10 print=print+"fermat.txt"
20 ' fermat.ub
30 dim T%(999)
40 for I%=2 to 999:T%(I%)=0:next I%
50 for I%=2 to 31:T%(I%^2)=1:next I%
60 for I%=2 to 9:T%(I%^3)=1:next I%
70 for I%=2 to 5:T%(I%^4)=1:next I%
80 T%(3^5)=1:T%(2^5)=1:T%(2^7)=1:T%(2^9)=1
90 J%=0
100 for I%=2 to 999
110 if T%(I%)=0 then inc J%:T%(J%)=I%
120 next I%:' total number is 959
130 ' case p=2
140 for I%=1 to J%
150 if T%(I%)@4=1 then print T%(I%);":";P
160 next I%
170 ' case p>2
180 P=3:N=2^32-5
190 Pm=(P-1)\2:P2=P^2:P2m=P2-1
200 for I%=1 to J%:A=modpow(T%(I%),Pm,P2)
210 if or{A=1,A=P2m} then print T%(I%);":";P
220 next I%
230 if P<N then P=nxtprm(P):goto 190
For much larger range, insert the following code
122 L%=2*3*5*7*11*13:dim Diff%(L%):C%=0:' L=30030 124 for I%=1 to L%-1 126 if gcd(I%,L%)=1 then inc C%:Diff%(C%)=I% 128 next I%:' c%=5760
and add the following code.
200 Base=((2^32-5)\L%)*L%:N=10^11
210 for K%=1 to C%:P=Base+Diff%(K%):if prmdiv(P)<>P then 260
220 Pm=P-1:P2=P^2:P2m=P2-1
230 for I%=1 to J%:A=modpow(T%(I%),Pm,P2)
240 if or{A=1,A=P2m} then print T%(I%);":";P
250 next I%
260 next K%
270 Base=Base+L%:if Base<N then 210
This program covers up to 10^11.
Wilfrid Keller and Jörg Richstein computed for;
100 < a < 1000, 104 < p < 1011
a < 100, 232 < p
(Wilfrid Keller, Jörg Richstein,
Solutions of the congruence ap-1≡1 (mod pr),
Mathematics of Computation, 74(2005), 927-936.)
Richard Fischer computed up to 2.311E+12.
For some data, the range reached 1.2E+13.
Current status is uploaded at here (in German).
(February 23, 2009).
Now the search range of this page is larger than Wilfrid Keller and Jörg Richstein's results.
This page covers the integer pair a and p which satisfies
ap-1- 1≡0 (mod p2), where
a : 2 ≤ a ≤ 999, non perfect power number
p : p ≤ 1.72 x 1012, prime
I searched up to 8.6 x 109
The search results larger than 8.6 x 109 are owe to Richard Fischer (June 18, 2008).
[In case of prime number]
a | p ----+------------------------------------------------------- 2 | 1093, 3511 3 | 11, 1006003 5 | 2, 20771, 40487, 53471161, 1645333507, 6692367337, 188748146801 7 | 5, 491531 11 | 71 13 | 2, 863, 1747591 17 | 2, 3, 46021, 48947, 478225523351 19 | 3, 7, 13, 43, 137, 63061489 23 | 13, 2481757, 13703077, 15546404183, 2549536629329 29 | 2 31 | 7, 79, 6451, 2806861 37 | 2, 3, 77867, 76407520781 41 | 2, 29, 1025273, 138200401 43 | 5, 103 47 | (could not find) 53 | 2, 3, 47, 59, 97 59 | 2777 61 | 2 67 | 7, 47, 268573 71 | 3, 47, 331 73 | 2, 3 79 | 7, 263, 3037, 1012573, 60312841 83 | 4871, 13691, 315746063 89 | 2, 3, 13 97 | 2, 7, 2914393, 76704103313 ----+------------------------------------------------------- 101 | 2, 5, 1050139 107 | 3, 5, 97, 613181 103 | 24490789 109 | 2, 3, 20252173 113 | 2, 405697846751 127 | 3, 19, 907, 13778951 131 | 17, 754480919 137 | 2, 29, 59, 6733, 18951271, 4483681903 139 | 1822333408543 149 | 2, 5, 29573, 121456243, 2283131621 151 | 5, 2251, 14107, 5288341, 15697215641 157 | 2, 5, 122327, 4242923, 5857727461, 275318049829 163 | 3, 3898031 167 | 64661497 173 | 2, 3079, 56087 179 | 3, 17, 35059, 126443 181 | 2, 3, 101 191 | 13, 379133 193 | 2, 5, 4877 197 | 2, 3, 7, 653, 6237773 199 | 3, 5, 77263, 1843757 ----+------------------------------------------------------- 211 | 279311 223 | 71, 349 227 | 7, 40277 229 | 2, 31 233 | 2, 3, 11, 157, 86735239 239 | 11, 13, 74047, 212855197, 361552687, 12502228667 241 | 2, 11, 523, 1163, 35407 251 | 3, 5, 11, 17, 421, 395696461 257 | 2, 5, 359, 49559, 648258371 263 | 7, 23, 251, 267541, 159838801 269 | 2, 3, 11, 83, 8779, 65684482177 271 | 3, 168629, 16774141, 235558417, 12145092821 277 | 2, 1993, 243547988443 281 | 2, 3443059 283 | 46301 293 | 2, 5, 7, 19, 83 ----+------------------------------------------------------- 307 | 3, 5, 19, 487 311 | (could not find) 313 | 2, 7, 41, 149, 181, 1259389 317 | 2, 107, 349, 2227301 331 | 211, 359, 6134718817 337 | 2, 13, 30137417 347 | (could not find) 349 | 2, 5, 197, 433, 7499 353 | 2, 8123, 465989, 17283818861 359 | 3, 23, 307, 24350087 367 | 43, 2213 373 | 2, 7, 113 379 | 3 383 | 28067251 389 | 2, 19, 373, 29569, 211850543 397 | 2, 3, 279421, 13315373041 ----+------------------------------------------------------- 401 | 2, 5, 83, 347, 115849 409 | 2, 34583, 1894600969 419 | 173, 349, 983, 3257, 22891217 421 | 2, 101, 1483, 350677, 1083982004309 431 | 3, 2393, 12755833 433 | 2, 3, 129497, 244403 439 | 31, 79, 170899693 443 | 5, 3406223 449 | 2, 3, 5, 1789 457 | 2, 5, 11, 919, 1589513 461 | 2, 1697, 5081 463 | 1667 467 | 3, 29, 743, 7393 479 | 47, 2833, 500239 487 | 3, 11, 23, 41, 1069 491 | 7, 79, 661763933, 121261604419 499 | 5, 109, 81307, 24117560837 ----+------------------------------------------------------- 503 | 3, 17, 229, 659, 6761 509 | 2, 7, 41, 7215975149 521 | 2, 3, 7, 31, 53, 8938997 523 | 3, 9907, 19289 541 | 2, 3 547 | 31, 1691778551 557 | 2, 3, 5, 7, 23, 39829 563 | 18920521 569 | 2, 7, 263, 25359067 571 | 23, 29, 308383 577 | 2, 3, 13, 17, 71, 1381277 587 | 7, 13, 31, 22091, 6343317671 593 | 2, 3, 5 599 | 5, 35771 ----+------------------------------------------------------- 601 | 2, 5, 61 607 | 5, 7, 40303229, 22035814429 613 | 2, 3, 4073, 81371669, 18419352383 617 | 2, 101, 1087, 6007 619 | 7, 73, 11682481, 52649183399 631 | 3, 1787, 5741 641 | 2, 43, 24481 643 | 5, 17, 307, 859, 460609, 7354807 647 | 3, 23, 15266862761 653 | 2, 13, 17, 19, 1381, 22171, 637699 659 | 23, 131, 2221, 9161, 65983 661 | 2, 441583073, 462147547073 673 | 2, 61 677 | 2, 13, 211 683 | 3, 1279 691 | 37, 509, 1091, 9157, 84131, 10843045487, 312679516579 ----+------------------------------------------------------- 701 | 2, 3, 5 709 | 2, 17, 199, 1663 719 | 3, 41, 4414200313 727 | 11 733 | 2, 17 739 | 3, 9719, 5681059 743 | 5 751 | 5, 151, 409 757 | 2, 3, 5, 17, 71, 242789 761 | 2, 41, 907 769 | 2, 1305827821 773 | 2, 3, 787711, 26259199, 142719149 787 | 37, 41, 427541 797 | 2, 8273, 14607661 ----+------------------------------------------------------- 809 | 2, 3, 59, 448110371 811 | 3, 211 821 | 2, 19, 83, 233, 293, 1229, 37871, 209140301 823 | 13, 2309 827 | 3, 17, 29, 9323 829 | 2, 3, 17 839 | 5227, 11840951 853 | 2, 1125407 857 | 2, 5, 41, 157, 1697, 32478247 859 | 71 863 | 3, 7, 23, 467, 12049 877 | 2, 78926821 881 | 2, 3, 7, 23, 22385723, 94626144313 883 | 3, 7 887 | 11, 607, 60623 ----+------------------------------------------------------- 907 | 5, 17, 3497891 911 | 127, 318917 919 | 3 929 | 2, 62199604679 937 | 2, 3, 41, 113, 853, 22343, 500861, 1031299, 258469889 941 | 2, 11, 1499 947 | 5021 953 | 2, 3, 513405611, 220564434997, 1082305363079 967 | 11, 19, 4813, 44830663 971 | 3, 11, 401, 9257, 401839, 7672759 977 | 2, 11, 17, 109, 239, 401, 37589 983 | (could not find) 991 | 3, 13, 431, 26437 997 | 2, 197, 1223
[In case of composite a]
a | p ----+------------------------------------------------------- 6 | 66161, 534851, 3152573 ----+------------------------------------------------------- 10 | 3, 487, 56598313 12 | 2693, 123653 14 | 29, 353, 7596952219 15 | 29131, 119327070011 18 | 5, 7, 37, 331, 33923, 1284043 ----+------------------------------------------------------- 20 | 281, 46457, 9377747, 122959073 21 | 2 22 | 13, 673, 1595813, 492366587, 9809862296159 24 | 5, 25633 26 | 3, 5, 71, 486999673, 6695256707 28 | 3, 19, 23 ----+------------------------------------------------------- 30 | 7, 160541, 94727075783 33 | 2, 233, 47441, 9639595369 34 | 46145917691 35 | 3, 1613, 3571 38 | 17, 127 39 | 8039 ----+------------------------------------------------------- 40 | 11, 17, 307, 66431, 7036306088681 42 | 23, 719867822369 44 | 3, 229, 5851 45 | 2, 1283, 131759, 157635607 46 | 3, 829 48 | 7, 257 ----+------------------------------------------------------- 50 | 7 51 | 5, 41 52 | 461, 1228488439 54 | 19, 1949 55 | 3, 30109, 7278001, 27207490529, 902060958301 56 | 647, 7079771, 115755260963 57 | 2, 5, 47699, 86197 58 | 131, 42250279 ----+------------------------------------------------------- 60 | 29, 9566295763, 6683052151409 62 | 3, 19, 127, 1291 63 | 23, 29, 36713, 401771 65 | 2, 17, 163 66 | 89351671, 588024812497 68 | 5, 7, 19, 113, 2741 69 | 2, 19, 223, 631, 2503037 ----+------------------------------------------------------- 70 | 13, 142963 72 | (could not find) 74 | 5, 1251922253819 75 | 17, 43, 347, 31247 76 | 5, 37, 1109, 9241, 661049, 20724663983 77 | 2, 32687 78 | 43, 151, 181, 1163, 56149, 4229335793, 5744393199187 ----+------------------------------------------------------- 80 | 3, 7, 13, 6343 82 | 3, 5 84 | 163, 653, 20101, 663840051067 85 | 2, 11779 86 | 68239, 6232426549 87 | 1999, 48121, 604807523183 88 | 2535619637 ----+------------------------------------------------------- 90 | 6590291053 91 | 3, 293 92 | 727, 383951, 12026117, 18768727, 1485161969 93 | 2, 5, 509, 9221, 81551 94 | 11, 241, 32143, 463033 95 | 2137, 15061, 96185643031 96 | 109, 5437, 8329, 12925267, 103336004179 98 | 3, 28627, 61001527 99 | 5, 7, 13, 19, 83 ----+------------------------------------------------------- 102 | 7559, 11813, 139409857 104 | 313, 237977, 11950711691 105 | 2, 7669 106 | 79399, 672799 108 | 3761, 10271, 1296018233 ----+------------------------------------------------------- 110 | 17, 5381, 9431, 1219715607577 111 | 131 112 | 11, 1037888513 114 | 9181 115 | 31, 2743780307 116 | 3, 7, 19, 47 117 | 2, 7, 31, 37, 182111 118 | 3, 5, 11, 23, 3152249, 10404887 119 | 1741 ----+------------------------------------------------------- 120 | 11, 653, 2074031, 124148023 122 | 11, 2791, 16522744709 123 | 34849 124 | 5, 11, 22511 126 | 5 129 | 2, 7, 113 ----+------------------------------------------------------- 130 | 11, 23, 62351, 70439 132 | 5 133 | 2, 5277179 134 | 3, 17, 406531, 73629977, 4962859085059 135 | 23147324413 136 | 3, 5153, 87249620417 138 | 97, 4889 ----+------------------------------------------------------- 140 | 14591 141 | 2, 192047, 42039743 142 | 143111, 12838109 143 | 3, 5, 67, 197, 1999, 12848347, 65451824959, 225413072431 145 | 2, 3, 31 146 | 7, 13, 79, 22639 147 | 13, 79, 103, 283, 24203, 4058948753 148 | 7, 11, 41, 14879, 161141, 2805469039 ----+------------------------------------------------------- 150 | 13, 21199069, 85877201, 103053130679 152 | 3, 22554863, 54504719 153 | 2, 8539, 5540099 154 | 3 155 | 17, 211691, 309131, 6282943, 1196757167 156 | 347, 1297 158 | 17, 1031, 820279 159 | 367, 5356051 ----+------------------------------------------------------- 160 | 72669541193 161 | 2, 3, 11, 83, 137, 6188401, 93405163 162 | 607, 142946059423 164 | 103, 107, 1493 165 | 2, 7, 211, 25102757, 11699444843 166 | 7, 877, 61819 168 | 5, 13, 739, 27427 ----+------------------------------------------------------- 170 | 3, 13, 23, 1163, 170613512651 171 | 269, 1803383 172 | 3, 47, 91303 174 | 5, 113, 199, 379 175 | 397, 487, 2199439603 176 | 5, 191, 5611481459 177 | 2, 7, 23, 42397, 123681208241 178 | 7, 1213, 67751, 296036443 ----+------------------------------------------------------- 180 | 269, 5737 182 | 5, 211, 8934721 183 | 1231487 184 | 89, 661, 1187, 2203, 6043 185 | 2, 12577 186 | (could not find) 187 | (could not find) 188 | 3, 13 189 | 2, 1847, 6199 ----+------------------------------------------------------- 190 | 3, 29, 236981, 382351, 753743 192 | 13, 4049, 302279, 465435739 194 | 439, 8338826207 195 | 7, 23, 13421, 3132631 198 | 147647, 545639981 ----+------------------------------------------------------- 200 | (could not find) 201 | 2, 5, 86722091 202 | 11, 47 203 | (could not find) 204 | 5431, 142061, 1070347, 15028133 205 | 2, 367 206 | 3, 151, 1201, 2087 207 | 5, 41, 269, 809, 26240063 208 | 3, 947 209 | 2, 229, 2203, 511654217, 6802750783 ----+------------------------------------------------------- 210 | 43, 449 212 | 1960573 213 | 2, 313, 1877 214 | 7, 17 215 | 3, 7, 11, 3327697, 502095466241 217 | 2, 3, 127447, 8468323 218 | 5, 163 219 | 7891033151 ----+------------------------------------------------------- 220 | 3581, 9619, 79867, 717967, 13477271, 32376410527, 34816906301 221 | 2, 29, 1669, 15233, 103361803, 406833359, 455317162337, 1180548631831 222 | (could not find) 224 | 3, 5, 17, 130677149 226 | 3, 5, 7, 97, 157 228 | 1361, 182353 ----+------------------------------------------------------- 230 | 47, 384533887 231 | (could not find) 232 | 5, 30851, 838667, 2250741293 234 | 19, 46441, 817766595407 235 | 3, 31, 118022689 236 | 29, 229 237 | 2 238 | 977, 8609, 4997219, 863039377, 64904716187 ----+------------------------------------------------------- 240 | 227797 242 | 3, 373, 2386301, 2434609, 167962252433, 2706669242327 244 | 3, 7, 16906680221 245 | 2, 11, 19, 229, 218173429 246 | 7, 877441867 247 | 5081, 105527103139 248 | 67, 101, 663893, 502608046943, 668677573093 249 | 2, 5, 13, 17 ----+------------------------------------------------------- 250 | 131, 509 252 | 211, 997, 3613, 394213789 253 | 2, 3, 167, 90901, 2905031 254 | 89, 2269, 18042251, 32984389 255 | 23, 463 258 | 13, 17827 259 | 173 ----+------------------------------------------------------- 260 | 3, 83, 15263, 27827, 1749229, 6647339, 19148231, 3977977109 261 | 2, 43, 71, 257 262 | 3, 19, 571 264 | 7, 61, 176051, 1446587 265 | 2, 10853 266 | 23, 163, 21401, 4673329018717 267 | 29, 20411, 46926349 268 | 5, 13, 101 ----+------------------------------------------------------- 270 | 29 272 | 3833, 14084849 273 | 2, 1086731, 7558891900249 274 | 5, 23, 16631 275 | 7, 6323, 134513, 138641, 455471, 40196043527, 279203122727 276 | 5, 7, 43, 193 278 | 3, 1741 279 | 67, 97, 557142359 ----+------------------------------------------------------- 280 | 3, 47, 401 282 | 5, 11, 13120561 284 | 197, 1103, 9127, 16189, 1601147, 10723208449, 4019853486967 285 | 2, 5791, 157907 286 | 71, 619, 15017, 1016689, 6489382948837 287 | 3, 653, 967, 10322313269, 405469792823 288 | 17, 43, 36979, 376721, 670507 ----+------------------------------------------------------- 290 | 17, 6659, 319811, 273354437 291 | 109, 16766930077 292 | 19, 43, 887, 941, 3239857 294 | 356135477, 592538407, 367003576739 295 | 7, 47, 26249 296 | 3, 971 297 | 2, 2480497, 2779225651 298 | 3, 59, 101, 181, 598421, 4809986918441 299 | 5, 19, 59, 374893957 ----+------------------------------------------------------- 300 | 37, 59, 29599 301 | 2, 5 302 | 607, 22621771, 123644663 303 | 43, 33873179 304 | (could not find) 305 | 2, 3, 1149209 306 | 73 308 | 521 309 | 2 ----+------------------------------------------------------- 310 | 67, 3617 312 | 7, 13622501 314 | 3, 181, 827, 3143117 315 | 13, 257, 1187, 40471, 4767799 316 | 3, 13, 51461, 898508623 318 | 5, 197, 131959, 11496420743, 69578772701 319 | 13, 79, 1439 ----+------------------------------------------------------- 320 | 13121, 27397, 452983, 6818771 321 | 2, 1401979, 78793807 322 | 3307, 4297, 2768017244933 323 | 3, 11, 291721 325 | 2, 3, 7, 157, 953, 568231, 68992603, 4507000559 326 | 5, 1249, 30589393, 302908877 327 | 17 328 | 139, 911, 1399 329 | 2, 17, 487068061 ----+------------------------------------------------------- 330 | 227 332 | 3, 5, 239, 15773 333 | 2, 19, 31, 3266479 334 | 3, 23, 257 335 | (could not find) 336 | 11, 78666481 338 | 31, 53 339 | 13, 47, 199, 466751783977 ----+------------------------------------------------------- 340 | 173, 641, 115574081561 341 | 2, 3, 101 342 | 7, 17167837 344 | 7, 55351, 7493623, 102089209 345 | 2, 463, 8941 346 | 499 348 | 37, 103, 161561 ----+------------------------------------------------------- 350 | 3, 103, 167 351 | 5 352 | 3, 23, 7723, 423017653829 354 | 11, 17, 37, 977, 13513, 1336241 355 | (could not find) 356 | 37, 113 357 | 2, 5, 13 358 | 157, 6382723111 ----+------------------------------------------------------- 360 | 11, 13, 19 362 | 7, 11, 19, 80233, 1794830107009 363 | 4153, 94565579, 1249344562091 364 | 11, 17, 1824271 365 | 2, 1453, 128587933 366 | 11, 36857 368 | 3, 5, 73, 21503, 70399321039 369 | 2, 139, 173, 211, 419 ----+------------------------------------------------------- 370 | 3, 22020497, 66065773, 4436281892011 371 | 1619, 101113 372 | 11, 2687 374 | 5, 7, 29, 31, 27463248607 375 | 701 376 | 5, 12799 377 | 2, 3, 79 378 | 41, 1453, 517298279 ----+------------------------------------------------------- 380 | 83, 109, 12007, 120313541 381 | 2, 827, 14449, 16943 382 | 5, 97, 1238371 384 | 519488341, 75918457357 385 | 2, 1548149, 4605659 386 | 3, 103 387 | 174426871193 388 | 3, 31 ----+------------------------------------------------------- 390 | 11, 5713733, 15819863 391 | 7, 103, 25679, 68903, 6259286339, 11993961787, 311215043773 392 | 101, 769, 773, 1553, 883201742719 393 | 2, 5, 7, 823, 22381, 1845595127527 394 | 251 395 | 3, 191, 651742019113 396 | 1947241, 17344004261 398 | 139, 205319 399 | 5, 17, 23 ----+------------------------------------------------------- 402 | 97, 109, 269 403 | 11, 43, 373, 1321 404 | 3, 3659 405 | 2, 601 406 | 3, 53, 216141619 407 | 5, 103001 408 | 13, 50513 ----+------------------------------------------------------- 410 | 7, 109, 239, 653, 11328969257, 19111351313 411 | 7, 23, 1367, 25888367 412 | 97 413 | 2, 3, 53, 249745603, 2832308863 414 | 31 415 | 3, 19, 10337, 107777, 924528047, 1465092947347 416 | 29, 181, 6988511 417 | 2, 101 418 | 5, 13, 822949 ----+------------------------------------------------------- 420 | 17, 181 422 | 3, 7, 571, 367277, 29170663 423 | 7, 17, 19, 43, 1669 424 | 3, 5, 37, 43, 131, 3037 425 | 2, 29, 1097, 64951, 106357, 433703 426 | 5, 89, 56861249, 2215508401 427 | 13, 547, 577, 1657, 93703, 568689487 428 | 6361, 1878059 429 | 2, 19, 1381, 2473, 36510613, 12994232161 ----+------------------------------------------------------- 430 | 19, 31, 557, 344621 432 | 5, 61, 1680023, 7308036881 434 | 863, 1831, 63527, 346517902547 435 | (could not find) 436 | 193, 30348797, 677213275049 437 | 2, 13, 37 438 | 47, 71, 6449465131 ----+------------------------------------------------------- 440 | 3, 7, 31, 797 442 | 3, 7, 29417408507 444 | 11, 17, 15667, 220688906759 445 | 2, 2659, 2753 446 | 797, 2687, 8629, 269063 447 | 17, 82780601 448 | 31, 67, 111121 ----+------------------------------------------------------- 450 | 1199923, 9445297441 451 | 3, 5, 53, 48869, 4855900311901 452 | 2141, 94847, 402341, 1454683, 163880093939 453 | 2, 1597, 405179 454 | (could not find) 455 | 101, 238931257 456 | 192037 458 | 3 459 | 7, 14537 ----+------------------------------------------------------- 460 | 3, 7, 19, 53, 8819831 462 | 849571, 14532863 464 | 73861878877 465 | 2, 795071 466 | 23 468 | 5, 17, 9858955373 469 | 2, 3, 107 ----+------------------------------------------------------- 470 | 79, 103, 83401 471 | 7, 41, 691409 472 | 7, 101, 1531, 363047 473 | 2, 37, 2311 474 | 5, 2141, 197699, 16069969 475 | 11, 117133 476 | 3, 5, 37, 109, 337, 401, 5527, 1169759 477 | 2, 19, 1576721 478 | 3 ----+------------------------------------------------------- 480 | 8293, 243589 481 | 2, 11, 54371927, 143432275871 482 | 5, 71 483 | 11, 1160559731 485 | 2, 3, 11, 13, 19051 486 | 563, 572843 488 | 13, 19, 1493, 3505277 489 | 2, 7 ----+------------------------------------------------------- 490 | 4787 492 | 1034239, 211096013 493 | 2, 5, 11, 163001522539 494 | 3, 37, 4271, 121607, 601961 495 | 1522057 496 | 3 497 | 2, 127, 157, 505780258937 498 | 61, 1187387, 45525923, 2149153512589 ----+------------------------------------------------------- 500 | 53, 109, 157, 49429 501 | 2, 5, 23, 14890530569, 24112920253 502 | 22877, 34318033 504 | 67, 229793929 505 | 2, 3, 41, 463, 297377071847 506 | 13, 59 507 | 5, 2377, 5153, 363211, 6111681437 508 | 7, 13, 1061, 1274084375749, 1311889799369 ----+------------------------------------------------------- 510 | 107, 19846129, 175868149, 228490481, 34656130219 511 | 11, 4787 513 | 2, 17, 31, 43787 514 | 3, 22549 515 | 101, 2089, 175186789, 2115451213 516 | 571 517 | 2, 59547517 518 | 5, 12650270891 519 | 157, 223, 8649842813, 37898634329 ----+------------------------------------------------------- 520 | 7, 36161687 522 | 31, 17477, 499292741 524 | 5, 11, 778717 525 | 2, 97, 34687, 497557, 2651387 526 | 5, 13, 83, 499, 647, 247073, 2394147047 527 | 73, 3373 528 | 23, 1303, 54467681 ----+------------------------------------------------------- 530 | 3, 13, 23, 5157793 531 | 31, 86384479603 532 | 3, 5, 179, 62929 533 | 2, 283, 417860291 534 | 101, 139, 631, 9931 535 | 13009, 574477 536 | 1619, 556072481, 1240525163 537 | 2, 43, 5021, 112142108971 538 | 7, 17, 2267, 28307 539 | 3, 101, 172297, 184693, 1178753, 4673137127 ----+------------------------------------------------------- 540 | 7, 17, 41, 9041 542 | (could not find) 543 | 5, 313 544 | 12527, 24095129 545 | 2, 11149, 2042119241 546 | (could not find) 548 | 3, 30949, 256561 549 | 2, 5, 10133, 512811707, 481691968193 ----+------------------------------------------------------- 550 | 3, 110619193, 332718585593 551 | 5, 1021, 108289, 1254577, 10781849409623 552 | 89925422513 553 | 2, 139, 347, 7541, 737291 554 | (could not find) 555 | 541, 162203773 556 | 197, 617, 19009 558 | 7, 193, 461, 1621, 65257, 47652991 559 | 3, 59, 151, 599, 12613 ----+------------------------------------------------------- 560 | 67, 2671, 5107, 18757, 411823, 712346863 561 | 2, 135913, 3458677 562 | 83, 337, 5229031 564 | 4813, 4388171 565 | 2, 11, 782707, 14615527, 362941373 566 | 3, 326537 567 | 67, 101 568 | 3, 5, 373, 1553 ----+------------------------------------------------------- 570 | 7 572 | 61, 4049, 29922449, 111170909, 7654073743 573 | 2, 31, 283, 50647 574 | 5, 29, 61, 2213, 598967 575 | 3, 46271, 61169, 6501209375021 578 | 11, 107747, 205657 579 | 17, 199, 1097 ----+------------------------------------------------------- 580 | 239, 57251, 974147, 69722080903 581 | 2, 37, 176431, 6924427 582 | 5, 37, 151 583 | 241, 479, 1889 584 | 3, 1447, 69857 585 | 2, 1327, 1580431 586 | 3, 136544960191 588 | 43, 599, 292969 589 | 2, 7, 17191, 1524529, 3501139 ----+------------------------------------------------------- 590 | 163, 443, 376021, 2239201, 4176404107, 3219042433511 591 | 419, 8447 592 | 23, 51217, 2070323 594 | 32485136899, 8784820622857 595 | 3, 19, 88499, 96727678693, 386120172551 596 | 11, 13, 94327 597 | 2, 558793 598 | 151, 3571 ----+------------------------------------------------------- 600 | 47, 14582963 602 | 3, 11, 1166849, 37310783 603 | 1579, 290512619 604 | 3, 11, 79, 157 605 | 2, 29, 89 606 | 7, 11, 13, 19, 71, 848297, 319155270953 608 | 11, 7759, 664579, 50092921 609 | 2 ----+------------------------------------------------------- 610 | (could not find) 611 | 3, 18503, 39569 612 | 59 614 | 11, 18234089 615 | 83 616 | 17, 479, 123001704037 618 | 5, 7, 17, 61, 1163, 220169 ----+------------------------------------------------------- 620 | 3, 29, 113, 5861, 81163, 7358177, 3533794899013 621 | 2, 73, 17609, 963223, 2031264307 622 | 3, 577, 1193 623 | 19, 31, 47 624 | 5, 109, 37199 626 | 5, 5641 627 | 181048811 628 | 31 629 | 2, 3, 47, 101 ----+------------------------------------------------------- 630 | 67, 163 632 | 5, 11, 37, 179, 389, 829 633 | 2, 71, 4513, 22643, 7329659 634 | 800243 635 | 8641, 3245689, 12675040709 636 | 7, 1270333 637 | 2, 547, 1021, 521429, 78225448229 638 | 3, 7, 3253 639 | (could not find) ----+------------------------------------------------------- 640 | 3 642 | 5302111 644 | 41, 223, 883 645 | 2, 11, 29, 319117, 1350061, 549461839 646 | 4136689 648 | 12295820941 649 | 2, 3, 5, 101, 179, 45840199 ----+------------------------------------------------------- 650 | 6211, 2135417656303 651 | 5, 29, 105021277 652 | 2113, 51059, 524251867, 5269346021 654 | 13, 19 655 | 7, 47, 53, 3940249, 54674441 656 | 3, 7, 4259, 404890928047 657 | 2, 5, 13, 883, 2899751 658 | 3, 242831101 ----+------------------------------------------------------- 660 | 19, 43, 3646427 662 | (could not find) 663 | 6961 664 | 24223, 245183 665 | 2, 3, 61 666 | 4503454574621, 4977652953109 667 | 3, 7, 199, 839, 4421, 59239 668 | 5, 7, 19 669 | 2, 397, 5857, 482683 ----+------------------------------------------------------- 670 | 83, 52289, 122323, 7267303 671 | 5397037 672 | 59, 73, 617, 2963, 483251, 880751, 8755297 674 | 3, 5 675 | 13, 761, 993913 678 | 37, 23841761 679 | 534607, 18514999 ----+------------------------------------------------------- 680 | 2677, 8737, 13125811 681 | 2, 71, 109, 16088557 682 | 5, 61, 857, 17934551077 684 | 2092667 685 | 2, 3, 7, 119659261 686 | 11, 118163, 283099, 1031483, 85481059, 464136932507 687 | 7, 103, 199337, 2747873, 36926501 688 | 17, 1429, 84391410869 689 | 2, 6547, 1863787, 24028099019 ----+------------------------------------------------------- 690 | 113 692 | 3 693 | 2, 5, 561931, 1362299, 112102492193 694 | 3, 19, 233 695 | 13, 107, 18127, 52667 696 | 617 697 | 2 698 | 13 699 | 5, 11, 13, 23, 67, 73, 398969 ----+------------------------------------------------------- 700 | 67, 3001 702 | 677, 40361, 100213 703 | 3, 4049, 591377 704 | 7, 29, 1949 705 | 2, 7, 1019, 3847, 48109, 16130783 706 | 23, 27297539, 209941187 707 | 5, 89, 317, 22469, 44417, 4728169429 708 | 701, 4146409, 51381922303 ----+------------------------------------------------------- 710 | 3, 163, 42834427 711 | 73, 163 712 | 3, 17, 9463, 476513, 1287467, 2686283 713 | 2, 11097981800233 714 | 191, 613 715 | 781059256409 716 | 7, 552341, 440416759, 5626714979 717 | 2, 7, 11, 643, 23917, 1304111, 16621877, 8512494329 718 | 5 ----+------------------------------------------------------- 720 | 69193 721 | 2, 3, 19, 379 722 | 67, 547, 15607 723 | 11, 19, 233, 239, 660658181, 2938943531 724 | 5, 23 725 | 2, 11 726 | 5, 31, 17377 728 | 3, 163, 18541, 57384358463 ----+------------------------------------------------------- 730 | 3, 107 731 | 277, 1873 732 | 5, 31, 9143354797 734 | 7, 73, 65957 735 | 11, 457, 79181 736 | 7, 17, 127, 5839 737 | 2, 3, 37, 53, 6007, 140846899, 43638688993, 3684324840109 738 | 3191, 8269, 3947883749 ----+------------------------------------------------------- 740 | 1087, 281975833, 15373986241 741 | 2, 269, 1433798129 742 | 113, 7027, 968761, 1859111 744 | 41, 2729, 29123 745 | 2, 31147, 474535783, 280232633477 746 | 3, 13, 191, 1621 747 | 101, 257, 271, 80567 748 | 3, 433, 1719107231 749 | 2, 5, 29759, 34549943161 ----+------------------------------------------------------- 750 | 19, 79, 97, 60773, 4888164324599 752 | 53, 876381797 753 | 2, 7, 11, 173, 491 754 | 7, 883, 5420057 755 | 3, 3583, 1299821, 143337647 756 | 13, 2551, 49822776853 758 | 1272207150661 759 | 257 ----+------------------------------------------------------- 760 | (could not find) 762 | 31019 763 | 61, 1822517 764 | 3, 43, 4943, 7459 765 | 2, 7, 13, 377369, 5330933, 17206283 766 | 3, 7, 11, 10163, 8922301 767 | 2203, 68903, 422249, 74991254231 768 | 5, 41, 345727 ----+------------------------------------------------------- 770 | 73, 4861, 1170023, 2771298845851 771 | 907, 2662193 772 | (could not find) 774 | 5, 8419 775 | 3, 13 776 | 5, 19, 41, 73, 1097, 33328795891 777 | 2 778 | 29, 15373, 1965283087 779 | 257, 2477, 4534883 ----+------------------------------------------------------- 780 | 53, 269, 48869, 10671151 781 | 2, 29, 499, 778187 782 | 3, 5, 563, 5683 783 | 7, 442084061 785 | 2, 7, 151, 74923, 123407, 111646712561, 559491826637 786 | 73, 3469, 14026409 788 | 37, 632114867, 22824986839, 118941702367 789 | 2, 2307345676481 ----+------------------------------------------------------- 790 | 19, 89, 461, 5125753 791 | 3, 19, 10998428929 792 | 17, 23, 21011, 255133, 80766939707 793 | 2, 3, 5, 173, 1103, 53407 794 | 1286720879 795 | 23, 79, 98909, 166657, 11173405591 796 | 54914297 798 | (could not find) 799 | 5, 2891032049 ----+------------------------------------------------------- 800 | 3, 29 801 | 2, 5, 683, 13807 802 | 3, 7, 17, 215420011 803 | 7, 23, 1973, 222216074029 804 | 148173282913 805 | 2, 59, 17401, 163193 806 | 59, 1051, 961613 807 | 5, 11 808 | (could not find) ----+------------------------------------------------------- 810 | 79, 35608871, 128710108069 812 | (could not find) 813 | 2, 193, 607, 142595731 814 | 7, 670786483, 122493320143 815 | 7, 233, 2030845176271 816 | 31, 1241086902527 817 | 2, 547, 659077 818 | 3, 5, 35097043, 89127571697 819 | 809, 1041203, 9411713, 7263800119 ----+------------------------------------------------------- 820 | 3, 11, 187477 822 | 13, 83, 17377, 18965973137 824 | 5, 41, 951427 825 | 2, 444113, 4100307667 826 | 5, 13, 89, 23459, 29264621 828 | 577, 1867, 7315489 ----+------------------------------------------------------- 830 | 84407 831 | 547, 2179, 16212571, 312049583 832 | 5, 7, 2213, 112246723, 223818256729 833 | 2, 498254423201 834 | 7, 41 835 | 131, 125941, 323294483, 954340601 836 | 3, 181 837 | 2, 109 838 | 3, 11, 19, 61 ----+------------------------------------------------------- 840 | 29, 730637329 842 | 29, 89 843 | 5, 509 844 | 11, 13, 31, 36052871, 70457839, 2025248413, 2816027947 845 | 2, 3 846 | 11, 13, 31 847 | 3, 41, 1319033, 28276121, 221393539, 409765111823 848 | 11, 101863 849 | 2, 5, 19, 13697, 590123, 10720751, 8987928353 ----+------------------------------------------------------- 850 | 11, 151, 17286019, 11046585983 851 | 5, 7, 53, 701 852 | 7, 269, 27457 854 | 3, 7377061, 230377339 855 | 29, 1549, 6779, 375481, 13214599, 7245558091, 30994657849 856 | 3, 11, 53, 229, 4951, 9947819971, 48082633801 858 | (could not find) ----+------------------------------------------------------- 860 | (could not find) 861 | 2, 84948797 862 | 53, 413952542813 864 | 7, 13, 121403 865 | 2, 3, 167, 2161, 8663 866 | 17, 97, 233, 1997 867 | 13, 47, 167, 431 868 | 5, 13, 17, 38201 869 | 2, 53 ----+------------------------------------------------------- 870 | 12907 871 | (could not find) 872 | 3, 7583 873 | 2, 193, 4547, 485509, 575959, 20856007, 58800361 874 | 3, 5, 11, 47, 193, 1181, 1607 875 | 37, 67, 937477, 1530709 876 | 5, 226451, 1299343, 3587347, 171702372643, 369801222673 878 | 277 879 | 243343 ----+------------------------------------------------------- 880 | 61, 1168308143, 12782825651, 38563175939, 107905234979 882 | 5, 29, 317, 60761, 2669321 884 | 1373, 7196186279251 885 | 2, 194057 886 | 29082802901 888 | 23, 143159 889 | 2, 491, 2014139 ----+------------------------------------------------------- 890 | 3, 162611, 321371 891 | 43, 43997, 112808526497 892 | 3, 157, 2339, 568091, 4742137, 6336193, 8672659, 234988626427 893 | 2, 5, 37, 59, 147341 894 | 41, 193, 389, 644519, 3319051, 21227900821 895 | 53, 193, 65927, 129169 896 | 37, 31238183, 8535320569 897 | 2, 67, 269, 1123 898 | 239 899 | 3, 5, 131, 1013 ----+------------------------------------------------------- 901 | 2, 3, 5, 7, 29, 3877, 175474967, 6338370677, 14981029537 902 | 407059, 482936260489 903 | 13831 904 | 29, 135469, 235523 905 | 2, 17, 41 906 | 1579, 17701979 908 | 3, 103, 269, 40819 909 | 2, 11487079, 54828001 ----+------------------------------------------------------- 910 | 3, 142886951, 1514654268719 912 | 7 913 | 2, 7, 41, 6079, 93187777, 89834287327 914 | 139, 769 915 | 13, 2549 916 | 5923 917 | 2, 3, 1061, 11909, 312589 918 | 5, 14009, 164071, 693582176263 ----+------------------------------------------------------- 920 | 41 921 | 2, 262739, 152874167483 922 | 16883 923 | 73, 283, 1627, 2447 924 | 5, 67399, 7084547 925 | 2, 13, 53, 83, 877, 8363, 604859, 3519539, 90281266927 926 | 3, 5, 14900443 927 | 89, 22511 928 | 3, 11, 23, 13913, 199549335169 ----+------------------------------------------------------- 930 | 7, 709, 70619, 85201 931 | 281 932 | 5, 7, 17, 37, 2851 933 | 2, 8592109 934 | 13, 1511, 12119, 19175934991 935 | 3, 593, 913331, 626872115449 936 | 61, 412330367, 446377909, 2607195499 938 | 191, 9467581 939 | 179, 83761 ----+------------------------------------------------------- 940 | 23, 419, 2837, 104479, 378289, 2514119 942 | 17, 313 943 | 5, 39025823 944 | 3, 13 945 | 2, 37, 5857, 1125121069, 2705324826961 946 | 3, 59, 211 948 | 409, 470461, 2584062913, 11058282821 949 | 2, 5, 7, 14806159, 30446387 ----+------------------------------------------------------- 950 | 7, 925577, 1179757 951 | 5, 848378279311 952 | 2856871 954 | 113, 193 955 | 3, 107, 607, 5521 956 | 19, 656300459, 2482219343 957 | 2, 5, 149, 2113, 67129, 196961579, 51716885683 958 | 43, 14479, 25229, 189713, 1813979414189 959 | 11, 736433, 933107653 ----+------------------------------------------------------- 960 | 31, 149, 449, 12157, 349227224611, 644232442639 962 | 3, 7, 31, 41, 5711 963 | 1933, 36758171 964 | 3, 9533 965 | 2, 11, 2356997 966 | 599, 7687, 2337073, 32558972119 968 | 5, 7669, 107641, 9506431657 969 | 2, 11, 71, 911, 103421, 2391503, 319792007 ----+------------------------------------------------------- 970 | 59, 269, 230551 972 | 227 973 | 2, 3, 26713, 21581257, 1108107413579 974 | 5, 7129, 1404071, 4204968197 975 | 2879 976 | 5, 991 978 | 29, 71, 97, 733 979 | 7, 191, 157799 ----+------------------------------------------------------- 980 | 3 981 | 2, 7, 719, 2153 982 | 3, 5, 1747, 2459, 1222777, 5494786229 984 | 19, 78791 985 | 2, 53, 1895057 986 | (could not find) 987 | 1399, 36721, 57943, 24858506161 988 | 14401, 63754777477 989 | 2, 3, 12743, 2085799, 1423932997, 10577489843279 ----+------------------------------------------------------- 990 | 1009 992 | 13, 140729, 24922021, 5043756649 993 | 2, 5, 25301, 92177, 31187620943 994 | 5431, 5449, 9029 995 | 11, 13, 23, 15324691 996 | 16931, 34031371421 998 | 3, 7, 17, 1551083, 627934621 999 | 5, 7, 50119, 806812352251, 5879307404213
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