Thema: Fermatquotient B^(P-1) == 1 (mod P^2) Main table of content: http://www.fermatquotient.com/ Die gefundenen Primzahlen der Fermatquotienten von der Basis 2 bis 1052 Die letzten 10 gefundenen Fermatquotienten haben folgende Basen: 458, 438, 895, 970, 948, 447, 853, 835, 655, 1023 Die Basen, die einen maximalen Primteiler bis 149 haben, sind durchsucht bis 1.630E+14 Die restlichen Basen sind gegenwärtig durchsucht bis 4.26E+13 Basis Primzahlen^2 2 P: 1093, 3511 (>6E+17) 3 P: 11, 1006003 (>1.2E+15) 5 P: 2, 20771, 40487, 53471161, 1645333507, 6692367337, 188748146801 (>1.2E+15) 6 P: 66161, 534851, 3152573 7 P: 5, 491531 (>1.2E+15) 10 P: 3, 487, 56598313 11 P: 71 12 P: 2693, 123653 13 P: 2, 863, 1747591 14 P: 29, 353, 7596952219 15 P: 29131, 119327070011 17 P: 2^4, 3, 46021, 48947, 478225523351 18 P: 5, 7^3, 37, 331, 33923, 1284043 19 P: 3, 7^3, 13, 43, 137, 63061489 20 P: 281, 46457, 9377747, 122959073 21 P: 2 22 P: 13, 673, 1595813, 492366587, 9809862296159 23 P: 13, 2481757, 13703077, 15546404183, 2549536629329 24 P: 5, 25633 26 P: 3^3, 5, 71, 486999673, 6695256707 28 P: 3^3, 19, 23 29 P: 2 30 P: 7, 160541, 94727075783 31 P: 7, 79, 6451, 2806861 33 P: 2^5, 233, 47441, 9639595369 34 P: 46145917691 35 P: 3, 1613, 3571 37 P: 2, 3, 77867, 76407520781 38 P: 17, 127 39 P: 8039 40 P: 11, 17, 307, 66431, 7036306088681 41 P: 2^3, 29, 1025273, 138200401 42 P: 23^3, 719867822369 43 P: 5, 103, 13368932516573 44 P: 3, 229, 5851 45 P: 2, 1283, 131759, 157635607 46 P: 3, 829 47 keine gefunden 48 P: 7, 257 50 P: 7 51 P: 5, 41, 14802884210119 52 P: 461, 1228488439 53 P: 2, 3^3, 47, 59, 97 54 P: 19, 1949 55 P: 3^3, 30109, 7278001, 27207490529, 902060958301 56 P: 647, 7079771, 115755260963 57 P: 2^3, 5^3, 47699, 86197 58 P: 131, 42250279 59 P: 2777, 18088417183289 60 P: 29, 9566295763, 6683052151409 61 P: 2 62 P: 3, 19, 127, 1291 63 P: 23, 29, 36713, 401771 65 P: 2^6, 17, 163 66 P: 89351671, 588024812497 67 P: 7, 47, 268573 68 P: 5^3, 7, 19, 113^3, 2741 69 P: 2, 19, 223, 631, 2503037 70 P: 13, 142963, 119079791436527 71 P: 3, 47, 331 72 keine gefunden 73 P: 2^3, 3 74 P: 5, 1251922253819 75 P: 17, 43, 347, 31247 76 P: 5, 37, 1109, 9241, 661049, 20724663983 77 P: 2, 32687 78 P: 43, 151, 181, 1163, 56149, 4229335793, 5744393199187 79 P: 7, 263, 3037, 1012573, 60312841, 8206949094581 80 P: 3^4, 7, 13, 6343 82 P: 3^4, 5 83 P: 4871, 13691, 315746063 84 P: 163, 653, 20101, 663840051067 85 P: 2, 11779 86 P: 68239, 6232426549 87 P: 1999, 48121, 604807523183 88 P: 2535619637 89 P: 2^3, 3, 13 90 P: 6590291053 91 P: 3, 293 92 P: 727, 383951, 12026117, 18768727, 1485161969 93 P: 2, 5, 509, 9221, 81551 94 P: 11, 241, 32143, 463033 95 P: 2137, 15061, 96185643031 96 P: 109, 5437, 8329, 12925267, 103336004179 97 P: 2^5, 7, 2914393, 76704103313 98 P: 3, 28627, 61001527 99 P: 5, 7, 13, 19, 83 101 P: 2, 5, 1050139 102 P: 7559, 11813, 139409857 103 P: 24490789 104 P: 313, 237977, 11950711691 105 P: 2^3, 7669 106 P: 79399, 672799 107 P: 3^3, 5, 97, 613181 108 P: 3761, 10271, 1296018233 109 P: 2, 3^3, 20252173 110 P: 17, 5381, 9431, 1219715607577, 14438374183481 111 P: 131 112 P: 11, 1037888513 113 P: 2^4, 405697846751 114 P: 9181 115 P: 31, 2743780307 116 P: 3, 7, 19, 47 117 P: 2, 7, 31, 37, 182111 118 P: 3, 5, 11, 23, 3152249, 10404887 119 P: 1741 120 P: 11, 653, 2074031, 124148023 122 P: 11, 2791, 16522744709 123 P: 34849 124 P: 5^3, 11^3, 22511 126 P: 5^3 127 P: 3, 19, 907, 13778951 129 P: 2^7, 7, 113 130 P: 11, 23, 62351, 70439 131 P: 17, 754480919 132 P: 5 133 P: 2, 5277179 134 P: 3^3, 17, 406531, 73629977, 4962859085059 135 P: 23147324413 136 P: 3^3, 5153, 87249620417 137 P: 2^3, 29, 59, 6733, 18951271, 4483681903 138 P: 97, 4889 139 P: 1822333408543 140 P: 14591 141 P: 2, 192047, 42039743 142 P: 143111, 12838109 143 P: 3, 5, 67, 197, 1999, 12848347, 65451824959, 225413072431 145 P: 2^4, 3, 31 146 P: 7, 13, 79, 22639 147 P: 13, 79, 103, 283, 24203, 4058948753 148 P: 7, 11, 41, 14879, 161141, 2805469039 149 P: 2, 5, 29573, 121456243, 2283131621 150 P: 13, 21199069, 85877201, 103053130679 151 P: 5, 2251, 14107, 5288341, 15697215641 152 P: 3, 22554863, 54504719 153 P: 2^3, 8539, 5540099 154 P: 3 155 P: 17, 211691, 309131, 6282943, 1196757167, 77322074223833 156 P: 347, 1297 157 P: 2, 5, 122327, 4242923, 5857727461, 275318049829 158 P: 17^3, 1031, 820279 159 P: 367, 5356051 160 P: 72669541193 161 P: 2^5, 3^4, 11^3, 83, 137, 6188401, 93405163 162 P: 607, 142946059423 163 P: 3^4, 3898031 164 P: 103, 107, 1493 165 P: 2, 7, 211, 25102757, 11699444843 166 P: 7, 877, 61819 167 P: 64661497 168 P: 5, 13, 739, 27427, 19145241526811, 47955919706207 170 P: 3, 13, 23, 1163, 170613512651 171 P: 269, 1803383 172 P: 3, 47, 91303 173 P: 2, 3079, 56087 174 P: 5, 113, 199, 379 175 P: 397, 487, 2199439603 176 P: 5, 191, 5611481459 177 P: 2^4, 7, 23, 42397, 123681208241, 49203761507753 178 P: 7, 1213, 67751, 296036443 179 P: 3, 17, 35059, 126443 180 P: 269, 5737 181 P: 2, 3, 101 182 P: 5^4, 211, 8934721 183 P: 1231487 184 P: 89, 661, 1187, 2203, 6043 185 P: 2^3, 12577 186 keine gefunden 187 keine gefunden 188 P: 3^3, 13 189 P: 2, 1847, 6199 190 P: 3^3, 29, 236981, 382351, 753743 191 P: 13, 379133, 11055229853299 192 P: 13, 4049, 302279, 465435739 193 P: 2^6, 5^3, 4877 194 P: 439, 8338826207 195 P: 7, 23, 13421, 3132631 197 P: 2, 3, 7, 653, 6237773, 16475012840609 198 P: 147647, 545639981 199 P: 3, 5, 77263, 1843757 200 keine gefunden 201 P: 2^3, 5, 86722091 202 P: 11, 47 203 keine gefunden 204 P: 5431, 142061, 1070347, 15028133 205 P: 2, 367 206 P: 3, 151, 1201, 2087 207 P: 5, 41, 269, 809, 26240063 208 P: 3, 947 209 P: 2^4, 229, 2203, 511654217, 6802750783 210 P: 43, 449 211 P: 279311 212 P: 1960573 213 P: 2, 313, 1877 214 P: 7, 17 215 P: 3^3, 7, 11, 3327697, 502095466241, 21451970877283 217 P: 2^3, 3^3, 127447, 8468323 218 P: 5, 163 219 P: 7891033151 220 P: 3581, 9619, 79867, 717967, 13477271, 32376410527, 34816906301 221 P: 2, 29, 1669, 15233, 103361803, 406833359, 455317162337, 1180548631831, 73446186360011 222 keine gefunden 223 P: 71, 349 224 P: 3, 5, 17, 130677149 226 P: 3, 5, 7, 97, 157 227 P: 7, 40277 228 P: 1361, 182353, 20866199378047 229 P: 2, 31, 3761059801469 230 P: 47, 384533887 231 keine gefunden 232 P: 5, 30851, 838667, 2250741293 233 P: 2^3, 3, 11, 157, 86735239 234 P: 19, 46441, 817766595407 235 P: 3, 31, 118022689 236 P: 29, 229 237 P: 2 238 P: 977, 8609, 4997219, 863039377, 64904716187 239 P: 11, 13^4, 74047, 212855197, 361552687, 12502228667 240 P: 227797 241 P: 2^4, 11, 523, 1163, 35407 242 P: 3^5, 373, 2386301, 2434609, 167962252433, 2706669242327 244 P: 3^5, 7, 16906680221 245 P: 2, 11, 19, 229, 218173429 246 P: 7, 877441867 247 P: 5081, 105527103139 248 P: 67, 101, 663893, 502608046943, 668677573093 249 P: 2^3, 5^3, 13, 17 250 P: 131, 509 251 P: 3, 5^3, 11, 17, 421, 395696461 252 P: 211, 997, 3613, 394213789 253 P: 2, 3, 167, 90901, 2905031 254 P: 89, 2269, 18042251, 32984389 255 P: 23, 463 257 P: 2^8, 5, 359, 49559, 648258371 258 P: 13, 17827 259 P: 173 260 P: 3, 83, 15263, 27827, 1749229, 6647339, 19148231, 3977977109 261 P: 2, 43, 71, 257 262 P: 3, 19, 571 263 P: 7, 23, 251, 267541, 159838801 264 P: 7, 61, 176051, 1446587 265 P: 2^3, 10853 266 P: 23, 163, 21401, 4673329018717 267 P: 29, 20411, 46926349 268 P: 5, 13, 101 269 P: 2, 3^3, 11, 83, 8779, 65684482177 270 P: 29 271 P: 3^3, 168629, 16774141, 235558417, 12145092821 272 P: 3833, 14084849 273 P: 2^4, 1086731, 7558891900249 274 P: 5, 23, 16631 275 P: 7, 6323, 134513, 138641, 455471, 40196043527, 279203122727 276 P: 5, 7, 43, 193 277 P: 2, 1993, 243547988443 278 P: 3, 1741 279 P: 67, 97, 557142359 280 P: 3, 47, 401 281 P: 2^3, 3443059 282 P: 5, 11, 13120561 283 P: 46301 284 P: 197, 1103, 9127, 16189, 1601147, 10723208449, 4019853486967 285 P: 2, 5791, 157907 286 P: 71, 619, 15017, 1016689, 6489382948837 287 P: 3, 653, 967, 10322313269, 405469792823 288 P: 17, 43, 36979, 376721, 670507 290 P: 17, 6659, 319811, 273354437 291 P: 109, 16766930077 292 P: 19, 43, 887, 941, 3239857 293 P: 2, 5, 7, 19, 83 294 P: 356135477, 592538407, 367003576739 295 P: 7, 47^3, 26249 296 P: 3^3, 971 297 P: 2^3, 2480497, 2779225651 298 P: 3^3, 59, 101, 181, 598421, 4809986918441 299 P: 5, 19, 59, 374893957 300 P: 37, 59, 29599 301 P: 2, 5 302 P: 607, 22621771, 123644663, 6681086808797 303 P: 43, 33873179 304 keine gefunden 305 P: 2^4, 3, 1149209 306 P: 73 307 P: 3, 5^3, 19, 487 308 P: 521 309 P: 2 310 P: 67, 3617 311 keine gefunden 312 P: 7, 13622501 313 P: 2^3, 7, 41, 149, 181, 1259389 314 P: 3, 181, 827, 3143117 315 P: 13, 257, 1187, 40471, 4767799 316 P: 3, 13, 51461, 898508623 317 P: 2, 107, 349, 2227301 318 P: 5^3, 197, 131959, 11496420743, 69578772701 319 P: 13, 79, 1439 320 P: 13121, 27397, 452983, 6818771 321 P: 2^6, 1401979, 78793807, 6628000247353 322 P: 3307, 4297, 2768017244933 323 P: 3^4, 11, 291721 325 P: 2, 3^4, 7^3, 157, 953, 568231, 68992603, 4507000559 326 P: 5, 1249, 30589393, 302908877 327 P: 17 328 P: 139, 911, 1399 329 P: 2^3, 17, 487068061 330 P: 227 331 P: 211, 359, 6134718817 332 P: 3, 5, 239, 15773 333 P: 2, 19^3, 31, 3266479 334 P: 3, 23, 257, 2887182434861 335 keine gefunden 336 P: 11, 78666481 337 P: 2^4, 13, 30137417 338 P: 31, 53 339 P: 13, 47, 199, 466751783977 340 P: 173, 641, 115574081561 341 P: 2, 3, 101 342 P: 7^3, 17167837 344 P: 7^3, 55351, 7493623, 102089209 345 P: 2^3, 463, 8941 346 P: 499 347 P: 14034413930219 348 P: 37, 103, 161561 349 P: 2, 5, 197, 433, 7499 350 P: 3^3, 103, 167 351 P: 5 352 P: 3^3, 23, 7723, 423017653829 353 P: 2^5, 8123, 465989, 17283818861 354 P: 11, 17, 37, 977, 13513, 1336241 355 keine gefunden 356 P: 37, 113 357 P: 2, 5, 13 358 P: 157, 6382723111 359 P: 3, 23, 307, 24350087 360 P: 11, 13, 19, 13842663034709 362 P: 7^3, 11, 19, 80233, 1794830107009 363 P: 4153, 94565579, 1249344562091 364 P: 11, 17, 1824271 365 P: 2, 1453, 128587933 366 P: 11, 36857 367 P: 43, 2213 368 P: 3, 5, 73, 21503, 70399321039 369 P: 2^4, 139, 173, 211, 419 370 P: 3, 22020497, 66065773, 4436281892011 371 P: 1619, 101113 372 P: 11, 2687 373 P: 2, 7, 113 374 P: 5^3, 7, 29, 31, 27463248607 375 P: 701 376 P: 5^3, 12799 377 P: 2^3, 3^3, 79 378 P: 41, 1453, 517298279 379 P: 3^3, 9308580172669 380 P: 83, 109, 12007, 120313541 381 P: 2, 827, 14449, 16943 382 P: 5, 97, 1238371 383 P: 28067251 384 P: 519488341, 75918457357 385 P: 2^7, 1548149, 4605659 386 P: 3, 103 387 P: 174426871193 388 P: 3, 31, 36826068382487 389 P: 2, 19, 373, 29569, 211850543 390 P: 11, 5713733, 15819863, 46950035940827 391 P: 7, 103, 25679, 68903, 6259286339, 11993961787, 311215043773 392 P: 101, 769, 773, 1553, 883201742719, 33906467435779 393 P: 2^3, 5, 7, 823, 22381, 1845595127527 394 P: 251 395 P: 3, 191, 651742019113 396 P: 1947241, 17344004261 397 P: 2, 3, 279421, 13315373041 398 P: 139, 205319 399 P: 5, 17^3, 23, 20125846752871 401 P: 2^4, 5, 83, 347, 115849 402 P: 97, 109, 269, 11174868949217 403 P: 11, 43, 373, 1321, 16296551797663 404 P: 3^4, 3659 405 P: 2, 601 406 P: 3^4, 53, 216141619 407 P: 5, 103001 408 P: 13, 50513 409 P: 2^3, 34583, 1894600969 410 P: 7, 109, 239, 653, 11328969257, 19111351313 411 P: 7, 23, 1367, 25888367 412 P: 97^3 413 P: 2, 3, 53, 249745603, 2832308863 414 P: 31 415 P: 3, 19, 10337, 107777, 924528047, 1465092947347, 9810493996903 416 P: 29, 181, 6988511 417 P: 2^5, 101 418 P: 5, 13^3, 822949 419 P: 173, 349, 983, 3257, 22891217 420 P: 17, 181 421 P: 2, 101, 1483, 350677, 1083982004309 422 P: 3, 7, 571, 367277, 29170663, 12757769381173 423 P: 7, 17, 19, 43, 1669 424 P: 3, 5, 37, 43, 131, 3037 425 P: 2^3, 29, 1097, 64951, 106357, 433703 426 P: 5, 89, 56861249, 2215508401 427 P: 13, 547, 577, 1657, 93703, 568689487 428 P: 6361, 1878059 429 P: 2, 19, 1381, 2473, 36510613, 12994232161 430 P: 19, 31, 557, 344621 431 P: 3^3, 2393, 12755833 432 P: 5^3, 61, 1680023, 7308036881 433 P: 2^4, 3^3, 129497, 244403 434 P: 863, 1831, 63527, 346517902547 435 keine gefunden 436 P: 193, 30348797, 677213275049, 88556282027663 437 P: 2, 13, 37 438 P: 47, 71, 6449465131, 130424397928207 439 P: 31, 79, 170899693 440 P: 3, 7, 31, 797 442 P: 3, 7, 29417408507 443 P: 5^4, 3406223 444 P: 11, 17, 15667, 220688906759 445 P: 2, 2659, 2753, 40768330434331 446 P: 797, 2687, 8629, 269063 447 P: 17, 82780601, 27856194112771, 146326546396711 448 P: 31, 67, 111121 449 P: 2^6, 3, 5, 1789 450 P: 1199923, 9445297441 451 P: 3, 5, 53, 48869, 4855900311901 452 P: 2141, 94847, 402341, 1454683, 163880093939 453 P: 2, 1597, 405179 454 keine gefunden 455 P: 101, 238931257, 6617214825917 456 P: 192037 457 P: 2^3, 5, 11, 919, 1589513 458 P: 3^3, 25185917998729 459 P: 7, 14537 460 P: 3^3, 7, 19, 53, 8819831 461 P: 2, 1697, 5081 462 P: 849571, 14532863 463 P: 1667 464 P: 73861878877 465 P: 2^4, 795071 466 P: 23 467 P: 3, 29, 743, 7393 468 P: 5, 17, 9858955373 469 P: 2, 3, 107 470 P: 79, 103, 83401 471 P: 7, 41, 691409 472 P: 7, 101, 1531, 363047 473 P: 2^3, 37, 2311 474 P: 5, 2141, 197699, 16069969 475 P: 11, 117133 476 P: 3, 5, 37, 109^3, 337, 401, 5527, 1169759 477 P: 2, 19, 1576721 478 P: 3, 7284323232409 479 P: 47, 2833, 500239 480 P: 8293, 243589 481 P: 2^5, 11, 54371927, 143432275871 482 P: 5, 71 483 P: 11, 1160559731 485 P: 2, 3^5, 11, 13, 19051, 60037905066809 486 P: 563, 572843 487 P: 3^5, 11, 23, 41, 1069 488 P: 13, 19, 1493, 3505277 489 P: 2^3, 7, 8157059583047 490 P: 4787 491 P: 7, 79, 661763933, 121261604419 492 P: 1034239, 211096013, 85750417002241 493 P: 2, 5, 11, 163001522539, 36843957223351 494 P: 3, 37, 4271, 121607, 601961, 34997771583587 495 P: 1522057 496 P: 3 497 P: 2^4, 127, 157, 505780258937 498 P: 61, 1187387, 45525923, 2149153512589 499 P: 5^3, 109, 81307, 24117560837 500 P: 53, 109, 157, 49429 501 P: 2, 5^3, 23, 14890530569, 24112920253 502 P: 22877, 34318033 503 P: 3, 17, 229, 659, 6761 504 P: 67, 229793929 505 P: 2^3, 3, 41, 463, 297377071847 506 P: 13, 59 507 P: 5, 2377, 5153, 363211, 6111681437 508 P: 7, 13, 1061, 1274084375749, 1311889799369 509 P: 2, 7, 41, 7215975149 510 P: 107, 19846129, 175868149, 228490481, 34656130219 511 P: 11, 4787 513 P: 2^9, 17, 31^3, 43787 514 P: 3^3, 22549 515 P: 101, 2089, 175186789, 2115451213 516 P: 571 517 P: 2, 59547517 518 P: 5, 12650270891 519 P: 157, 223, 8649842813, 37898634329 520 P: 7, 36161687 521 P: 2^3, 3, 7, 31, 53, 8938997 522 P: 31, 17477, 499292741 523 P: 3, 9907, 19289 524 P: 5, 11, 778717, 87702160913599 525 P: 2, 97, 34687, 497557, 2651387 526 P: 5, 13, 83, 499, 647, 247073, 2394147047 527 P: 73, 3373 528 P: 23, 1303, 54467681 530 P: 3, 13, 23, 5157793 531 P: 31, 86384479603 532 P: 3, 5, 179, 62929 533 P: 2, 283, 417860291 534 P: 101, 139, 631, 9931 535 P: 13009, 574477 536 P: 1619, 556072481, 1240525163 537 P: 2^3, 43, 5021, 112142108971 538 P: 7, 17, 2267, 28307 539 P: 3^3, 101, 172297, 184693, 1178753, 4673137127 540 P: 7, 17, 41, 9041 541 P: 2, 3^3 542 P: 810202662271 543 P: 5, 313 544 P: 12527, 24095129 545 P: 2^5, 11149, 2042119241 546 keine gefunden 547 P: 31, 1691778551 548 P: 3, 30949, 256561 549 P: 2, 5, 10133, 512811707, 481691968193, 83997567503807 550 P: 3, 110619193, 332718585593 551 P: 5, 1021, 108289, 1254577, 10781849409623 552 P: 89925422513 553 P: 2^3, 139, 347, 7541, 737291 554 keine gefunden 555 P: 541, 162203773 556 P: 197, 617, 19009, 54930985557421 557 P: 2, 3, 5^3, 7, 23, 39829 558 P: 7, 193, 461, 1621, 65257, 47652991 559 P: 3, 59, 151, 599, 12613 560 P: 67, 2671, 5107, 18757, 411823, 712346863 561 P: 2^4, 135913, 3458677 562 P: 83, 337, 5229031 563 P: 18920521 564 P: 4813, 4388171 565 P: 2, 11, 782707, 14615527, 362941373 566 P: 3^4, 326537 567 P: 67, 101 568 P: 3^4, 5^3, 373, 1553 569 P: 2^3, 7, 263, 25359067 570 P: 7 571 P: 23, 29, 308383 572 P: 61, 4049, 29922449, 111170909, 7654073743 573 P: 2, 31, 283, 50647 574 P: 5, 29, 61, 2213, 598967 575 P: 3, 46271, 61169, 6501209375021 577 P: 2^6, 3, 13, 17, 71, 1381277 578 P: 11, 107747, 205657 579 P: 17, 199, 1097 580 P: 239, 57251, 974147, 69722080903 581 P: 2, 37, 176431, 6924427 582 P: 5, 37, 151 583 P: 241, 479, 1889 584 P: 3, 1447, 69857 585 P: 2^3, 1327, 1580431 586 P: 3, 136544960191 587 P: 7, 13, 31, 22091, 6343317671 588 P: 43, 599, 292969, 37497252977117 589 P: 2, 7, 17191, 1524529, 3501139 590 P: 163, 443, 376021, 2239201, 4176404107, 3219042433511 591 P: 419, 8447 592 P: 23, 51217, 2070323 593 P: 2^4, 3^3, 5 594 P: 32485136899, 8784820622857 595 P: 3^3, 19, 88499, 96727678693, 386120172551 596 P: 11^3, 13, 94327 597 P: 2, 558793 598 P: 151, 3571 599 P: 5, 35771 600 P: 47, 14582963 601 P: 2^3, 5, 61 602 P: 3, 11, 1166849, 37310783 603 P: 1579, 290512619 604 P: 3, 11, 79, 157, 3294062720537 605 P: 2, 29, 89 606 P: 7, 11, 13, 19, 71, 848297, 319155270953 607 P: 5, 7, 40303229, 22035814429 608 P: 11, 7759, 664579, 50092921 609 P: 2^5 610 keine gefunden 611 P: 3, 18503, 39569 612 P: 59 613 P: 2, 3, 4073, 81371669, 18419352383 614 P: 11, 18234089 615 P: 83, 18895408512917 616 P: 17, 479, 123001704037 617 P: 2^3, 101, 1087, 6007 618 P: 5, 7, 17, 61, 1163, 220169 619 P: 7, 73, 11682481, 52649183399, 6162516725413 620 P: 3^3, 29, 113, 5861, 81163, 7358177, 3533794899013, 15145894824163 621 P: 2, 73, 17609, 963223, 2031264307 622 P: 3^3, 577, 1193 623 P: 19^3, 31, 47 624 P: 5^4, 109, 37199 626 P: 5^4, 5641 627 P: 181048811 628 P: 31 629 P: 2, 3, 47, 101 630 P: 67, 163 631 P: 3, 1787, 5741 632 P: 5, 11^3, 37, 179, 389, 829 633 P: 2^3, 71, 4513, 22643, 7329659 634 P: 800243 635 P: 8641, 3245689, 12675040709 636 P: 7, 1270333, 3258471060043 637 P: 2, 547, 1021, 521429, 78225448229 638 P: 3, 7, 3253 639 keine gefunden 640 P: 3 641 P: 2^7, 43, 24481, 5025104010547 642 P: 5302111 643 P: 5, 17, 307, 859, 460609, 7354807 644 P: 41, 223, 883 645 P: 2, 11, 29, 319117, 1350061, 549461839 646 P: 4136689 647 P: 3^4, 23, 15266862761 648 P: 12295820941 649 P: 2^3, 3^4, 5, 101, 179, 45840199 650 P: 6211, 2135417656303 651 P: 5, 29, 105021277 652 P: 2113, 51059, 524251867, 5269346021 653 P: 2, 13, 17^3, 19, 1381, 22171, 637699 654 P: 13, 19, 61515814197403 655 P: 7, 47, 53, 3940249, 54674441, 158039872478141 656 P: 3, 7, 4259, 404890928047 657 P: 2^4, 5, 13^3, 883, 2899751 658 P: 3, 242831101, 26213234261509 659 P: 23, 131, 2221, 9161, 65983 660 P: 19, 43, 3646427 661 P: 2, 441583073, 462147547073 662 keine gefunden 663 P: 6961 664 P: 24223, 245183 665 P: 2^3, 3, 61 666 P: 4503454574621, 4977652953109 667 P: 3, 7^3, 199, 839, 4421, 59239 668 P: 5, 7^3, 19 669 P: 2, 397, 5857, 482683, 4663313116307 670 P: 83, 52289, 122323, 7267303 671 P: 5397037 672 P: 59, 73, 617, 2963, 483251, 880751, 8755297 673 P: 2^5, 61 674 P: 3^3, 5 675 P: 13, 761, 993913 677 P: 2, 13, 211 678 P: 37, 23841761 679 P: 534607, 18514999 680 P: 2677, 8737, 13125811 681 P: 2^3, 71, 109, 16088557 682 P: 5^3, 61, 857, 17934551077 683 P: 3, 1279 684 P: 2092667 685 P: 2, 3, 7^3, 119659261 686 P: 11, 118163, 283099, 1031483, 85481059, 464136932507 687 P: 7^3, 103, 199337, 2747873, 36926501 688 P: 17, 1429, 84391410869 689 P: 2^4, 6547, 1863787, 24028099019 690 P: 113 691 P: 37^3, 509, 1091, 9157, 84131, 10843045487, 312679516579 692 P: 3 693 P: 2, 5^3, 561931, 1362299, 112102492193 694 P: 3, 19, 233 695 P: 13, 107, 18127, 52667 696 P: 617 697 P: 2^3 698 P: 13 699 P: 5, 11^3, 13, 23, 67, 73, 398969 700 P: 67, 3001, 65442059485993 701 P: 2, 3^3, 5 702 P: 677, 40361, 100213 703 P: 3^3, 4049, 591377 704 P: 7^3, 29, 1949 705 P: 2^6, 7^3, 1019, 3847, 48109, 16130783 706 P: 23, 27297539, 209941187 707 P: 5, 89, 317, 22469, 44417, 4728169429, 47679740053003 708 P: 701, 4146409, 51381922303 709 P: 2, 17, 199, 1663 710 P: 3, 163, 42834427 711 P: 73, 163 712 P: 3, 17, 9463, 476513, 1287467, 2686283 713 P: 2^3, 11097981800233 714 P: 191, 613 715 P: 781059256409 716 P: 7, 552341, 440416759, 5626714979 717 P: 2, 7, 11, 643, 23917, 1304111, 16621877, 8512494329 718 P: 5 719 P: 3, 41, 4414200313 720 P: 69193 721 P: 2^4, 3, 19, 379 722 P: 67, 547, 15607 723 P: 11, 19, 233, 239, 660658181, 2938943531 724 P: 5, 23 725 P: 2, 11 726 P: 5, 31, 17377 727 P: 11 728 P: 3^6, 163, 18541, 57384358463 730 P: 3^6, 107 731 P: 277, 1873, 82300301372323 732 P: 5, 31, 9143354797 733 P: 2, 17 734 P: 7, 73, 65957 735 P: 11^3, 457, 79181 736 P: 7, 17, 127, 5839 737 P: 2^5, 3, 37, 53, 6007, 140846899, 43638688993, 3684324840109 738 P: 3191, 8269, 3947883749 739 P: 3, 9719, 5681059 740 P: 1087, 281975833, 15373986241 741 P: 2, 269, 1433798129 742 P: 113, 7027, 968761, 1859111 743 P: 5 744 P: 41, 2729, 29123 745 P: 2^3, 31147, 474535783, 280232633477 746 P: 3, 13, 191, 1621 747 P: 101, 257, 271, 80567, 32799228019681 748 P: 3, 433, 1719107231 749 P: 2, 5^3, 29759, 34549943161 750 P: 19, 79, 97, 60773, 4888164324599 751 P: 5^3, 151, 409 752 P: 53, 876381797 753 P: 2^4, 7, 11, 173, 491 754 P: 7, 883, 5420057, 87185343382273 755 P: 3^3, 3583, 1299821, 143337647, 7334497678121 756 P: 13, 2551, 49822776853 757 P: 2, 3^3, 5, 17, 71, 242789 758 P: 1272207150661, 6369167671939 759 P: 257 760 keine gefunden 761 P: 2^3, 41, 907 762 P: 31019 763 P: 61, 1822517 764 P: 3, 43, 4943, 7459 765 P: 2, 7, 13, 377369, 5330933, 17206283 766 P: 3, 7, 11, 10163, 8922301 767 P: 2203, 68903, 422249, 74991254231 768 P: 5, 41, 345727, 14847328283687 769 P: 2^8, 1305827821, 2586456935177 770 P: 73, 4861, 1170023, 2771298845851 771 P: 907, 2662193 772 keine gefunden 773 P: 2, 3, 787711, 26259199, 142719149 774 P: 5, 8419 775 P: 3, 13 776 P: 5, 19, 41, 73, 1097, 33328795891 777 P: 2^3 778 P: 29, 15373, 1965283087 779 P: 257, 2477, 4534883 780 P: 53, 269, 48869, 10671151 781 P: 2, 29, 499, 778187 782 P: 3^3, 5, 563, 5683 783 P: 7, 442084061 785 P: 2^4, 7, 151, 74923, 123407, 111646712561, 559491826637 786 P: 73, 3469, 14026409 787 P: 37, 41, 427541 788 P: 37, 632114867, 22824986839, 118941702367 789 P: 2, 2307345676481 790 P: 19, 89, 461, 5125753 791 P: 3, 19, 10998428929 792 P: 17, 23, 21011, 255133, 80766939707, 36313481871019 793 P: 2^3, 3, 5, 173, 1103, 53407 794 P: 1286720879 795 P: 23, 79, 98909, 166657, 11173405591 796 P: 54914297 797 P: 2, 8273, 14607661 798 keine gefunden 799 P: 5, 2891032049 800 P: 3, 29 801 P: 2^5, 5, 683, 13807 802 P: 3, 7, 17^3, 215420011 803 P: 7, 23^3, 1973, 222216074029 804 P: 148173282913 805 P: 2, 59, 17401, 163193, 59098152210389 806 P: 59, 1051, 961613 807 P: 5^4, 11 808 keine gefunden 809 P: 2^3, 3^4, 59, 448110371 810 P: 79, 35608871, 128710108069 811 P: 3^4, 211 812 keine gefunden 813 P: 2, 193, 607, 142595731 814 P: 7, 670786483, 122493320143, 22863373360561 815 P: 7, 233, 2030845176271 816 P: 31, 1241086902527 817 P: 2^4, 547, 659077 818 P: 3, 5^3, 35097043, 89127571697 819 P: 809, 1041203, 9411713, 7263800119 820 P: 3, 11, 187477 821 P: 2, 19, 83, 233, 293, 1229, 37871, 209140301 822 P: 13, 83, 17377, 18965973137 823 P: 13, 2309 824 P: 5, 41, 951427 825 P: 2^3, 444113, 4100307667 826 P: 5, 13, 89, 23459, 29264621 827 P: 3, 17^3, 29, 9323 828 P: 577, 1867, 7315489 829 P: 2, 3, 17 830 P: 84407, 2261347020859 831 P: 547, 2179, 16212571, 312049583 832 P: 5, 7, 2213, 112246723, 223818256729 833 P: 2^6, 498254423201 834 P: 7, 41 835 P: 131, 125941, 323294483, 954340601, 39628173693533 836 P: 3^3, 181 837 P: 2, 109, 50998592653399 838 P: 3^3, 11, 19, 61 839 P: 5227, 11840951 840 P: 29, 730637329 842 P: 29, 89 843 P: 5, 509 844 P: 11, 13, 31, 36052871, 70457839, 2025248413, 2816027947, 2943803595533 845 P: 2, 3, 40987021669961 846 P: 11, 13, 31 847 P: 3, 41, 1319033, 28276121, 221393539, 409765111823 848 P: 11, 101863 849 P: 2^4, 5, 19, 13697, 590123, 10720751, 8987928353 850 P: 11, 151, 17286019, 11046585983 851 P: 5, 7, 53, 701 852 P: 7, 269, 27457 853 P: 2, 1125407, 39453473334461 854 P: 3, 7377061, 230377339 855 P: 29, 1549, 6779, 375481, 13214599, 7245558091, 30994657849 856 P: 3, 11, 53, 229, 4951, 9947819971, 48082633801, 83943401059799 857 P: 2^3, 5, 41, 157, 1697, 32478247 858 keine gefunden 859 P: 71 860 keine gefunden 861 P: 2, 84948797 862 P: 53, 413952542813 863 P: 3^3, 7, 23, 467, 12049 864 P: 7, 13, 121403 865 P: 2^5, 3^3, 167, 2161, 8663 866 P: 17, 97, 233, 1997 867 P: 13, 47, 167, 431 868 P: 5, 13, 17, 38201, 16917592332617 869 P: 2, 53 870 P: 12907 871 keine gefunden 872 P: 3, 7583, 9714810872587 873 P: 2^3, 193, 4547, 485509, 575959, 20856007, 58800361 874 P: 3, 5^3, 11, 47, 193, 1181, 1607 875 P: 37, 67, 937477, 1530709 876 P: 5^3, 226451, 1299343, 3587347, 171702372643, 369801222673 877 P: 2, 78926821, 10052723287699 878 P: 277 879 P: 243343 880 P: 61, 1168308143, 12782825651, 38563175939, 107905234979 881 P: 2^4, 3, 7, 23, 22385723, 94626144313 882 P: 5, 29, 317, 60761, 2669321 883 P: 3, 7 884 P: 1373, 7196186279251 885 P: 2, 194057 886 P: 29082802901 887 P: 11, 607, 60623 888 P: 23, 143159 889 P: 2^3, 491, 2014139, 73547302792739 890 P: 3^4, 162611, 321371, 8179693110613 891 P: 43, 43997, 112808526497 892 P: 3^4, 157, 2339, 568091, 4742137, 6336193, 8672659, 234988626427 893 P: 2, 5, 37, 59, 147341 894 P: 41, 193, 389, 644519, 3319051, 21227900821 895 P: 53, 193, 65927, 129169, 26718272312891 896 P: 37, 31238183, 8535320569 897 P: 2^7, 67, 269, 1123, 92896514864623 898 P: 239 899 P: 3, 5, 131, 1013 901 P: 2, 3, 5, 7, 29, 3877, 175474967, 6338370677, 14981029537 902 P: 407059, 482936260489 903 P: 13831 904 P: 29, 135469, 235523 905 P: 2^3, 17, 41 906 P: 1579, 17701979 907 P: 5, 17, 3497891 908 P: 3, 103, 269, 40819 909 P: 2, 11487079, 54828001 910 P: 3, 142886951, 1514654268719, 12342837395351 911 P: 127, 318917 912 P: 7 913 P: 2^4, 7, 41, 6079, 93187777, 89834287327 914 P: 139, 769 915 P: 13, 2549, 98985693983999 916 P: 5923 917 P: 2, 3^3, 1061, 11909, 312589 918 P: 5, 14009, 164071, 693582176263 919 P: 3^3 920 P: 41 921 P: 2^3, 262739, 152874167483 922 P: 16883 923 P: 73^3, 283, 1627, 2447 924 P: 5, 67399, 7084547 925 P: 2, 13, 53, 83, 877, 8363, 604859, 3519539, 90281266927 926 P: 3, 5, 14900443 927 P: 89, 22511 928 P: 3, 11, 23, 13913, 199549335169 929 P: 2^5, 62199604679 930 P: 7, 709, 70619, 85201, 24287395851751 931 P: 281 932 P: 5^3, 7, 17, 37, 2851 933 P: 2, 8592109 934 P: 13, 1511, 12119, 19175934991 935 P: 3, 593, 913331, 626872115449, 41007656409263 936 P: 61, 412330367, 446377909, 2607195499 937 P: 2^3, 3, 41, 113, 853, 22343, 500861, 1031299, 258469889 938 P: 191, 9467581 939 P: 179, 83761 940 P: 23, 419, 2837, 104479, 378289, 2514119 941 P: 2, 11, 1499 942 P: 17, 313 943 P: 5^3, 39025823 944 P: 3^3, 13 945 P: 2^4, 37, 5857, 1125121069, 2705324826961 946 P: 3^3, 59, 211 947 P: 5021 948 P: 409, 470461, 2584062913, 11058282821, 140030971047007 949 P: 2, 5, 7, 14806159, 30446387 950 P: 7, 925577, 1179757 951 P: 5, 848378279311 952 P: 2856871 953 P: 2^3, 3, 513405611, 220564434997, 1082305363079 954 P: 113, 193 955 P: 3, 107, 607, 5521 956 P: 19^3, 656300459, 2482219343 957 P: 2, 5, 149, 2113, 67129, 196961579, 51716885683 958 P: 43, 14479, 25229, 189713, 1813979414189 959 P: 11, 736433, 933107653 960 P: 31, 149, 449, 12157, 349227224611, 644232442639 962 P: 3, 7, 31, 41, 5711 963 P: 1933, 36758171 964 P: 3, 9533, 5871394053781 965 P: 2, 11, 2356997 966 P: 599, 7687, 2337073, 32558972119 967 P: 11, 19, 4813, 44830663 968 P: 5, 7669, 107641, 9506431657 969 P: 2^3, 11, 71, 911, 103421, 2391503, 319792007 970 P: 59, 269, 230551, 137893087979557 971 P: 3^5, 11, 401, 9257, 401839, 7672759 972 P: 227 973 P: 2, 3^5, 26713, 21581257, 1108107413579 974 P: 5, 7129, 1404071, 4204968197 975 P: 2879 976 P: 5, 991 977 P: 2^4, 11, 17, 109, 239, 401, 37589 978 P: 29, 71, 97, 733 979 P: 7, 191, 157799 980 P: 3 981 P: 2, 7, 719, 2153 982 P: 3, 5, 1747, 2459, 1222777, 5494786229 983 keine gefunden 984 P: 19, 78791 985 P: 2^3, 53, 1895057 986 keine gefunden 987 P: 1399, 36721, 57943, 24858506161 988 P: 14401, 63754777477 989 P: 2, 3, 12743, 2085799, 1423932997, 10577489843279 990 P: 1009 991 P: 3, 13, 431, 26437 992 P: 13, 140729, 24922021, 5043756649 993 P: 2^5, 5, 25301, 92177, 31187620943 994 P: 5431, 5449, 9029 995 P: 11, 13, 23, 15324691 996 P: 16931, 34031371421 997 P: 2, 197, 1223 998 P: 3^3, 7, 17, 1551083, 627934621 999 P: 5^3, 7, 50119, 806812352251, 5879307404213, 83815456559981 1001 P: 2^3, 5^3, 17, 140712037 1002 keine gefunden 1003 P: 61, 528691 1004 P: 797, 3889, 739279337 1005 P: 2, 63179, 2304851 1006 P: 7487, 15685394713 1007 P: 3, 5, 7240001, 48720886411 1008 P: 11, 103, 18919553717, 1085992774211 1009 P: 2^4, 3, 53, 20369, 1609302041 1010 P: 7^3, 211, 373, 101113 1011 P: 7^3, 78827589641 1012 P: 1123, 1556039 1013 P: 2, 13, 37, 33894929 1014 P: 19, 601, 13643248337, 2957593441709 1015 P: 13, 19, 37, 22853, 23339, 99235831 1016 P: 3, 23, 2411, 8783, 34781, 88707097, 110379811 1017 P: 2^3, 11447 1018 P: 3, 5 1019 P: 17761 1020 P: 83, 824723, 1526187617 1021 P: 2, 19, 37, 6947, 3728789, 144682870477 1022 P: 17^3, 163 1023 P: 162857063428079 1025 P: 2^10, 3^3, 17, 61, 12923, 53980169 1026 P: 5, 5009, 66173, 539503 1027 P: 3^3, 113, 2099, 28279, 987383219, 205899385621, 18639957895541 1028 P: 7^3, 12753113, 316153139 1029 P: 2, 19, 4229, 990397 1030 P: 7^3, 23, 59, 251, 683, 417643, 49618109, 594835481101, 3105232218721 1031 P: 29, 100767113 1032 P: 5, 53, 73, 1523, 2281292790859 1033 P: 2^3, 13, 61, 131, 401, 63499 1034 P: 3, 159737, 16303699, 47726604579847 1035 P: 13397, 1036513 1036 P: 3, 13^3 1037 P: 2, 13^3, 29, 41, 2351 1038 P: 7159, 42793633 1039 P: 5209, 7438153 1040 P: 167, 173, 491 1041 P: 2^4 1042 P: 47, 151, 203383 1043 P: 3, 5, 277, 24281687, 4144713913 1044 P: 5087, 21247, 1405367, 14588311, 4261392131 1045 P: 2, 3, 37, 397, 123581, 1981409 1046 P: 17, 102953 1047 P: 7^4, 1237891481 1048 P: 7^4, 1577761033 1049 P: 2^3, 5, 11, 3574693731373 1050 P: 83, 641, 777979 1051 P: 5, 14699, 40325433091 1052 P: 3^4, 152311, 310721 65537 P: 2^16, 3, 131, 151, 163 (>1.2E+14) (Fermatprimbasis) Die Basen 4, 8, 16, 32, ... haben die gleichen Primzahlen, wie die Basis 2, wobei bei der Basis 8 und 64 die Primzahl 3, bei der Basis 32 die Primzahl 5 und bei der Basis 128 die Primzahl 7 dazukommt. Sinngemässes gilt dies auch bei den Basen 9, 25, 27, 36, ..., die die gleichen Primzahlen haben, wie deren Grundbasen. 24.12.2022 Richard Fischer