199,136 607, 21 95 093 4-23773 233,202 — — — 95101 4-3-25-3!7 270,149 — 7,i78 54i, 57 95 107 2.3.121. 131 — 97,207 3°8, 9 616, 6 95111 2.5.9511 — — — — 95 131 2.9.5. 7.151 — 307, 21 116,165 232,110 95 143 2.3.101.157 — 34,177 68,118 95 153 16.19.313 17,308141,15 — 95177 8. 1 1897 299, 76 93,208 — — 95 189 4-53-449 265,158 — — — 95 191 2.3.5.19.167 — — 158,153 316,102 95 203 2.27.41.43 — 305, 33 184,143 245,109 95 213 4.13.1831 163,262 — — — 95 219 2.47609 — 159,187 — — 95 231 2.5.89.107 — — — — 95 233 1024.3.31 153,268 299, 54 161,152 617, 3 95 239 2.9.11. 13.37 — — 58,175 583, 39 95 257 8.243.49 189,244 197,168 293, 5 6 461, 79 95 261 4-5-H-433 181,250 — — — 95 267 2. 19.23.109 — 33,2i7 — — 95 273 8. 1 1909 307, 32 15,218 — — 95 279 2.47639 — — — — 95 287 2.3.15881 — — 98,169 409, 89 95 311 2-27-5-353 — — 302, 37 i9 I > II 3 95 317 4.3-13-13-47 41,306 — 67,i74 134,116 95 327 2. 7. 11. 619 — — — — 95 339 2-73- 6 53 — 291, 73 — — 95 369 8.7.13.131 245,188 237,140 — — 95 383 2.9-7-757 — — 230,119 587, 37 95 393 32. 11. 271 23,308 219,154 — — 95 401 8.9.25.53 251,180 307, 24 301, 40 421, 87 95 413 4-3-795 1 263,162 — 19,178 553, 53 95 419 2.81. 19.31 — 181,177 296, 51 592, 34 95 429 4-23857 65,302 — — — 95 441 16.5. 1193 55,304 183,176 — — 95 443 2.3.15907 — 121,201 140,159 280,106 QUADRATIC PARTITIONS. 231 p p — 1 a b c d A B L M 95 461 4.3-5-37.43 95, 2 94 — 187,142 613, 15 95 467 2.3.7.2273 — I55>i8 9 88,171 176,114 95 471 2 -5-9547 — — — — 95 479 2-3-I59I3 — — 202,135 404, 90 95 483 2.47741 — 3°9, 1 — — 95 507 2.17-53-53 — 3°3, 43 — — 95 527 2.27.29.61 — — 242,111 484, 74 95 531 2.5.41.233 — 309, 5 — — 95 539 2-3-15923 — 169,183 308, 15 616, 10 95 549 4.23887 107,290 — — — 95 561 8.5.2389 131,280 63,214 — — 95 569 8.3.11.181 225,212 131,198 137,160 343, 99 95 581 4.81.5.59 309, 10 — 23*178 5"> 67 95 597 4.23899 211,226 — 95 603 2.13.3677 — 81,211 — — 95 617 128.9.83 161,264 3°5, 36 265, 92 11,119 95 621 4.5.7.683 289,110 — — — 95 629 4.3-13-613 227,210 — 271, 86 13*119 95 633 16.43-139 257,172 291, 74 — — 95 651 2.25.1913 — 297, 61 — — 95 701 4.3.25.11.29 151,270 — 307, 22 373* 95 95 707 2.9.13.409 — 307, 27 292, 59 "5>"7 95 713 32.3.997 113,288 49,216 241,112 577, 43 95 717 4.23929 241,194 — : — — 95 723 2. n. 19. 229 — 3°9, JI — — 95 731 2.3.5-3191 — *93,i7* 308, 17 359, 97 95 737 8.3.3989 309, 16 295, 66 53,176 581, 41 95 747 2.49.977 — 273» io 3 — — 95 773 4.3-23.347 277,138 — 295* 54 59o, 36 95 783 2.83.577 — — 95 789 4.7.11.311 275,142 — — 95 791 2.3.5.31. 103 — 154,155 3"»io3 95 801 8.25.479 299, 80 249,130 — 95 803 2.3.7.2281 — 3°i, 5i 176,147 352, 98 95 813 4. 1 7. 1 409 193,242 — — 95 819 2.23.2083 — 309, 13 — — 95 857! 16.3.1997 249,184 247,132 223,124 595, 33 95 869| 4.9.2663 165,262 7**174 142,116 95 873 128.7. 107 103,292 309, 14 — 95 881 8.3.5-I7.47 309, 20 259,120 163,152 293,io5| 232 QUADRATIC PARTITIONS. p p-l a b c d A B L M 95 891 2.5.43.223 — 279> 95! — — 95 911 2-3.5-23.i39 — — 218,127 163,115 95 917 4.3.7993 291,106 — 145^58 329,101 95 923 2.9.73.73 — 1,219: 44,177 88,118 95 929 8.3.7-57I 77,300 149,192:277, 80 37,n9 95 947 2.3.15991 — 5,219308, 19 251,109 95 957 4.7.23.149 119,286 — — — 95 959 2.27.1777 — — 166,151 619, 5 95 971 2.3.5.7.457 — 7,219 64,^75 589, 37 95 987 2. 11. 4363 — 207,163 — — 95 989 4-3.19.421 183,250 — 179,146 617, U 96 001 256.3.125 255>i76 113,204 247,108 494, 72 96 013 4.27.7.127 3°7, 42 — 31,178 565, 49 96 017 i6.i7.353 191,244 285, 86 — — 96 043 2.3.16007 — 11,219 296, 53 455, '81 96 053 4-II.37-59 137,278 — — — 96 059 2.48029 — 3°9, 1 7 — — 96 079 2.3.67.239 — — 286, 69 572, 46 96 097 32.3.7. 11. 13 201,236 133,198 3°5, 32 401, 91 96 137 8.61. 197 61,304 33,2i8 — — 96149 4.I3.43.43 7,3 IQ — — — 96 157 4.9.2671 309, 26 — 73, J 74 146,116 96167 2.7.6869 — — — — 96 179 2.19.2531 — 201,167 — — 96181 4.3.5.7.229 9,3 X ° — 227,122 593, 35 96199 2.3- l6o 33 — — 182,145253,109 96 211 2.9.5.1069 — 17,219 112,167 389, 93 96 221 4.5.17.283 11,310 — — — 96 223 2.3.7.29.79 — — 10,179 527, 63 96 233 8.23.523 37,308 291, 76 — — 96 259 2.3.61.263 — 281, 93 136,161 347, 99 96 263 2.48131 — — — — 96 269 4.41.587 i3>3 10 — — — 96 281 8.5.29.83 125,284 309, 20 — — 96 289 32.3- I 7-59 105,292 283, 90 281, 76 53,H9 96 293 4.7.19.181 287,118 — — — 96 323 2.17.2833 — 249,131 — — 96 329 8. 1 2041 277,140 99,208 — — 96 331 2.3.5,13.13.19 — 277, 99 208,133 607, 25 96 337 16.27.223 279,136 55,2i6 175^48 619, 9 QUADEATIC PARTITIONS. 233 p ^-1 a b c a A B L M 96 353 32.3011 247,188 69,214 96 377 8.7.1721 301, 76 267,112 ■ — — 96 401 16.25.241 215,224 297, 64 — — 96 419 2.7.71.97 — 63,215 — — 96 431 2.5.9643 — — — — 96 443 2.48221 — 261,119 — 96 451 2-3- 2 5- 6 43 — 23,219 3°8, 23 377, 95 96 457 8.3.4019 299, 84 115,204 253, IQ 4 59,n9 96 461 4-5-7-I3-53 i9>3 10 — — — 96 469 4.3.8039 265,162 — 221,126 442, 84 96 479 2.48239 — — — — 96 487 2.3.13.1237 — — 5o,i77 100,118 96 493 4.3.11. 17.43 173,258 — 305, 34 203,113 96 497 16.37.163 241,196 237,142 96 517 4-9 7-383 289,114 — 283, 74 61,119 96527 2.17. 17. 167 — — — 96 553; 8.81. 149 3°7, 48 305, 42 109,168 218,112 96 557 4. 101.239 179,254 — — — 96 58l! 4.5. 11.439 209,230 — — — 96 587; 2.7.6899 — 243,137 — — 96 589 4-9-2683 195,242 — 289, 66 578, 44 96 601 8.3.25.7.23 285/124J299, 60307, 28 39 1 , 93 96 643 2.9.7.13.59 — 289, 81 284, 73 65,119 96 661; 4.5.27.179 55,306, — 269, 90 538, 60 96 6671 2.3.16111 — ! 77,213268, 91 54i, 59 96 671 2.5.7.1381 — — — — 96 697 8.9.17.79 269,156 235, I 44 ! 203,i36 205,113 96 703 2.3.71.227 — — 266, 93532, 62 96 731 2.5.17.569 — 3°9, 25 — — 96 737 32.3023 3ii, 4 123,202 — — 96 739 2.3.23.701 — 311, 3308, 25 233,iu 96749:4.19.19.67 3°7, 5° — — 96 757 4.3.1 1.733 3 11 , 6 — 77,174:154,116 96 763 2.3.16127 — 29,219236,117472, 78 96 769 512.27.7 287,120 271,108311, 4299,105 96 779 2.11. 53.83 — 5!,2i7 — — 96 787 2.9.19.283 — 215,159 220,127601, 31 96 797 4-7-3457 299, 86 — — 96 799 2.3.13.17.73 — — 26,179:563, 5i 96 821 4.5.47.103 311, 10 — 2h 234 QUADRATIC PARTITIONS. p p-l a b i c d A B L M 96 823 2. 27. II. 163 — — 230,121133,117 96 827 2.48413 — 267,113 96 847 2.3.1614I — — 250,107 71,119 96 851 2.25.I3.I49 — 177,181 — — 96 857 8.I2I07 251,184 183,178 — . i — 96 893 4.24223 277,142 — — — 96 907 2. 3.3I. 52I — 173,183 28,179509, 69 96 911 2. 5. II. 88l — — — — 96 931 2.27-5-359 — 127,201 184,145^19, 13 96 953 8. 121 19 307. 52 171,184 — — 96 959 2.48479 — — — — 96 973 4.3.8081 237,202 — i9i,i42'235,in 96 979 2.3.7.2309 — 79,213:304, 39608, 26 96 989 4.24247 283,130 — — — 96 997 4.3.59-I37 191,246 — 235,118589, 39 97 001 8.125.97 301, 80 273,106 — — 97 003 2.9.17.317 — 269,111 260, 99520, 66 97 007 2.7.13.13.41 — — — — 97 021 4.9.5.49. 1 1 261,170 — 311, 10281,107 97 039 2.81.599 — — 158,155623, 1 97 073 16.6067 47>3°8| 45>2i8 — — 97 081 8.3.5.809 309, 40167,186 259,ioo559, 53 97 103 2.47.1033 — — 97117 4-3-8093 59>3°6 — 295, 58469, 79 97127 2 48563 — — 97151 2.25.29.67 97 157 4.107.227 271,154 — 1 — — 97159 2.3.16193 — 146,159292,106 97169 16.6073 137,280 231,148, 97 171 2-3-5-4I-79 311, 15292, 63584, 42 97177 8.3.4049 69,304 137,198187,144 374, 96 97187 2.48593 '297, 67 — — 97 213 4.3.8101 133,282 — 281, 78 562, 52 97 231 2.3.5-7-463 298, 53 i39,n7 97 241 8.5.11. 13.17 221,220 21,220 — — 97 259 2.7.6947 — 219,157 — — 97 283 2.127.383 — 255,127 — — 97 301 4.25.7-139 215,226 — — — 97 303 2.3.16217 — 170,151 283,107 97 327 2.9.5407 — ~~ 98,171 196,114 QUADRATIC PARTITIONS. 235 p p — 1 a be d A B L M 97 367 2.89.547 — 97 369 8.3-4057 5.312 311, 18 13,180 26,120 97 373 4.11.2213 197,242 — — — 97 379 2. 181. 269 — 249^33 — — 97 381 4.9.5.54I 3°5, 66 — 293, 62 479, 77 97 387 2.3.16231 — 283, 93 308, 29 395, 93 97 397 4.13-1873 311, 26 — — 97 423 2.3.13.1249 — 310, 21 620, 14 97 429 4.3.23.353 295,102 *13>*5° 346,100 97 441 32.3.5.7.29 279,140 229,150 113,168 226,112 97 453 4.9.2707 93,298 — 49,178 583, 43 97 459 2.3.37.439 — 247>i35 3°4, 4i 181,115 97 463 2.48731 — — — 97 499 2. 29.41.41 — 141,197 — — 97 501 4.3.625.13 299, 90 137,162 274,108 97 511 2.5.49.199 — — — — 97 523 2.48761 — 201,169 — — 97 547 2.17.19.151 — 123,203 — — 97 549 4-3-H-739 157,270 — 209,134 611, 25 97 553 16.7.13.67 233,208 105,208 — 97 56l' 8.9.5.271 195.244 181,180 19,180 38,120 97 571 2. 5. 11. 887 — 183,179 — 97 577 8.12197 179,256 177,182 — — 97 579 2.27. 13.139 — 109,207 176,149 623, 9 97 583 2.97.5 3 — — — — 97 607 2.37. 1319 — — — — 97 609 8.3.49.83 285,128 97,210 197,140 617, 19 97 613 4.23. 1061 3°7, 58 — — — 97 649 i6.i7.359 305, 68 51,218 — — 97 651 2.9.25.7.31 — 217,159 76,i75 601, 33 97 673 8.29.421 53,308 189,176 — — 97 687 2.729.67 — — 310, 23241,111 97 711 2.3.5-3257 — — 238,1171476, 78 97 729 64.3.509 185,252 139,198 23,180 46,120 97 771 2 -3-5-3 2 59 — 43,219 268, 93536, 62 97 777 16.9.7.97 271,156 3°7, 42 95,172421, 89 97 787 2.13.3761 — 285, 91 — — 97 789 4.3.29.281 117,290 — 217,130607, 29 97 813 4.9.11.13.19 297, 98 >75, 86533, 63 97 829 4.37.661 95,298 — — 236 QUADRATIC PARTITIONS. > p-l a b c d 1 A B L M 97 841 16.5.1223 295,104279,100 — — 97 843 2.3.23.709 — 241,141244,113 95,119 97 847 2.7.29.241 — — 97 849 8.81. 151 307, 60251,132 131,164623, 11 97 859 2.H3-433 — 303, 55 97 861 4-3-5-7-233 65,306 — 53,178481, 77 97 871 2.5.9787 — — 97 879 2.3. 11. 1483 — — 298, 55 463, 81 97 883 2.109.449 — 195,173 — — 97 919 2.173.283 — — — — 97 927 2.3.19.859 — — ,142,161341,101 97 931 2 -5-7-i399 — 309, 35! — 97 943 2.13.3767 — — — 97 961 8.5.31.79 269,160 207,166 — — 97 967 2.11.61.73 — — 97 973 4-7-3499 313, 2 — — — - 97 987 2 -3-7- 2 333 — 3i3, 3 172,151 625, 7 98 009 8.12251 155^72 297, 70 — — 98 011 2. 81. 5. 121 — 163,189 212,133 187,115 98 017 32.3.1021 3"* 36 293, 78 313, 4 3 2 5, io 3 98 041 8.3.5.19.43 75,304 3i3, 6 29,180 58,120 98 047 2.9.13.419 — — 262, 99 524, 66 98 057 8.7. 17. 103 259,176 225,154 — — 98 081 32-5-613 241,200 303, 5° — 98101 4.9.25.109 249,190 301, 50 i5 J , TI 7 98 123 2. 71. 691 — 21,221 — 98129 16.6133 223,220 291, 82 — — 98143 2.3.11.1487 — — 250,109 577, 47 98179 2.3.16363 — 3 11 , 27 236,119 593, 39 98 207 2.49103 — — — — 98 213 4-43-571 97,298 — — — 98 221 4-3-5- I 637 189,250 — 289, 70 499, 73 98 227 2.27. 17. 107 305, 5 1 112,169 619, 19 98 251 2.3-125.131 i49,i95 92,173 611, 27 98 257, 16.3.23.89 169,264 313, !2 73,176 455, 83 98 269 ( 4.3-i9-43i 213,230 3*3, 10 343,ioi 98 297: 8.11,1117 181,256 57,218 — — 98 299 2.9.43.127 — 307, 45 4,181 547, 59 98 317 4.9.2731 109,294 305, 42 610, 28 98 321 1 16.5. 1229 311, 40 39,220 — — QUADRATIC PARTITIONS. 237 p p-1 a b c d A B L M 98 323 2.3.7.2341 49,219 220,129 440, 86 98 327 2. 211. 233 — — — 98 347 2-3-37-443 — 227,153 8,181 535, 63 98 369 64.29.53 3 J 3, 20 3°9, 38 — — 98 377 8.3.4099 149,276 157,^2 1 33^64 359, 99 98 387 2.49193 — 105,209 — — 98 389 4.27.911 233,210 — 211,134 *9M*5 98 407 2. 9.7. 11. 71 — — 302, 49 i55,n7 98 411 2-5- I 3-757 — 27,221 — — 98 419 2.3.47.349 — 3i3, J 5 188,145 247,111 98 429 4. 11. 2237 85,302 — — — 98 443 2.27.1823 — 235,!47 284, 77 5 J 5, 6 9 98 453 4.151.163 3 r 3, 22 — — — 98 459 2. 19.2591 — 291, 83 — — 98 467 2.3.16411 — 113,207 248,111 496, 74 98 473 8-3-U-373 187,252 205,168 181,148 625, 11 98 479 2.9.5471 — — 14,181 529, 65 98 491 2.3.5.49.67 — 133,201 3°4, 45 608, 30 98 507 2.49253 — 213,163 — — 98 519 2.7.31.227 — — — — 98 533 4.9.7.17.23 303, 82 — 59,178 475, 79 98 543 2.29.1699 — — — — 98 561 256.5.7.11 281,140 117,206 — — 98 563 2.3.16427 — 281, 99 224,127 i57,n7 98 573 4.19.1297 173,262 — — — 98 597 4-i57.i57 1,314 — — — 98 621 4-5-4931 S>314 — — — 98627j2.11.4483 207,167 — — 98 639 2. 149.331 — — — — 98 641| 16.9.5. 137 105,296 73,216247,112 583, 45 98 663 2.49331 — — — — 98 669 ! 4.17.1451 205,238 — — — 98 689 128.3.257 295,108 11,222 191,144 382, 96 98 711 2.5.9871 — — 98 713| 8.27.457 37,3*2 215,162301, 52 1 457, 83 98 717 4.23.29.37 n 5 3i4 — 98 729 8.7.41.43 275^52 273, 110 ! — — 98 731! 2.9.5.1097 — 53,219292, 67 493, 75 98 737J 16.3.121.17 239,204 13,2221313, 16 361, 99 98 773! 4.3.8231 87,302 — 61,178 595, 39 238 QUADRATIC PARTITIONS. p P -l a b c d 1 A B L M 98 779 2.3.101.163 — 277,105296, 61 H3, IT 9 98 801 16.25. 13.19 3°5, 76 237,146 — — 98 807 2.127.389 — — — — 98 809 8.3.23.179 203,240 103,210299, 56 467, 81 98 837 4.24709 3". 46 — — . — 98 849 32.3089 143,280 111,208 — — 98 867 2.49433 — 297, 73 — — 98 869 4.3.7. 11. 107 3*3, 30 — 269, 94 13,121 98 873 8.17.727 307, 68 261,124 — — 98 887 2.3.16481 — — 70,177 140,118 98 893 4.9.41.67 147,278 — 239, Il8 ii5, II 9 98 897 16.7.883 289,124 285, 94 — — 98 899 2-3-53-3H — 3ii, 33 268, 95 17,121 98 909 4.79.3!3 53,3 10 — — — 98 911 *-$$-1'*S1 — — I 5 8 ,i57 3 I 3,io5 98 927 2.49463 — — __ 98 929 16.27.229 177,260 19,222 161,1561322,104 98 939 2. 7. 37.191 — 69,217 — 98 947 2.9.23.239 — 55,2i9 i5 2 , I 59 3°4,io6 98 953 8.3.7.19.31 117,292 275,108 101,172415, 91 98 963 2.49481 — 23 I , I 5 I __ — 98 981 4.5.49.101 191,250 — — 98 993 16.23.269 3 T 3, 32249,136 — — 98 999 2.49499 — — — — 99 013 4-3-37-223 223,222 — 245,114490, 76 99 017 8.12377 221,224 63,218 99 023 2. 7. 11. 643 — — — — 99 041 32.5.619 271,160 177,184 — • — 99 053 4.24763 227,218 — 99 079 2-3-49-337 — — 146,1611629, 5 99 083 2.107.463 — 141,199 — — 99 089 16.11.563 65,308 189,178 — — 99 103 2.3.83.199 — — 314, 13275,109 99 109 4-9-2753 305, 78 — 91,174 182,116 99119 2-49559 — — — — 99131 2-5-23-431 . — 291, 85 99 133 4-3-i I -75i 283,138! 281, 82 35,121 99137 64.1549 199,244 267,118 — — 99139 2.3.13.31.41 — ii9i, I 77 116,169391, 95 99149 4-7-3541 307, 70 — — QUADRATIC PARTITIONS. 239 V p-l a b c d A B L M 99173 4-24793 257,182 — — — 99181 4.9.5.19.29 285,134 — 143,162 286,108 99 191 2. 5. 7. 13.109 — — — — 99 223 2.3-23-7 I 9 — — 290, 71 503, 73 99 233 32.7.443 233,212 3*5, 2 — — 99 241 8.3.5.827 3i5. 4 77,216 I 73 ) I 5 2 629, 7 99 251 2.125.397 — 3°3, 6l — — 99 257 8.19.653 269,164 3i5. 4 — — 99 259 2.3.71.233 — 229,153 56,179 593, 4i 99 277 4.3.8273 211,234 — 65,178 469, 81 99 289 8.9.7.197 315, 8 233> I 5° 283, 80 43, J 2i 99 317 4-7-3547 169,266 — — — 99 347 2.13.3821 — 255^31 — — 99 349 4.3.17.487 57 5 3io 301, 54 602, 36 99 367 2.3.16561 — — 3io, 33 620, 22 99 371 2.5- I 9.5 2 3 — 261,125 — — 99 377 16.6211 209,236243,142 — — 99 391 2.3.5-3313 — — 98,i73 617, 25 99 397 4.9.11.251 289,126 — 5,182 55i, 59 99 401 8.25.7.71 299,100 51,220 — — 99 409 16.3. 19. 109 97,300 29,222 47,180 94,120 99 431 2.5.61. 163 — — — — 99 439 2.3-16573 — — 34,i8i 577, 49 99 469 4.81.307 163,270 — 113,170 623, 19 99 487 2.9.55 2 7 — — 58,i79 479, 79 99 497 8.12437 109,296 303, 62 — — 99 523 2.27.19.97 — 305, 57 296, 63 592, 42 99 527 2.7.7109 — — — — 99 529 8.3.11. 13.29 195,248 31,222 259,104 53,!2I 99 551 2. 25. 11. 181 — — — 99 559 2-9-5531 — — IS4»IS9 308,106 99 563 2.67.743 — 315, 1 3 — — 99 571 2.3-5.3319 — 137,201 208,137 203,115 99 577 8.27.461 309, 64 217,162 163,156 326,104 99 581 4-5- I 3-383 59,3 IQ — — — 99 607 2.3.13.1277 — — 118,169 625, 17 99 611 2.5.7.1423 — 267,119 — — 99 623 2.4981 1 — — — — 99 643 2.3.16607 — 61,219 200,141 400, 94 99 661 4-3^5-* 1-151 115,294 — 17,182 563, 55 240 QUADRATIC PARTITIONS. p P -l a b c d A B | L M 99 667 2.9.49.113 — 287, 93 148,161 335,io3 99 679 2.3.37.449 — — 3i4» 19 257>m 99 689 8.17.733 283,140 99,212 — — 99 707 2.49853 — 45,221 — — 99 709 4.3.7. 1187 3*5, 22 — 169,154 631, 5 99 713 128.19.41 167,268 309, 46 — — 99 719 2.73.683 — — — — 99 721 8.9.5.277 285,136 289, 90 293, 68 497, 75 99 733 4.3- 8 3 J i 3 J 3> 42 — 19,182 527, 67 99 761 16.5.29.43 185,256 297, 76 — 99 767 2.83.601 — — 99 787 2.3.16631 — 245,141 100,173 419, 91 99 793 16.81. 7.11 287,132 35>222 3 11 , 3 2 407, 93 99 809 32.3119 265,172 69,218 — 99 817 8.3.4159 301, 96 175,186 83,176 611, 31 99 823 2. 3.127. 131 — ■ 110,171 220,114 99 829 4.9-47-59 105,298 131,166 367, 99 99 833 8.12479 277,152 135,202 — — 99 839 2.49919 — — 99 859 2.3.11.17.89 — 119,207 3 l6 , 1 319,105 99 871 2.3-5-3329 — 142,163 63 1 , 7 99 877 4.3.7.29.41 79,306 235,122 I3MI9 99 881 8.5. 11. 227 5,3 l6 141,200 — — 99 901 4-27-25-37 3*5, 26 23,182 569, 53 99 907 2.3.16651 — 193,177 308, 41 43i, 89 99 923 2.47.1063 — 225,157 — — 99 929 8.12491 227,220 I7I,l88 — — 99 961 8.3.5.49.17 275^56 293, 84 277, 88541, 63 99 971 2.5.13.769 — 207,169 — 99 989 4.7.3571 217,230 — — — 99 991 2.9.5.11.101 — — 278, 87556, 58 QUADRATIC PARTITIONS. 241 p = 12w+l = A' 2 - -3B' 2 , [A' > 3B']. p A' B' P A' B' P A'B' V A' B' 13 4, i 1093 40,13 2293 49, 6 3613 61, 6 37 7, 2 1117 35, 6 2341 52,11 3637 65,H 61 8, i 1129 34, 3 2377 53, 1 2 3673 61, 4 73 to. 3 1153 34, 1 2389 49, 2 3697 62, 7 97 TO, I 1201 38, 9 2437| 55,14 3709 61, 2 109 II, 2 1213 35, 2 2473,1 50, 3 3733 64,11 157 I3> 2 1237 40,11 2521! 61,20 3769 62, 5 181 16, 5 1249 41,12 2557! 52, 7 3793 65,12 193 14, i 1297 38, 7 2593 55,i2 3853 64, 9 229 1 6, 3 1321 37, 4 2617 53, 8 3877 73,22 241 i7. 4 1381 41,10 2677 52, 3 3889 74,23 277 17, 2 1429 44,i3 2689 58,15 4021 64, 5 313 19, 4 1453 40, 7 2713 59,16 4057 67,12 337 22, 7 1489 41, 8 2749 61,18 4093 64, 1 349 19, 2 1549 43,io 2797 53, 2 4129 73,2o 373 20, 3 1597 40, 1 2833 55, 8 4153 74,21 397 20, 1 1609 46,13 2857 58,13 4177 65, 4 409 22, 5 1621 47,14 2917 55, 6 4201 77,24 421 23. 6 1657 43, 8 2953 61,16 4261 68,11 433 25, 8 1669 41, 2 3001 58,n 4273 71,16 457 22, 3 1693 44, 9 3037 67,22 4297 67, 8 541 28, 9 1741 43, 6 3049 59,i2 4357 73,i8 577 25, 4 1753 46,11 3061 56, 5 4441 67, 4 601 26, 5 1777 47,12 3109 56, 3 4513 79,24 613 25, 2 1789 44, 7 3121 58, 9 4549 68, 5 661 31, i° 1801 43, 4 3169 62,15 4561 73,i6 673 26, 1 1861 44, 5 3181 59,1° 4597 68, 3 709 28, 5 1873 46, 9 3217 5^ 7 4621 68, 1 733 29, 6 1933 44, 1 3229 64,17 4657 70, 9 757 28, 3 1993 5°, x 3 3253 65,18 4729 77,2o 769 3i, 8 2017 47, 8 3301 68,21 4789 79,22 829 29, 2 2029 52,15 3313 70,23 4801 74,15 853 3i, 6 2053 55,i8 3361 58, 1 4813 80,23 877 32, 7 2089 46, 3 3373 59, 6 4861 83,26 937 37,i2 2113 46, 1 3433 59, 4 4909 76,17 997 32, 3 2137 5°, " 3457 65,16 4933 71, 6 1009 34, 7 2161 47, 4 3469 59, 2 4957 77,i8 1021 32, 1 2221 53,M 3517 67,18 4969 74,i3 1033 35, 8 2269 5 6 ,i7 3529 61, 8 4993 7i, 4 1069 37,io 2281 58,19 3541 68,19 5077 80,21 2i 242 QUADRATIC PARTITIONS. p - 12 3B']. p A' B' P A' B' p.\ATW P A' B' 5101 76,15 6553 91,24 7873 89, 4 9277 112,33 5113 74,ii 6577 82, 7 7933:104,31 9337 "5,36 5197 85,26 6637 85,14 7993109,36 9349 116,37 5209 86,27 6661 88,19 8017 98,23 9397 97, 2 5233 74, 9 6673 95,28 8053 95,i8 9421 107,26 5281 73, 4 6709 97,3o 8089 91, 8 9433iioi,i6 5413 76,11 6733 100,33 8101 92,11 9601 98, 1 5437 83,22 6781 83, 6 8161 94,15 9613 101,14 5449 74, 3 6793 85,12 8209 97,20 9649 106,23 5521 86,25 6829 91,22 8221 92, 9 9661 112,31 5557 88,27 6841 83, 4 8233 9 1 , 4 9697 H3<32 5569 89,28 6949 89,18 8269 91, 2 9721 107,24 5581 9i,3° 6961 94,2 5 8293 104,29 9733 104,19 5641 82,19 6997 95, 26 8317 92, 7 9769 101,12 5653 79> J 4 7057 97,28 8329 94,i3 9781 116,35 5689 83,20 7069 88,15 8353 106,31 9817 118,37 5701 76, 5 7129 101,32 8377^07,32 9829 119,38 5737 77, 8 7177 85, 4 8389; 92, 5 990Hioi,io 5749 76, 3 7213 85, 2 8461: 92, 1 9949 ! io 4 ,i7 5821 77, 6 7237 88,13 8521 98,19 9973ioo, 3 5857 82,17 7297 95> 2 4 8581 103,26 5869 88,25 7309 91,18 862910427 5881 77, 4 7321 86, 5 8641 97,16 5953 94,3! 7333 89,14 8677 100,21 6037 80,11 7369 86, 3 8689 94, 7 6073 86,21 7393 86, 1 8713 106,29 6121 83,16 7417 98,27 8737 98,17 6133, 79, 6 7477 100,29 8761 94, 5 6217! 82,13 7489 80,12 8821 97, J 4 6229 79, 2 7537io3,32 8893 H5,38 6277 92,27 7549jio 4 ,33 8929 98,15 6301 83,14 756II106.35 8941 104,25 6337 97,32 7573 95,22 9001 101,20 6361 82,11 7621 89,10 9013 95, 2 6373 80, 3 7669 88, 5 9049 106,27 6397 80, 1 7681 97,24 9109 97,10 6421: 88,21 7717 88, 3 9133 100,17 6469 89,22 7741 88, 1 9157 103,22 6481 82, 9 7753 94,19 9181 109,30 6529 86,17 7789 92,15 9241 98,11 QUADRATIC PARTITIONS. p - 20M 3761 54,i3 6481 i,3 6 9241 94, 9 1181 24,11 3821 21,26 6521 51,28 9281 6,43 1201 34, 3 3881 5 1 , 16 6581 81, 2 9341 96, 5 1301 3 6 , ' 4001 9,28 6661 71,18 9421 76,27 1321 14,15 4021 49,18 6701 24,35 9461 96, 7 1361 9,16 4201 59,i2 6761 69,20 9521 39,4o 1381 16,15 4241 6,29 6781 56,27 9601 86,21 1481 6,17 4261 56,15 6841 I 9,3 6 9661 29,42 1601 39, 4 4421 36,25 6961 79,12 9721 46,39 1621 1,18 4441 61,12 7001 66,23 9781 3 X ,42 1721 21,16 4481 66, 5 7121 54,29 9901 91,18 1741 11,18 4561 41,24 7321 29,36 9941 81,26 1801 26,15 4621 n,3° 7481 66,25 1861 41, 6 4721 54,i9 7541 81,14 1901 36,11 4801 34,2 7 7561 46,33 2081 9,20 4861 19,3° 7621 4,39 2141 36,13 5021 5 1 , 22 7681 74,2i 2161 46, 3 5081 69, 8 7741 64,27 2221 4,21 1 5101 59, 18 7841 81,16 2281 34, 15 1 5261 69,10 7901 84,13 244 QUADRATIC PARTITIONS. p = 20w + ( ) = x' 2 - H5y". p x' y P x' y p x' y p x' y 2£ 1 3, 2 2309 48, 1 5189 72, 1 7949 27,38 88 > 3, 4 2388 47, 6 5209 67,12 800£ > 3,4o 108 > 8, 3 2549 48, 7 5309 72, 5 8068 ) 87,10 148 > 12, I 2608 42,13 5449 2,33 8088 N 22,39 228 7, 6 2689 22,21 5569 58,21 8208 1 73,24 268 12, 5 2729 27,20 5669 57,22 8269 ! 68,27 349 i3, 6 2749 52, 3 5689 53,24 8328 i 43,3 6 388 12, 7 2789 12,23 5749 68,15 8369 1 57,32 409 2, 9 2909 48,11 5849 27,32 8389 28,39 449 18, 5 2969 18,23 5869 37,30 8429 48,35 509 3, IQ 3049 13,24 6029 72,13 8609 42,37 569 18, 7 3089 33,2o 6089 78, I 8629 32,39 709 23, 6 3109 52, 9 6229 28,33 8669 93, 2 769 7,12 3169 17,24 6269 I2 ,35 8689 47,36 809 27, 4 3209 42,17 6329 78, 7 8849 87,16 829 28, 3 3229 32,21 6389 63,22 8929 82,21 929 18,11 3329 57, 4 6449 18,35 8969 93, 8 1009 17,12 3389 3,26 6469 32,33 9029 57,34 1049 27, 8 3449 18,25 6529 7,36 9049 38,39 1069 32, 3 3469 43,i8 6569 42,31 9109 17,42 1109 33, 2 3529 53, J 2 6689 78,11 9209 78,25 1129 2,15 3709 8,27 6709 473° 9349 23,42 1229 27,10 3769 58, 9 6829 68,21 9629 93,M 1249 23,12 3889 62, 3 6869 33,34 9649 98, 3 1289 3,!6 3929 3,28 6949| 73,18 9689 3,44 1409 33, 8 3989 63, 2 7069 83, 6 9749 63,34 1429 32, 9 4049 63, 4 7109, 48,31 9769 83,24 1489 38, 3 4129 22,27 7129! 82, 9 9829 73,3o 1549 37, 6 4229 57,14 7229 1 3,38 9929| 93,i6 1609 22,15 4289 63, 8 7309 53,30 9949; 88,21 1669 7,18 4349 12,29 7349 63,26 1709 27,14 4409 42,23 7369, 67,24 1789 13,18 4549 7,3° 7489 62,27 1889 42, 5 4649 27,28 7529 78,17 1949 12,19 4729 43,24 7549 77,i8 2029 43, 6 4789 17,30 7589! 87, 2 2069 33,14 4889 42,25 7649 87, 4 2089 37,i2 4909 52,21 7669 8,39 2129 18,19 4969 62,15 7789 88, 3 2269 8,21 5009 33,28 7829 72,23 1 QUADRATIC PARTITIONS. 245 p = 24tr+l, 7 = G 2 + 6H 2 . p G H P G H P G H p' I G H 7 i, i 112< } 23,10 231l! 31,15 36311 59, 5 3 I 5, i 115: * 17,12 2377 29,16 3673; 53,12 7 $ 7, 2 120: i 5> T 4 2383 37,13 3697 59, 6 79 5, 3 123" L 35, J 2473 23,18 3727 61, 1 97 i, 4 124< * 35, 2 2503 47, 7 3769 37,20 103 7, 3 1271 * 35, 3 2521 11,20 3793 43, 1 8 1271 ii, i 129' r 11,14 2551 49, 5 3823 53,i3 151 I i. 5 130? * I7»i3 2593| 47, 8 3847 41,19 19r * I3> 2 132] ! 35, 4 261' 7 49, 6 388£ > 55,!2 191 ' 7, 5 132 1 ; 7 ; 29, 9 264 h ' 1,21 391S 1 13,25 22;- > *3, 3 139£ > 7,i5 2671 5,2i 394; 47,17 24] 5, 6 142S : 37, 3 268£ ) 17,20 3967 59, 9 27] ". 5 1447 3 T , 9 271? 43, 1 2 4057 1,26 318 17, 2 1471 IM5 271£ 1 37, J 5 4111 ! J 9, 2 5 337 : n ? 6 1489 25,12 2767 4129 ; 35,22 367 : 19. j 1543 23,13 2791 ! 25,19 4153 47,18 409 5, 8 1567 29,11 2833 53, 2 4159 53, J 5 433 7, 8 1609 35, 8 2857 41,14 4177 11,26 439 ! J 7, 5 1657 11,16 2887 49, 9 4201 55, r 4 457 i9> 4 1663 37, 7 2953 7,22 4231 65, 1 463 13, 7 1753 37, 8 3001 49,10 4273 37,22 487 i, 9 1759 5, J 7 3049 55, 2 4297 29,24 577 19, 6 1777 4i, 4 3079 55, 3 4327 41,21 601 1,10 1783 7,i7 3121 55, 4 4423 7,27 607 ii, 9 1801 25, J 4 3169 35,18 4441 65, 6 631 25, 1 1831 41, 5 3217 41,16 4447 61,11 673 17, 8 1873 43, 2 3271 25,21 4513 67, 2 727 1, 11 1879 2 3> I 5 3313 37,18 4519 6 5, 7 751 5, 11 1951 35> IJ 3319 55, 7 4561 55, 16 769 13,10 1993 7,18 3343 J 3, 2 3 4567 49,i9 823 2 3, 7 1999 43, 5 3361 31,20 4591 29,25 919 2 5, 7 2017 29,14 3391 35> I 9 4639 67, 5 937 29, 4 2089 35, 12 3433 23,22 4657 59,i4 967 3 1 , 1 2113 13,18 3457 1,24 4663 17,27 991 29, 5 2137 31, 14 3463 J 7,23 4729 5,28 1009 25, 8 2143 43, 7 3511 55, 9 4759 55,i7 1033 13,12 2161 25,16 3529 25,22 4783 67, 7 1039 5»*3 2239 35,!3 3559 47>*5 4801 49,20 1063 7,13 1 41,10 3583 43, 1 7 4831 59,i5 1087 i9,n| 2287 11,19 3607 3 x ,2i 4903 23,27 246 QUADRATIC PARTITION'S. 24m +1, 7 - G' + 6ir G H p G H G H G H 4951 4969 4993 4999 5023 5113 5119 5167 5209 5233 5281 5407 5431 5449 5479 5503 5521 5527 5569 5623 5641 5647 5689 5737 5743 5791 583^ 5857 5881 5953 6007 6073 6079 6121 6151 6199 6217 6247 6271 6337 65,11 17,28 25,27 43.2S 47,22 37,25 11,29 5 3, 20 23,28 35> 26 19,29 41,25 7,3<> 73, 5 67,13 n>3° 7i, 9 *3,3° 73, 7 71,10 59, J 9 *7,-3<> 41,26 37,27 5,3i 67,15 49» 2 4 59,20 77, 2 31,29 37,28 77r 5 61,20 49,25 55,23 7i,i4 79, 1 35^29 79, 4 6343 6361 6367 6481 6529 6553 6577 6607 6673 6679 6703 6793 6823 6841 6871 6961 6967 6991 7039 7057 J 7129! 7150j 7177! 7207: 7297J 7821 7351 7369! 7393 7417 7489 7537 7561 7591 7639 7681 7687 7753 7759 7873 73,i3 3 J ,3° 61,21 55,24 77,io 43,28 29,3* 23,32 73,i5 13,33 77,12 17,33 79,10 65,21 5:34 79, 11 35,3i 83, 5 ii,34 65,22 2-5,33 61,24 7i,i9 I9r34 85, 4 i,35 35,32 67,22 79> T 4 &3,i° 59,26 25r34 79.15 *7r35 65,24 71,21 83,12 35,33 77,i8 7879 23,35 7927 &q, 1 795 i 7993 8017 8161 81671 8191 8209| 8233 8263 8287 8311 8329 8353 8377 8431 8521 8527 8599 8623 8641 8647 8689 8713 8719 8737 8761 8839 8863 8887 8929 9001 9007 9049 9103 9127 9151 9199 &5,n 43,32 89, 4 S 5 ,I2 35,34 49,3 s 2"9,35 53,3° 73,22 7,37 91, 1 3*,35 77,20 47' 32 9*, 4 9*r 5 89,10 59,29 65,27 83,17 79,20 89,11 5,38 7,38 37.35 31,36 S 5 ,i6 25,37 67,27 79,21 65,28 35,36 91,11 95. 2 77,23 i,39 5,39 43,35 9241 9319 9337 9343 95, 6 95, 7 49,34 - 53,33 9391 85,19 9433 9439 9463 9511 9601 9631 9649 9679 9697 9721 9769 9817 9871 9967 97, 2 35,37 97, 3 95, 9 1,40 9!**5 7,40 77,25 79,24 11,40 13,40' 91,16 85,21 29,39* ^QUADRATIC PARTITIONS. 247 p = 24-or + 1, 19 = G'' ! -6H' 2 , [G'> 3H']. V Gt' H' F O f IT |) G'ff p G ? H f 19 5. ■ 1123 43,ii 2371 61,15 3643 1 97,31 43 7, * 1129 35, 4 2377 49, 2 3673 103,34 67 «i 3 1153 37, 6 2467 59, J 3 3691 71,15 73 i3> 4 1171 35, 3 2473 77,24 3697 61, 2 97 II, 2 1201 35, 2 2521 85,28 3739 65, 9 139 17, 5 1249 43, IO 2539 55, 9 3769J 85.24 163 13, i 1291 55, * 7 2593 53, 6 3793; 73,i6 193 17, 4 1297 41, 8 2617 59 <*2 3889 67,10 211 19, 5 1321 61,20 2659 53, 5 3907! 91,27 241 25, s 1459 53,i5 2683 73,2i 3931 65, 7 283 17, 1 1483 47,ii 2689 65,16 4003 67, 9 307 19, 3 1489 55,J6 2707 61,13 4027! 71,13 313 *3i 6 1531 41, 5 2713 53, 4 4051 85,23 331 25, 7 1579 65,21 2731 55, 7 4057 101,32 337 19, 2 1609 47,10 2803 53, 1 4099107,35 379 23, 5 1627 4i, 3 2833 83,26 4129' 65, 4 409 25, 6 1657 41, 2 2851 85,27 4153| 73» I 4 433 23, 4 1699 43, 5 2857 61,12 41771 7 1 , 12 457 29, 8 1728 47, 9 2953 67,16 4201 65, 2 499 35, 11 1747 59,*7 2971 55, 3 4219 65, 1 523 23, * 1753 43, 4 3001 55, 2 4243 83,21 547 29, 7 1777 61,18 3019 55, 1 4273 67, 6 571 25, 3 1801 49,10 3049 65,14 4297 79,18 577 3i, 8 1867 71,23 3067 79,23 4339 67, 5 601 25, 2 1873 73,24 3121 61,10 4363 97,29 619 25, 1 1987 61,17 3163 73,*9 4441 71,10 643 37>n 1993 47, 6 3169 85,26 4483 67, 1 673 43, 1 4 2011 55,i3 3187 59, 7 4507 79, J 7 691 29, 5 2017j 49, 8 3217 89,28 4513 io7,34 739 35, 9 2083 53,ii 3259 95,3i 4561 H5,38 769 37,i° 2089 67,20 3307 7M7 4603 73, 11 787 29, 3 2113 47, 4 3313 67,14 4651 95,27 811 3 1 , 5 2131 59,*5 3331 59, 5 4657 71, 8 859 47,i5 2137 71,22 3361 65,12 4723 83,19 883 37, 9 2161 55, I2 3433 83,24 4729 73, IQ 907 3 1 , 3 2179 77,25 3457 59, 2 4801 101,30 937 3 1 , 2 2203 47, 1 3499 65,11 4969 95,26 1009 35, 6 2251 49, 5 3529 77,20 4987 7i, 3 1033 47»M 2281 65,18 3547 89,27 4993 113,36 1051 49, 1 5 2347 49, 3 3571 61, 5 5011 H5-37 p = 24w+l, 19 = G 2 -6H' \ [CK> 3H'] p G' H' p G' H' p ; G' H! V G' H' 5059 85,19 6451 101,25 7963 103,21 9403 97, 1 5107 9^23 6481 109,30 7993107,24 9433103,14 5113 73. 6 6529 127,40 8011 95,13 9547.i5i,47 5179 73, 5 6547 9M7 8017!fi 9 ,32 9601|ioi,io 5209 103,3° 6553 103,26 8059 97,i5 9619i55,49 5227 79,i3 6571 89,15 8089 i33i4o 9643 !37,39 5233 73, 4 6577 13M2 8161 95,i2 9649 r 57,5o 5281 85,18 6619 J 37,45 8179 115,29 9697 161,52 5323 73, 1 6673 83, 6 8209 103,20 9721 i39,4o 5347 io9,33 6691 n5,33 8233 97,14 9739 r °7,55 5419 H3,35 6763 97,21 8329 145,46 9769 115,24 5443 77, 9 6793 ^3, 4 8353 127,36 9787 119,27 5449 ^5,36 6841| 85, 8 8377 149,48 9811 J 3i,35 5521 89,20 6883J 83, r 8419 ^s 1 9817 101, 8 5563 103,29 6907 89,13 8443 103,19 9859 l2 5,3* 5569 95, 2 4 6961|i2 5 , 3 8 8467 101,17 9883 103,11 5641 79,10 7027lioi,23 8521 115,28 9907 101, 7 5659 97,25 7057 89,12 8539 95, 9 9931 M5,43 5683 107,31 7129 85, 4 8563 T 33,39 5689 85,16 7177jio 9 ,28 8641 95, 8 5737 109,32 7219 85, 1 8689 125,34 5779 77, 5 7243 97,19 8707 100,23 5827 101,27 7297|ioi,22 8713 113,26 5851 95,23 7321, 89,10 8731 95, 7 5857 79, 8 7369*13,30 8737 139,42 5881 91,20 7393107,26 8761 119,30 5923 77, 1 7411125,37 8779 127,35 5953 97,24 7417| 91,12 8803 107,21 6043 127,41 7459|iis,3i 8923 97, 9 6067 i3i,43 7489 95, 1 6 8929 95, 4 6073 133,44 7507sio9,27 8971 95, 3 6091 79, 5 7537 89, 8 9001 95, 2 6121 95,22 7561 131,40 9043 157,5! 6163 83,11 7603 133,41 9049 107,20 6211 85,i3 7681 91, to 9067 l6l ,53 6217 79, 2 7699 107,25 9091 125,33 6337! 91,18 7723113,29 9187 101,13 6361! 85,12 7753 143,46 9241 121,30 6379| 95,2i 7867 89, 3 9283 107,19 6427i 121,37 7873 97,t6 9337 101,12 QUADRATIC PARTITIONS. 249 p = 28w+ 1, 9, 25 = t ,2 -7u' 2 , [if > 3u']. p \t' u' 39 t' 11' p t' u' V t' u' 29 6, i 1117 37, 6 2333 66,17 3581 117,38 37 to, 3 1129 52,15 2377 100,33 3593 60, 1 53 9 , 2 1201 47,12 2381 78,23 3613 106,33 109 19, 6 1213 59,i8 2389 74,21 3637 82,21 113 15, 4 1229 5**4 2417 60,13 3677 102,31 137 12, 1 1289 36, 1 2437 5°, 3 3697 113,36 149 18, 5 1297 73, 2 4 2473 59,i2 3733 94,27 193 16, 3 1373 69,22 2521 64,15 3761 81,20 197 15, 2 1381 38, 3 2549 57,io 3833 75, J 6 233 24, 7 1409 39, 4 2557 53, 6 3889 89,24 277 23, 6 1429 41, 6 2633 99,32 3917 93,26 281 27, 8 1453 61,18 2657 72,19 3929 123,40 317 18, 1 1481 72,23 2689 76,21 4001 72,13 337 20, 3 1493 39, 2 2713 61,12 4013 66, 7 373 25, 6 1549 46, 9 2741 54, 5 4057 68, 9 389 33>i° 1597 43, 6 2753 60,11 4153 U5,36 401 24, 5 1621 82,27 2797 58, 9 4201 76,15 421 22, 3 1709 78,25 2801 57, 8 4229 ni,34 449 3 6 ,n 1733 54,i3 2837 87,26 4253 75,H 457 32, 9 1789 58,15 2857 83,24 4337 72,11. 541 46,15 1801 53,i2 2909 54, 1 4349 66, 1 557 3o> 7 1873 44, 3 2969 69,16 4397 90,23 569 24, 1 1877 57,i4 3049 68,15 4421 U4,35 613 26, 3 1901 5 1 , 10 3061 73,i8 4481 132,43 617 27, 4 1913 45, 4 3089 108,35 4517 102,29 641 33, 8 1933 5°, 9 3109 97,3o 4561 68, 3 653 45, J 4 1997 45, 2 3137 57, 4 4621 83,18 673 41,12 2017 55, 12 3217 65,12 4649 69, 4 701 27, 2 2053 4 6 , 3 3221 57, 2 4657 88,21 709 $*s 6 2069 54,ii 3229 59, 6 4673 135,44 757 55,i8 2081 87,28 3257 60, 7 4729 124,39 809 $1,16 2129 48, 5 3301 58, 3 4733 69, 2 821 39,io 2137 52, 9 3313 80,21 4789 71, 6 877 38, 9 2153 5*i 8 3329 96,29 4813 13^42 953 36, 7 2213 90,29 3361 92,27 4817 120,37 977 33, 4 2221 67,18 3389 69,14 4909 74, 9 1009 64,21 2237 75,22 3413ji i4,37 4937 108,31 1033 40, 9 2269 62,15 3469 61, 6 4957 85,18 1061 33, 2 2293 86,27 3529 64, 9 4993 95,24 1093 34, 3 2297 48, I 3557 78,19 5009 72, 5 2k 250 QUADRATIC PARTITIONS. p = 28 3u']. P t' u' p 1 t' u' P t' u' P t' a' 5021 123,38 6553 125,36 7933 101,18 9293 114,23 5077 73. 6 6577 103,24 7949 93, IO 9349 166,51 5153 111,32 658lii62,53 8009 99,16 9377 177,56 5189 81,14 6637 83, 6 8017 95, 12 9433 100, 9 5209 76, 9 6661 82, 3 8089 i3 J ,36 9437 162,49 5233 79,12 6673 15^48 8093 90, 1 9461 138,37 5237 78,11 6689 96,19 8101 143,42 9473 129,32 5261 93,22 6701 102,23 8117 135,38 9521 111,20 5273 144,47 6829 86, 9 8233 176,57 9601 103,12 5413 74, 3 6833 111,28 8269 94, 9 9613 109,18 5441 129,40 6841 172,57 8297 165,52 9629 198,65 5569 121,36 6857 93,!6 8317 190,63 9661 106,15 5573 90,19 6869 87,10 8353 116,27 9689 99, 4 5581 109,30 6917 9 ,!3 8369 96,11 9697 137,36 5653 89,18 6997 110,27 8429 99, 1 4 9769 187,60 5657 132,41 7001 99,20 8513 120,29 9781 122,27 5693 i5°,49 7057 127,36 8521 157,48 9829 127,30 5737 128,39 7109ii 14,29 8537 93, 4 9857 153,44 5741 78, 7 7121 87, 8 8597 153,46 9941 183,58 •5749 94,21 7177 88, 9 8677 *45,42 9949 101, 6 5821 86,15 7193 96,17 8681 141,40 5849 93,20 7253 90,11 8689! 1 6a, 5 1 5861 81,10 7309 !34,39 8737ii3,24 5881 83,12 7333 86, 3 8761 128,33 6029 102,25 7393 160,51 8821 118,27 6073 149,48 7417 107,24 8849 132,35 6101 138,43 7457 87, 4 8929 152,45 6113 81, 8 7477 ^7,54 8933 111,22 6133 106,27 7529 i5 6 ,49 8941 178,57 6197 87,14 7541 87, 2 8969i 44 , 4 i 6217 85,12 7561 181,60 9013,iio,2i 6269 114,31 7589 111,26 9041 96, s 6301 JI 8,33 7669 89, 6 9109 199,66 6329 141,44 7673 120,31 9137 108,19 6337 80, 3 7681 88, 3 9157 97, 6 6353 159,52 7753 124,33 9181 107,18 6421 137,42 7757 90, 7 9209 96, 1 6449 81, 4 7793 144,43 9221102,13 6469 ; 1 13,30 7841 !32,37 9241 104,15 6521117,32 7877 102,19 92771130,33 QUADRATIC PARTITIONS. 251 p = 40w+l, 9, 11, 19 = $*+l(hj a . p £ v P £ v P £ V P 1 £ 1 11 h i 1051 31, 3 2339 43, 7 3529 17,18 19 3, i 1091 29, 5 2371 n,i5 3539 43, 1 3 41 I, 2 1129 33, 2 2411 49, 1 3571 59, 3 59 7, i 1171 19, 9 2441 49, 2 3659 7, J 9 89 7, 2 1201 29, 6 2459 47, 5 3691 9,19 131 ii, i 1249 33, 4 2521 39,io 3739 57, 7 139 7, 3 1259 7,ii 2531 29,13 3761 61, 2 179 '3, i 1289 17,10 2539 17,15 3769 23,18 211 «> 3 1291 9,11 2579 37,ii 3779 i3,!9 241 9, 4 1321 Sh 6 2609 7,16 3851 3M7 251 i. 5 1361 19,10 2659 43, 9 3881 61, 4 281 ii, 4 1409 37, 2 2689 27,14 3889 57, 8 331 9, 5 1451 3 1 , 7 2699 47, 7 3929 37,i6 379 i7> 3 1459 37, 3 2729 13, 16 3931 41,15 401 19, 2 1481 29, 8 2731 39,ii 4001j 1,20 409 7, 6 1489 7,12 2801 29,14 4019| 53,ii 419 *3, 5 1499 17,11 2819 53, 1 4049J 7,20 449 i7, 4 1531 39, * 2851 5*i 5 4051 21,19 491 1. 7 1571 19,11 2939 7,i7 4091! 49,13 499 3, 7 1579 33, 7 2969 53, 4 4099] 43,15 521 i9, 4 1601 31, 8 2971 9,i7 4129 63, 4 569 23, 2 1609 I3,!2 3001 21,16 4139! 23,19 571 9, 7 1619 37, 5 3011 11,17 42011 31,18 601 21, 4 1699 3,i3 3019 47, 9 4211 61, 7 619 23, 3 1721 41, 2 3041 49, 8. 4219 63, 5 641 1, 8 1801 19,12 3049 33, J 4 4241 41,16 659 13, 7 1811 11,13 3089 23,16 4259 37,17 691 21, 5 1889 43, 2 3121 41,12 4289 17,20 739 27, 1 1931 41, 5 3169 53, 6 4339 27,19 761 11, 8 1979 i7,i3 3209 47,io 4409 43, l6 769 27, 2 2011 39, 7 3251 i9,i7 4441 21,20 809 i3, 8 2081 11,14 3259 57, 1 4451 29,19 811 h 9 2089 33, IQ 3299 53, 7 4481 59,io 859 7, 9 2099 43, 5 3329 37,M 4561 5M4 881 29, 2 2129 13^4 3331 21,17 4649 67, 4 929 17, 8 2131 21,13 3361 11,18 4651 49, 1 5 971 3 1 , 1 2161 39, 8 3371 41,13 4691 59,ii 1009 3,io 2179 37, 9 3449 53, 8 4721 61,10 1019 23. 7 2251 ii*5 3491 59, 1 4729 27,20 104^ 1 7,io 1 2281 29,12 3498 57, 5 4801 69, 2 252 QUADRATIC PARTITIONS. p m 40w+ 1, 9, 11, 19 = ?+ 10t? 2 . V t V P i v P i v P € V 488< ) 7,22 6451 69,13 8011 89, 3 9491 9Mi 4931 . 6i,n 6481 71,12 8059 87, 7 9521 41,28 496£ ) 63,10 6491 79, 5 8081 89, 4 9539 77,i9 500£ ) 13,22 652] L 41,22 8089 57,22 9601! 69,22 501] 69, 5 652! ) 63,16 816] [ 49,24 9619 3,31 5051 7i, 1 656< ) 77, 8 817] 1 89, 5 9649 93,io 5059 53,15 6571 L 81, 1 8179 77,i5 9689 43,28 5081 71, 2 661< ) 47,21 820£ ) 87, 8 9721 - 91,12 5099 47,i7 665£ > 37,23 8219 > 73,i7 9739 73,21 5171 59,13 6689 1 43,22 8291 91, 1 9769 1 97, 6 5179 63,11 6691 21,25 8329 83,12 9811 1 99, 1 5209 57,i4 6761 1,26 8369 23,28 9851 79,i9 5281 21,22 6779 23,25 8419 3,29 9859 ; 93,11 5419 73, 3 6841 9,26 8521 81,14 9929 77,2o 5441 59,14 6899 83, 1 8539 57,23 9931 \ 39,29 5449 47,i8 6961 61,18 8609 43,26 5521 39,2o 6971 41,23 8641 91, 6 5531 7i, 7 7001 7i,i4 8681 29,28 5569 27,22 7019 73,i3 8689 93, 2 5641 49,18 7121 19,26 8699 17,29 5651 19,23 7129 37,24 8731 89, 9 5659 6 3,i3 7211 31,25 8761 69^0 5689 73, 6 7219 53,2i 8779 87,11 5779 37,2i 7321 69,16 8819 77,17 5801 31,22 7331 61,19 8849 83,14 5849 43,2o 7369 77,12 8929 33,28 5851 7i, 9 7411 11,27 8969 47,26 5881 11,24 7451 79," 8971 41,27 5939 77, 1 7459 13,27 9001 1,30 6011 49,i9 7481 59,2o 9011 61,23 6089 77, 4 7489 27,26 9041 71,20 6091 41,21 7499 47,23 9049 7,3o 6121 19,24 7529 83, 8 9059 53,25 6131 29,23 7561 81,10 9091 9 1 , 9 6211 5i,i9 7649 53,22 9161 49,26 6299 7,25 7681 79,12 9209 37,28 6329 73, IQ 7691 49,23 9241 59,24 6361 39,22 7699 ^ 9 9281 91,10 6379 33,23 7841 1,28 9371 3 J ,29 6449 67,14 8009 13,28 9419 97, 1 QUADRATIC PARTITIONS. 253 p = 40w+ 1, 9, 31, 39 - ^-lO/, [{' > -yV]. p e i p e- v' P £' v f P ? i 3] n, 3 1049 33, 2 239< > 93,25 3769 1 13,30 41 9, 2 1129 83,24 2441 - 5i, 4 388] ■ 141,40 71 9. i 1151 69,19 252] - 91,24 3889 73,12 7£ 1 i3, 3 120llioi,3o 2551 I5i,45 3911 . 111,29 88 ► 27, 8 1231 59,i5 2591 5i, 1 391* > 173,51 151 3i, 9 1249 1 67,18 2608 57, 8 392£ ► 63, 2 191 2 i, 5 1279 37, 3 2671 59, 9 4001 81,16 198 i7, 3 1289! 57,i4 2688 77,i8 4048 153,44 239 2 7, 7 1319 87,25 2711 111,31 4078 117,31 241 41,12 1321| 41, 6 2719 53, 3 4111 139,39 271 19, 3 1361 39, 4 2729 87,22 4129 67, 6 281 11, 4 1399 47, 9 2791 7i,i5 4159 107,27 311 39,ii 1409 63,16 2801 69,14 4201 131,36 359 57,i7 1439,ii7,3.1 2879 I2 3,35 4231 7i, 9 401 21, 2 1471 61,15 2969 63,10 4241 171,50 409 43, 1 2 1481 39, 2 2999 57, 5 4271 69, 7 431 21, 1 1489 43, 6 3001 79,18 4289 177,52 439 23, 3 1511 39, 1 3041 99,26 4391 129,35 449 33, 8 1559 57,13 3049 67,12 4409 207,62 479 27, 5 1601 51,10 3079 73,i5 4441 101,24 521 39,io 1609 103,30 3089 57, 4 4481 111,28 569 27, 4 1721 81,22 3119 147,43 4519 73, 9 599 33, 7 1759 43, 3 3121 59, 6 4561 149,42 601 31, 6 1801 71,18 3169 127,36 4591 109,27 631 71,21 1831 79,21 3191 159,47 4639 83,15 641 5i,i4 1871 69,17 3209 57, 2 4649 93,2o 719 27, 1 1879 H3,33 3271 H9,33 4679 87,i7 751 29, 3 1889 93,26 3319 103,27 4721; 69, 2 761 69,20 1951 i3i,39 3329 63, 8 4729 133,36 769 47,12 1999 53, 9 3359 93,23 4751 69, 1 809 87,26 2039 57,ii 3361 61, 6 4759 193,57 839 33, 5 2081 111,32 3391, 59, 3 4799 i47,4i 881 39, 8 2089 73,i8 3449 117,32 4801 79,i2 911 5i,i3 2111 5i, 7 351l! 89,21 4831 211,63 919 73,2i 2129 n7,34 3529 163,48 4871 81,13 929 ! 33, 4 2161 89,24 3559; ^37,39 4889 ^23,32 991 91,27 2239 67,15 3631 61, 3 4919 t53,43 1009 37, 6 2281 61,12 3671 81,17 49511 7i, 3 1031; 39, 7 2311 49, 3 3719 63, 5 4969 73, 6 1039 43. 9 2351 5i» 5 3761 1 69,10 4999 l 97,21 254 QUADRATIC PARTITIONS. p = 40w + 1, 9, 31, 39 = | /2 -10rj' 2 , [£' > -^tj']. p (' v' P i'j p ! e v' P £' v' 5009 87,16 6481 89,12 7951 101,15 9319 97, 3 5039 93,*9 6521 81, 2 8009 93, 8 9391 101, 9 5081 129,34 6529 ^ 6 8039 207,59 9431in,i7 5119 77, 9 6551 81, 1 8081 171,46 9439; 1 57,39 5209 203,60 6569 87,10 8089 T 93,54 9479183,49 5231 17^49 6599 i53,4i 8111 99,i3 9511239,69 5279 117,29 6679 233,69 8161 i3 I ,3° 9521219,62 5281 221,66 6689 93,H 8191 9 1 , 3 9551 99, 5 5351 81,11 6719 123,29 8209 107,18 9601301,90 5399 183,53 6761 201,58 8231 129,29 9631, 109, 1 5 5431 79, 9 6791 159,43 8311 169,45 9649197,54 5441 141,38 6841 91,12 8329 263,78 9679i73,45 5449 83,12 6871 119,27 8369 123,26 9689 117,20 5471 i89,55 6911 99,i7 8431 !39,33 9719i 53 ,37 5479 113,27 6959 93,*3 8521 211,60 9721i8i,48 5519 123,3! 6961 101,18 8599 97, 9 97691 137,30 5521 169,48 6991 149,39 8609 93, 2 9791 t 99, 1 5569 77, 6 7001 219,64 8641 109,18 9839,123,23 5591 201,59 7039 107,21 8681 189,52 9871 ! i 3 i,2 7 5639 207,61 7079 87, 7 8689 !33,3° 9929237,68 5641 121,30 7121 231,68 8719 203,57 5689 107,24 7129 127,30 8761 101,12 5711 219,65 7151 i7i,47 8831 261,77 5791 101,21 7159 97,i5 8839 127,27 5801 99,20 7321 i9 J ,54 8849 117,22 5839 77, 3 7351 121,27 8929 163,42 5849 117,28 7369 103,18 8951 279,83 5879 87,13 7481 111,22 8969 x 53,38 5881 79, 6 7489 i43,3 6 8999 297,89 6079 83, 9 7529 87, 2 9001 179,48 6089 93, l6 7559 87, 1 9041 201,56 6121 109,24 7561 89, 6 9049 97, 6 6151 79, 3 7591 i5i,39 9151 221,63 6199 103,21 7639 167,45 9161 99, 8 6271 i3i,33 7649 93,i° 9199 107,15 6311 81, 5 7681 209,60 9209 207,58 6329 177,5° 7759,253,75 9239 177,47 6359 87,11 7841| 99,14 9241 ; 149,36 6361 r 39,36 7879|i 37 ,33 9281 159,40 16449 183,52 7919 147,37 9311 ; 99, 7 1 QUADRATIC PARTITIONS. 255 p = 44-W + 1, 5, 9 , 25, 37 - = v' 2 -] Llw' 2 , [ v' > ^w 7 ]. V v'w' P V w' p V w' p V w' 5 4, i 1093 57,H 2357 49, 2 3701 95,22 37 9, 2 1109 47,10 2377 54, 7 3733 68, 9 53 8, i 1153 63,16 2381 59,io 3793 63, 4 89 IO, I 1181 35, 2 2473 58, 9 3821 64, 5 97 14, 3 1193 37, 4 2557 5*i 2 3833 62, 1 113 17, 4 1213 72,19 2621 61,10 3853 72,11 137 26, 7 1237 81,22 2633 53, 4 3877 84,17 157 16, 3 1277 56,13 2677 79,18 3881 91,20 181 15, 2 1301 49,10 2689 95,24 3917 76,13 229 25, 6 1321 45, 8 2693 52, 1 4013 107,26 257 3i, 8 1373 52,11 2729 98,25 4049 65, 4 269 37,io 1409 65,16 2753 82,19 4057 69, 8 313 18, 1 1433 38, 1 2777 59, 8 4073 83,16 317 19, 2 1453 43, 6 2797 104,27 4093 67, 6 353 23, 4 1489 42, 5 2861 56, 5 4129 90,19 389 20, 1 1549 80,21 2897 119,32 4217 86,17 397 21, 2 1609 5°, 9 2909 125,34 4229 73,io 401 26, 5 1621 64,15 2953 62, 9 4261! 1 19,30 421 39, IQ 1637 41, 2 2957 91,22 4273 103,24 433 42,11 1697 49, 8 3001 74,i5 4337 71, 8 449 25, 4 1709 53,io 3037 56, 3 4349 68, 5 509 28, 5 1721 70,17 3041 70,13 4357 89,18 521 35, 8 1741 60,13 3061 60, 7 4409 85,16 577 26, 3 1753 42, 1 3089, 58, 5 4481 134,35 617 34, 7 1873 82,21 3169! 87,20 4493 92,19 641 50,13 1901 85,22 3217io6,27 4513 137,36 653 53tl4 1973 97,26 3221: 80,17 4621 155,42 661 56,15 2017 46, 3 3257jio 9 , 2 8 4657 79,12 709 40, 9 2029 48, 5 33011 76,15 4673 118,29 757 36, 7 2069 65,14 3389 67,10 4733 83,14 773 28, 1 2113 78,19 3413i27,34 4789 108,25 797 29, 2 2137 61,12 3433,133,36 4801 70, 3 829 35, 6 2161 81,20 3457; 71,12 4877 101,22 881 34, 5 2237 64,13 3469J 75,14 4889 70, 1 929 70,19 2269 60,11 3529 ! io2,25 4909 72, 5 977 41, 8 2281 90,23 3557 64, 7 4933 73, 6 1013 32, 1 2293 48, 1 3613 92,21 4937 74, 7 1021 36, 5 2297 74,i7 3617 74,13 4973:i33,34 1049 35, 4 2333 67,14 3677 61, 2 5009| 97,20 1061 40, 7 2341 96,25 3697 111,28 5021 !36,35 256 QUADRATIC PARTITIONS. p = 44w+ 1, 5, 9, 25, 37 = v^-llV 2 , [V > ^w']. p v' w' P v' w' P V w' P V w' 5113 107,24 6449 82, 5 7753 162,41 9029 140,31 5153 73, 4 6469 87,10 7789 133,30 9109 100, 9 5197 84,13 6473 ! i58, 4 i 7793io3,i6 9133,203,54 5237 76, 7 6521 85, 8 7841|i46,35 9157 169,42 5261 160,43 6581 116,25 7877 89, 2 9161 206,55 5273 163,44 6637 101,18 7901 115,22 9221 215,58 5281 166,45 6653 173,46 8009 122,25 9241 221,60 5333 113,26 6689 142,35 80171129,28 9277156,37 5393 82,11 6733 188,51 8053177,46 9293io7,i 4 5413 87,14 6737 191,52 8089 90, 1 9337|i 4 6,33 5417 106,23 6781 84, 5 8101 180,47 9377io6,i 3 5437 116,27 6829 85, 6 8209 105,16 9397159,38 5449 75, 4 6857 86, 7 8221 189,50 9421139,30 5501 76, 5 6869 95, J 4 8233ji 5 8, 39 9461 100, 7 5569 138,35 6917 i5!,38 8237' 91, 2 9497ioi, 8 5581 75, 2 6961 135,32 8273 98,11 9601135,28 5641 85,12 6977 94,i3 82971 94, 7 9629i 5 2,35 5657 94,i7 6997 111,22 8317 109,18 9661ii5,i8 5669 112,25 7001 125,28 8353207,56 9689 190,49 5701 105,22 7109 160,41 8369,ii3,2o 9733i68,4i 5801 101,20 7121 86, 5 8429148,35 9749193,50 5813 128,31 7129; 98,15 8501124,25 9769 155,36 5857 81, 8 7177ii4,23 8537ii3i,28 9817jii4,i7 5861 80, 7 7253 97,i4 8573 112,19 9857199,52 5897 i3 J ,32 7297 86, 3 8581 120,23 9901 100, 3 6029 100,19 7309 172,45 8629 95, 6 9949 205,54 6037 96,17 7349 175,46 8669 100,11 6053 137,34 7393 87, 4 8677 96, 7 6073 78, 1 7417 181,48 8693 127,26 6121 114,25 7481 109,20 8713 98, 9 6197 79, 2 7489 190,5! 8737 94, 3 6229 127,30 7517 196,53 8761 106,15 6257 146,37 7529 202,55 8837 119,22 6301 80, 3 7549 93, IQ 8849 95, 4 6317 149,38 7561 90, 7 8893 147,34 6329 I3Q.3 1 7573 92, 9 8933 188,49 6337 89,12 7577 91, 8 8941 96, 5 6361 94,i5 7621 140,33 8969 163,40 6373 !52,39 7649 130,29 9001126,25 6389 80, 1 7681 i59,4o 9013 97, 6 QUADRATIC PARTITIONS. 257 p or 2p = t 2 ±Du 2 , [D = 13, 14]. t 2 +13u 3 t 2 -13u 2 t 2 -13u 2 t 2 +14u 2 t 2 -14u 2 ISt > 65u 18t > 65u jp l t>4u P t u P t u P t U p 4 157j 12, 1 61 23, 6 563; 24, 1 151 5, 3 163 17, 3 173 ii, 2 79 14, 3 569i89, 52 2.191 16, 3 179 23, 5 181! 8, 3 101 123, 34 57l|i6 4j 45 2.193 6, 5 193 33, 8 233! 5 , 4 103, 34, 9 599| 66, 17 233 3, 4 211 i5, 1 257 7 , 4 107| 48, !3 6OII347, 96 239 J 5, 1 233 17, 2 269 1 6, 1 113,159, 44 607 250, 69 2.263 20, 3 281 41, 10 277 15, 2 127 98, 27 641 63, 16 281 J 5, 2 331 45, I][ 313 14, 3 131 12, 1 647 150, 4i 2.337 18, 5 337 29, 6 337 18, 1 139 16, 3 653225. 62 359 3, 5 347 19, 1 373 16, 3 157 25, 6 659 36, 7 2.401 26, 3 379 27, 5 389! 8, 5 173 15, 2 673 i75, 48 431 9, 5 401 25, 4 433 15, 4 179 84, 23 677 27, 2 449 15, 4 443 53, 13 521! 1 4| 5 18liio9, 30 701 57, i4 2.457 30, 1 449 43, 10 569 19, 4 19l| 42, 11 719 54, 13 2.463 24, 5 457 3 1 , 6 601 22, 3 199!2o6, 57 727i22, 33 487 19, 3 491 29, 5 641 2, 7 211 56, 15 751 35 8 , 99 2.569 2, 9 499 25, 3 653 4, 7 233 21, 4 757 35, 6 2.599 8, 9 547 41, 9 673 6, 7 251 24, 5 797 297, 82 2.617 10, 9 569 25, 2 677 25, 2 257 33, 8 809 147, 40 2.631 24, 7 571 61, J 5 701 8, 7 263 30, 7 823 466,129 2.641 34, 3 617 29, 4 757 17, 6 269 81, 22 829 71, 18 673 T 3, 6 641 65, 16 797 28, 1 277 67, 18 857 333, 92 743 27, 1 659 55, J 3 809 22, 5 283 20, 3 859 2 72, 75 751 ^5, 3 673 27, 2 829 19, 6 311 18, 1 881 33, 4 2.809 22, 9 683 37, 7 857 5, 8 313 131, 36 883 44, 9 2.823 36, 5 739 33, 5 881 7, 8 337 47, 12 887 30, 1 2.863 40, 3 809 47, IO 937 27, 4 347 192, 53 907 3 2 , 3 911 15, 7 827 29, I 953 11, 8 367 22, 3 911 222, 61 2.919 12, 11 883 57, J 3 997 23, 6 373 29, 6 919 62, 15 953 27, 4 907 5 1 , I][ 389 21, 2 937 53, I2 967 29, 3 947 3i, 1 419 264, 73 953 405,112 977 9, 8 953 43, 8 433 89, 24 971 36, 5 2.991 36, 7 977 61, 14 439 58, 15 991 82, 21 443 300, 83 997 283, 78 2l 258 QUADRATIC PARTITIONS. p or 9p = t 2 ±Dn 2 , [D = 15, 17]. t 2 +15u 2 t 2 -15u 2 t 2 +17u 2 t 2 -17u 2 t 2 -17u 2 t>5u „ 4t > 17u 1 4t>17u P t u P t u 9p t u P t u 2> t u 19 2, 1 6l| 11, 2 9.13 10, 1 18 9, 2 461 23, 2 31 4, 1 109 13, 2 53 6, 1 19 6, 1 463 36, 7 611 i, 2 181 14, 1 9.89 28, 1 43 14, 3 467 22, 1 79 8, 1 229 17, 2 9.101 29, 2 47 8, 1 491 58, 13 109' 7, 2 241 16, 1 9.137 3 1 , 4 53 11, 2 509 47, IO 139 2, 3 349 22, 3 149 9, 2 59 22, 5 523 I 26, 3 151 4 , 3 409 28, 5 157i 2, 3 67 30, 7 557 25, 2 181 n, 2 421 31, 6 9.229 19, 10 831 10, 1 563 74, 17 199 8, 3 541 26, 3 9.257 35, 8 89 19, 4 569 29, 4 211 14, 1 601 29, 4 281 3, 4 1011 13, 2 577 55, I 2 229 *3j 2 661 26, 1 293 J 5, 2 103! 16, 3 587 82, 19 241 i, 4 709 38, 7 349 14, 3 127! 12, 1 593 4i, 8 271 1 6, 1 769 28, 1 353 9, 4 137! 35, 8 599 3 2 , 5 331 i4, 3 829 37, 6 9.373 22, 13 149 43, 10 613 35, 6 349 17, 2 9.389 38, 11 151 24, 5 631 28, 3 379 2, 5 409 16, 3 157 15, 2 647 52, 11 409 T 3, 4 9.421 61, 2 179 14, 1 659 26, 1 421 19, 2 9.433 53, 8 191 3 2 , 7 661 27, 2 439 8, 5 9.457 64, 1 223 40, 9 701 49, 10 499 22, 1 461 6, 5 229 29, 6 727 60, 13 541 1. 6 509 21, 2 239 16, 1 733 79, 18 571 14, 5 9.557 4i, 14 251 26, 5 739 46, 9 601 19, 4 569 12, 5 257 2 3, 4 757 37, 6 619 22, 3 9.577 56, 11 263 56, 13 761 43, 8 631 16, 5 593 24, 1 271 64, 15 769 87, 20 661 11, 6 613 1, 6 281 37, 8 773 29, 2 691 26, 1 661 7, 6 293 19, 2 797 95, 22 709 13, 6 9.701 79, 2 307 18, 1 829 in, 26 739 2, 7 733 11, 6 331 22, 3 859 54, 11 751 4, 7 9.757 59, 14 349 3i, 6 863 76, 17 769 23, 4 9.761 44, 17 353 25, 4 883 3°, 1 811 26, 3 9.769 28, 19 359 28, 5 919 84, 19 829 17, 6 9.773 ^ 2 373 21, 2 937 45, 8 859 22, 5 797 27, 2 383 20, ! 953 35, 4 919 28, 3 9.829 78, 9 389 61, H 967 92, 21 991 16, 7 937 28, 3 409 69, 16 97l! 62, 13 9.953 88, 7 421 77, 18 977| 73, 16 977 12, 7 433 443 457 39, 50, 27, 8 11 4 QUADRATIC PARTITIONS. 259 p or 4p = = t 2 ±Du 2 , [D = ] L9]. t 2 + 19u 2 t 2 + 19u 2 t 2 -19u 2 p & 4p t u 4p 1 t u ■ 13t > 57u 4.5 i, 1 4.463 41, 3 5 9) 2 4.7 3, 1 4.467 43, 1 17 6, 1 4.11 5, 1 479 2, 5 61 40, 9 4.17 7, 1 491 4, 5 73 53, 12 23 2, 1 4.499 39, 5 101 24, 5 4.43 i, 3 503 22, 1 137 21, 4 4.47 J 3, 1 4.541 25, 9 149 15, 2 4.61 i5, 1 4.557 47, 1 157 29, 6 4.73 ii, 3 571 20, 3 197 84, 19 4.83 1 6, 2 4.577 3, 11 229 20, 3 101 5, 2 4.587i 7, 11 233 123, 28 4.131 7, 5 593 17, 4 277 31, 6 4.137 23, 1 4.613 39, 7 313 22, 3 4.139 9, 5 4.617 13, 11 349 68, 15 4.149 ii, 5 619 12, 5 353 102, 23 157 9, 2 4.63l| 15, 11 389 60, 13 163 12, 1 4.643; 49, 3 397 44, 9 4.191 i7, 5 4.647 17, 11 457 94, 21 197 ii, 2 4.653 41, 7 461 180, 41 4.199 25, 3 4.691 35; 9 541 35, 6 4.229 21, 5 7011 25, 2 557 24, 1 4.233 1, 7 709 5, 6 577 46, 9 4.239 5, 7 4.719 49, 5 593 78, 17 4.251 23, 5 4.727 37, 9 613 28, 3 4.263 11, 7 733 7, 6 617 54, 11 271 10, 3 4.739 45, 7 653 27, 2 4.277 33, 1 4.757 27, 11 701 51, i° 4.283 3i, 3 4.761 55, 1 709 185, 42 4.311 35, 1 4.769 5i, 5 733 83, 18 313 3, 4 4.809 5, 13 757 224, 51 4.347 37, 1 4.821 53, 5 761 75, 16 4.349 35, 3 4.823 9, 13 769 25°, 57 353 7, 4 853 13, 6 809 45, 8 4.359 3i, 5 4.859 i5, 13 821 36, 5 367 14, 3 4.881 35, 11 853 32, 3 4.389 25, 7 4.883 5i, 7 881 3°, 1 4.397 7, 9 919 30, 1 929 i77, 40 419 20, 1 929 25, 4 937 109, 24 4.443 29, 7 4.937 47, 9 997 41, 6 4.457 17, 9 947 4, 7 4.461 37, 5 967 4.997 6, 63, 7 1 260 QUADRATIC PARTITIONS. Least Solutions of t 2 -D.v 2 = ±1, [D zfc 8 J and > 100], T 2_ D.i/ 2 - +1 D T V D T V D T V 2 3, 2 47 48, 7 46 24335, 3588 3 2, I 48 7, 1 53 66249, 9100 5 9, 4 50 99, 14 58 I9603, 2574 6 5, 2 51 5°, 7 61 1766319049,226153980 7 8, 3 52 649, 90 67 48842, 5967 8 3, I 54 485, 66 73 2281249, 267000 10 19, 6 55 89, 12 76 57799, 6630 11 10, 3 56 15, 2 85 285769, 30996 12 7, 2 57 151, 20 86 10405, 1122 13 649, 180 59 53o, 69 89 500001, 53000 14 I5> 4 60 3i, 4 93 12151, I26o 15 4, 1 62 63, 8 94 2143295, 221064 17 33, 8 63 8, 1 97 62809633, 6377352 18 17* 4 65 129, 16 19 i7°> 39 66 65, 8 2 -,-. .2 20 9, 2 68 33, 4 T —D.v = = -1 21 55, I 2 69 7775, 93 6 22 23 197, 42 70 71 251, 348o, 3° D T V 24, 5 413 24 5, 1 72 17, 2 2 I, I 26 5 1 , IO 74 3699, 43° 5 2, I 27 26, 5 75 26, 3 10 3, I 28 127, 24 77 35 1 , 40 13 18, 5 29 9801,1820 78 53, 6 17 4, 1 30 11, 2 79 80, 9 26 5, 1 31 1520, 273 80 9, 1 29 70, 13 32 i7, 3 82 163, 18 37 6, 1 33 23, 4 83 82, 9 41 32, 5 34 35, 6 84 55, 6 50 7, 1 35 6, 1 87 28, 3 53 182, 25 37 73, I2 88 i97, 21 58 99, 13 38 37, 6 90 *9i 2 61 29718, 3805 39 25, 4 91 1574, 165 65 8, 1 40 19, 3 92 "5 1 ! 120 73 1068, 125 41 2049, 320 95 39, 4 74 43, 5 42 13, 2 96 49, 5 82 9, 1 43 3482, 531 98 99, 10 85 378, 4i 44 199, 3° 99 10, 1 89 5°°, 53 45 161, 24 97 5 6o 4, 569 QUADRATIC PARTITIONS. 261 D Multiple Solutions of ■D.v ! = Tl 10 — T V 10 + T V 11 + T V 12 + T V 13 — r V 13 + T V 14 + T V 15 + T 17 — T V 17 + V 18 + T V 19 + T 20 + T V h 7.41,239,1393, 8119, 47321,275807,1607521; 1, 5,29,169, 985, 5741, 33461,195025,1136689; 3, i7> 99, 577, 33 6 3, 19601, 114243, 665857, 3880899 ; 2, 12, 70, 408, 2378, 13860, 80782, 470832, 2744210 ; 2, 7, 26, 97, 362, 1351, 5042, 18817, 70226, 262087, 978122 ; i,4, 15, 5 6 , 2 °9, 780, 2911,10864,40545,151316,564719; 2, 38, 682, 12238, 219602, 3940598; h i7, 305, 5473, 98209,1762289; 9, 161, 2889, 51841, 93° 2 49; 4, 72,1292,23184,416020; 5, 49, 485, 4801, 47525, 470449, 4656965 ; 2, 20, 198, i960, 19402, 192060, 1901198; 8, 127, 2024, 32257, 514088, 8193151 ; 3, 48, 765,12192,194307,3096720; 3, 17. 99, 577, 3363, i9 6oi » 114243* 665857, 3880899 ; 1, 6,35,204,1189, 6930, 40391,235416,1372105; 3, 1 1 7, 4443, 168717, 6406803 ; if 37, 1405, 53353, 2026009 ; 19, 721, 27379, 1039681 ; 6,228, 8658, 328776; 10, 199, 397o, 79201, 1580050 ; 3, 60, 1 197, 23880, 476403; 7,97, i35!> l88l 7, 262087; 2, 28, 390, 5432, 75658 ; 18, 23382, 30349818; 5, 6485, 8417525; 649, 842401 ; 180, 233640; I5> 449, 13455, 403201, 12082575; 4, 120, 3596, 107760, 3229204; 4, 31, 244, 1921, 15124, 119071, 937444 ; 1, 8, 63, 496, 3905, 30744, 242047 ; 4, 268, 17684,1166876; 1, 65, 4289, 283009; 33, 2177, 143649,9478657; 8, 528, 34840,2298912; T 7, 577, 19601,665857; 4, 136, 4620, 156944; i7o,57799, i9 6 5 I 49°; 39, 13260, 4508361 ; 9, 161, 2889, 51841,930249; 2, 36, 646,11592,208010; QUADRATIC PARTITIONS. Least (odd) Solutions (t, v) of t 2_dv = + 2, [D = 88-l]; = -2, [D = 88 + 3]; D > 500. D T V =F D T V =F D T V =F D T V =F 3 h I 123 II, I 291 17, I — 151 1 4I57I, 3383 + 7 3. i + 127 2175,193 + 307 9409,537 — 199 127539, 9041 + 11 3, i — 131 103, 9 — 311 4109,233 + 211 527593, 30321 — 19 i3, 3 — 139 8807,747 — 339 3*3, 17 — 271 34O55I, 20687 + 23 5, 1 + 163 8005,627 — 347 801, 43 — 283 I 1759, 699 — 27 5. 1 — 167 13, 1 + 359 19, 1 + 331 52778687,2900979 — 31 39, 7 + 171 13, I — 363 19, 1 — 343 II427, 6l7 + 43 59, 9 — 179 2047,153 — 383 i37, 7 + 367 I379I3, 7199 + 47 7, 1 + 187 41, 3 — 387 59, 3 - 379 113759383,5843427 — 51 7, 1 — 191 2999,217 + 391 2709,137 + 419 16437, 803 — 59 23, 3 — 223 15, 1 + 411 223, 11 — 431 12311, 593 + 67 221,27 — 227 15, 1 — 439 21, 1 + 463 15732537, 73^53 + 71 59. 7 + 239 2489,161 H- 443 21, 1 — 487 7204587, 326471 + 79 9, 1 + 243 265, 17 — 451 6817,321 — 491 305987, J 38o9 — 83 9, 1 — 251 1917,121 — 459 707, 33 — 103 477,47 + 263 373, 23 + 467 1275, 59 — 107 3i, 3 — 267 49, 3 — 479 1729, 79 + 119 11, 1 + 287 17, 1 + 499 67, 3 — D.v 2 = =F2, [D = 168 + 2]; =-2, [D = 168 + 6] = +2, [D = 168-2]. D T V =F I) T V =F D T V =F D T V T 2 O, 1 I — 114 32, 3 258 l6, I 166 41242, 32OI 6 2, I — 118 554,51 — 278 5°, 3 — 214 833882, 57OO3 — 14 4, I + 134 382,33 — 302 2068,119 f 262 IO246, 633!- 18 4, I — 142 12, I + 322 18, 1 + 334 7987764, 437071 + 22 14, 3 — 146 12, I — 326 18, 1 — 358 420214, 22209 — 34 6, 1 + 158 88, 7 + 354 5°8, 27 — 382 406200, 20783 + 38 6, 1 — 162 140,11 - 374 58, 3 446 10496, 497 + 46 156, 23 + 178 40, 3 — 386 334, 17 + 454 130061678,6104097 — 54 22, 3 — 194 14, 1 + 398 20, 1 + 466 30632, 1419 — 62 8, 1 + 198 1+ 1 — 402 20, 1 ~ 478 40215912,1839433 + 66 8, 1 — 206244,17 + 418 184, 9 — 86 102, 11 — 238 108, 7 + 422 2650,129 — 94 1464,] '5« + 242 140, 9 — 482 22, 1 + 98 10, 1 + 246 298,19 — 486 22, 1 — 102 10, 1 — 254 16, 1 + 498 424, 19 — QUADRATIC PARTITIONS. 263 Least (odd) Solutions (t, v) of t »-Di;» = =f4; [ D = 8S + 5,> 1000.] [* Both + solutions exist when D is marked *.] D T V =F D T V =F D T V =F *5 h I •445 21, I 301 22745, I3II + *13 3, I — 453 149, 7 f *421 444939, 21685 — 21 5, I + *461 365, 17 — 501 28225, 1261 + *29 5, I — 469 65, 3 + ♦517 i°573, 465 + 45 7, I -r 477 2599, 119 + *541 1396425, 60037 — •53 7, I — *493 III, 5 — 589 4359377,179625 + •61 39, 5 — *509 925, 41 — •613 98763, 3989 — 69 25, 3 + 525 23, 1 +- 637 14159, 561 + 77 9, 1 + *533 23, 1 — *661 1789539, 69605 — *85 9, 1 — *549 I5 2 3, 65 + 669 305285, 11803 + 93 29, 3 + *565 309, 13 — 749 12945, 473 + *109 26lj 25 — 581 6725, 279 + 789 31825, 1133 + 117 ii, 1 + 597 9749,399 + •821 16189, 565 — *125 11, 1 — 605 123, 5 + *853 27483, 94i — 133 173, i5 + 621 25, 1 + 869 49377, 1675 + *149 61, 5 — *629 25, 1 — *949 32685, 1061 — •157 213, 17 — 645 127, 5 + 981 68123, 2175 + 165 13, 1 + *653 1661, 65 — 989 103245, 3283 + *173 13, i3°5, 1 # 685 759, 79, 29 3 •181 97 — 693 + 205 43, 3 + 717 241, 9 + 213 73, 5 + 725 27, 1 + 221 *229 237 15, i5» 77, 1 1 5 + + •733 741 765 27, 245, ^3, 1 9 3 + + No (odd) solutions (t, v) 245 47, 3 + •773 139, 5 of t 2 -Dv 2 = ±4. 253 1861,] 17 + *797 367, 13 — D = 85 + 5, >1500. 261 727, 45 + 805 1447, 5i + *277 2613,] '57 — 837 29, 1 + 37, 405, 877, 1173 285 17, 1 + *845 29, 1 — 101, 485, 885, 1213 *293 17, 1 — 861 1027, 35 + 141, 557, 901, 1269 309 5°45,; •87 + 893 2301, 77i + 189, 573, 909, 1293 *317 89, 5 — 917 1181, 39, + 197, 677, 925, 1301 341 277, 15 + *941 H35> 37| — 269, 701, 933, 1325 357 19, 1 + 957 3*i 1 + 325, 709, 973, 1389 *365 19, 1 — *965 31, 1 — 333, 757, 997, 1405 *397 3447,i 73 — 349, 781, 1053, 1421 413 61, 3 + 373, 813, 1149, 1445 429 145, 7 + 381, 829, 1157, 1485 437 a i, 1 + 389, 264 QUADRATIC PARTITIONS. Least (odd) Solutions (t, v) of t 1 -Dv 3 = ±8 and ±16, [D = 88 + 1, >500], [* Both ± solutions exist when D is marked *.] T 2 -Du- = ±8 T 2 -Du 2 = ±16 T 2 -D W * = ±8 t*-Di/- = ±16 D T V |=fc T V ± D T V ± T V =fc 1 3, 1 + O, I *241 6lOI, 393 1- 1 i£ . — 9 h 1 — 5, 1 + 249 931, 59!" 79, 5 + ♦17 3, 1 — I, I — *265 ... 49, 3 + 25 3, 1 — 273 i7, 1 + 33 5, 1 — 7, 1 + *281 17, 1 + 285, 17 + •41 7, 1 + 5, 1 — 297 17, 1 — 293, 17 + 57 7, 1 — 53, 7 + 305 ... L. 17, 1 — *65 7, 1 — *313 53, 3 - 2813, 159 + *73 9, 1 + 77, 9 + 329 127, 7j + ii79, 65 4- *89 9, 1 — 47, 5 — *337 55, 3 — 3029, 165 + ♦97 69, 7 + 9, 1 — 345 ... ... J9, T | + 105 11, 1 + *353 19, « + 357, 19 + •113 11, 1 + 53, 5 — 369 19, 1 365, 19 + 129 11, 1 — 125,11 + 377 19, 1 — *137 35, 3 — 11, 1 — 385 59, 3 + 153 37, 3 — 13, 1 + 393 337, i7 — 3271, 165 + 161 13, 1 + 165,13 + *409 4429, 219 — 45645,2257 — 177 13, 1 — i73,i3 + 417 ' 2185, 107 - 143, 7 _i_ *185 13, 1 — *425 21, I + *193i2 5 , 9 — 9 3,65 — *433 21, 1 + 437, 21 + 201241,17 — 7i, 5 + *449 21, 1 — 445, 21 + 209|i59>n — i5, 1 + *457 149365,6987 — 21, 1 — 217 15, 1 + 221,15 + 465 15*1 7 + •233 15, 1 — 229,15 + *481 ... 329= 15 + 489 J 99, 9|~ 39605,1791 + 497 379, 17 + 67, 3 + No (odd) Solutions of t 2 -Du 2 = + 16, [D =88 + 1, > 1500.] D= 25, 49, 81, 121, 145, 169, 225, 257, 289, 305, 321, 361, 377, 401, 44i, 473, 5°5, 5 2 9, 545, 577, 625, 689, 697, 729, 745, 761, 777, 785, 793, 817, 841, 897, 905, 961, 985, 993, 1009, 1025, 1089, 1129, 1 145, 1225, 1257, 1297, 1305, i3 J 3, J 345, 13691 *393> 1425, 1489. Printed by C. F. Hodgson & Son, 2 Newton Street, High Holborn, London. W,C APPENDIX. 265 APPENDIX. CORRIGENDA ON TABLES USED IN THIS WORK. 1. J. H. Lambeet's Zusatze zu den logarn. und trign. Tabellen, &c., Berlin, 1770. — Tab. VI., pages 73-117, styled Numeri Primi, gives a List of Primes up to p > 102,000. Errata below : Page Col. For Head Page Col. For Read 75 2 3381 3581 105 1 72529 70529 81 5 16587 16567 105 6 70467 72467 87 1 22541 28541 106 1 72373 72973 88 5 30083 32083 109 4 81347 81547 89 5 34587 34537 109 5 81837 81937 91 6 36551 39551 2. P. Baelow's New Mathematical Tables, London, 1814. — Tab. I., pages 1-167, gives the factorisation of all Numbers up to 10000 into their Prime Factors. [For reference to Errata List, see No. 2 below.] Tab. V., pages 194-209, of Prime Numbers gives a List of Primes up to p ^> 100104 in columns containing 60 Primes each. Errata as below : Page Col. For Read Page Col. For Read 194 198 10 7 7253 25441 4253 25471 201 205 9 10 46659 43251 45659 72251 3. Fe. Schalleb's Primzah len- Tafel, von 1 bis 10000, oder Zerlegung oiler Zahlen von 1 bis 10000 in ihre Factoren, Weimar, 1855. 4. B. GtOLDbeeg's Primzahlen- und Factoren- Tafel, von 1 bis 251617, Leipzig, 1862. 2, 3, 4. Errata. — For full List of Errata found in Barlow's, Schaller's, and Goldberg's Factor -Tables, see the present Author's Paper on Errata in Factor- Tables, in Mess, of Math., Vol. 34, 1904. 5. C. G. J. Jacobi's Mathematische Werke, Berlin, 1846, Bd. I., pages 326-331. [Art. 23 i. above.] [The references given below will suffice to fix the position of Errata ; the Corrigenda can be taken from the present work.] Erratum. Table of p = a? + b 2 . Table of p = A 2 + 3B 2 . p omitted: 197, 2713, 6997, 11173 ; 883, 6427, 11311 p misprinted: 2357, 3253, 3469, 3529, 5693 ; 3631, 6433 2-ic parts wrong : a, b of 5261, 8609 ; A, B of 6481 2m APPENDIX. 6. C. G-. Rettschle's Neue zahlentheoretische Tabellen, Stuttgart, 1856. [Art. 23 ii. above.] [The references given below suffice to fix the position of Errata ; the Corrigenda can be taken from the present work.] Tables III. a, b, c of (A, B), (L, M) ; pages 23-32. Errata as below. [Argument^.] L, M wrong p omitted. p wrong. A, B incorrect of p below. of 883 25747 p below. 6433 313 12823 20071 29179 139 11311 27431 17137 5011 16561 21391 30529 397 12739 33037 25189 5453 18301 22651 35257 1123 12967 34519 26479 8293 18427 23557 37363 2377 12973 35437 30703 8707 18481 25147 37507 2713 19891 37699 31051 9871 18553 26317 38449 4003 20443 39181 32353 10957 19423 27691 45307 4339 21499 43201 40759 12211 19477 29059 45361 5437 25453 44563 41197 45361 5503 Tables IV. a, b, c of (a, b), (c, d) ; pages 32-41. Errata as below. [Argument^.] p missing. p wrong. a, b wrong of p below. e, d incorrect of p below. 197 3469 4421 18289 17 11057 12281 17729 11173 23893 14009 21613 4177 11153 14009 19001 12269 15361 23197 6553 11329 14081 19489 12301 16249 23561 6653 12049 14369 23929 12373 17317 24281 7481 12097 14929 22129 8969 12161 17489 Tables V.a, b, c, giving Factors of (p—1) ; pages 42-61. These contain about 94 Errata, besides numerous dots (.) omitted between factors. A complete List is given in the present Author's Paper On JSaupt- Exponent Tables, in Mess, of Math., Vol. 33, 1904. 7. A. Cayley's Table des plus petites solutions impaires de Vequation x 2 — Dy 2 = ±4; in Crelle's Journal, t. liii., 1857, page 371 ; and Cayley's Coll. Math. Tapers, Vol. rv., 1891, page 43. D = 253 : Read x = 1861, y = 117. D = 597 : Head x = 9749. D = 917: Head y = 39. 8. H. W. Lloyd Tanner's Paper On the Complex Primes formed with the Fifth Roots of Unity, in Proc. Lond. Math. Soc, Vol. xxrv., 1873. Table of Least Solutions of p = \ (X 2 — 5Y 2 ), page 258 : p = 3371 missing. UNIVERSITY)) UNIVERSITY OF CALIFORNIA LIBRARY BERKELEY Return to desk from which borrowed. This book is DUE on the last date stamped below. MAY 11 1948 6Jan'56R£Q '5Jun'56JliVi RETURNED TO MATH.-STAT. UB. jun 3 195: JAN i f . JUN 9 '61 N 2 I9E1 eT FEB 16 1973 84 nv BECDLD ITBl 5 73 -11 AM LD 21-100m-9,'47(A5702sl6)476