Thema: Potenz-Differenz-Quotient (B+1)^(P-1)-B^(P-1) == 0 (mod P^2) Quotient by the difference neighbour bases with same exponent Main table of content: http://www.fermatquotient.com/ Die gefundenen Primzahlen P der Potenz-Differenz-Quotienten von der unteren Basis 1 bis 1029 (B+1)^(P-1)-B^(P-1) = {(B+1)^[(P-1)/2]-B^[(P-1)/2]} * {(B+1)^[(P-1)/2]+B^[(P-1)/2]} Beispiele (Examples): 3^(23-1) + 6 x 23 == 1 (mod 23^2) 2^(23-1) + 6 x 23 == 1 (mod 23^2) Differenz = 0 (mod 23^2) 3^(23-1) - 2^(23-1) = 5 x 23^2 x 331 x 35839 3^(3842760169-1) + 900406756 x 3842760169 == 1 (mod 3842760169^2) 2^(3842760169-1) + 900406756 x 3842760169 == 1 (mod 3842760169^2) Differenz = 0 (mod 3842760169^2) 3^(41975417117-1) - 6555614430 x 41975417117 == 1 (mod 41975417117^2) 2^(41975417117-1) - 6555614430 x 41975417117 == 1 (mod 41975417117^2) Difference = 0 (mod 41975417117^2) Die letzten 10 gefundenen Quotienten haben folgende Basis: 649, 953, 21, 165, 536, 209, 213, 533, 426, 888 Durchsucht bis zu den Primzahlen (Search until primes) 1.200E+13 (Pause) Basis Primzahlen^2 1 1093, 3511 (>6E+17) 2 23, 3842760169, 41975417117 3 5, 250829 4 3, 67 5 3457, 893122907 6 72673, 1108905403, 2375385997 7 13, 819381943, 438740909071 8 67, 139, 499, 26325777341 9 67, 887, 9257, 83449, 111539, 31832131 10 11 107, 4637, 239357 12 5, 11, 51563, 363901, 224189011 13 3^3 14 11, 5749, 17733170113, 140328785783 15 292381 16 4157 17 751, 46070159, 1132025487407 18 7^3, 142671309349 19 17, 269 20 29, 162703 21 5, 2711, 104651, 112922981, 331325567, 13315963127, 10712734785199 22 3, 7, 13, 94447, 1198427, 23536243 23 43, 179, 1637, 69073 24 7, 353, 402153391 25 43, 5399, 21107, 35879 26 7, 131, 653, 5237, 97003 27 2437, 1704732131 28 5^3, 617, 677, 2273, 16243697 29 73, 101, 6217 30 7, 11, 23, 3301, 48589, 549667 31 3, 41, 416797 32 95989, 2276682269 33 139, 1341678275933 34 83, 139 35 36 107, 137, 613, 2423, 74304856177 37 5 38 167, 2039 39 659, 9413 40 3^4, 23, 21029249 41 31, 71, 1934399021, 474528373843 42 4639, 1672609 43 31, 4962186419 44 36677, 17786501 45 241, 26120375473 46 5, 13877 47 13, 311, 797, 906165497 48 49 3, 13, 2141, 281833, 1703287, 4805298913 50 2953, 22409, 99241, 5427425917 51 52 359, 1672799, 6920803 53 5, 79, 5693, 44027, 16142359 54 6959, 14933407691 55 31, 354469 56 29 57 31, 751, 80471 58 3, 31, 37, 53, 6997, 32189, 67547, 920209, 542798336407, 937735496003 59 11, 947, 838553, 88478371187, 193709116789 60 11, 773, 359430671, 3181817140981 61 11 62 5^3, 37397, 9052343, 11920837 63 43, 271, 116141 64 103, 78328867, 7851774433, 8316486229 65 682499247923 66 125107, 251478559 67 3^3, 7, 1951, 4555163, 41796283 68 19, 29, 1549 69 70 19 71 5, 7, 1093, 4999319783, 28641507071, 3378347479693, 8433534582679 72 23, 37, 43, 528791, 402221020027 73 7, 49739, 1797637, 11154369619 74 14591 75 7, 53, 121883, 19226147 76 3, 13, 109507, 3319829 77 59011 78 5, 127 79 7, 459990330329 80 67, 3905336259817 81 17, 137, 307, 2477, 422072353819 82 78877 83 84 13, 22679, 23539, 2693071 85 3 86 5813 87 5, 41, 157, 21526889 88 89 29, 1033, 2099, 4019, 9643, 9167989 90 11, 4736153, 9692329249, 940428489727 91 29 92 13 93 103848881, 1957377517 94 3^3, 101 95 197, 223, 23796407, 213544339 96 5^3, 41, 653641, 335527499 97 19, 113^3, 1693 98 23 99 241, 115849 100 787 101 102 139, 6365231, 3700368571 103 3, 5 104 23, 181 105 19, 2027 106 11, 79, 139, 31307, 12748432423 107 19, 79, 7227109, 3876082253 108 11, 90052394363 109 19, 1503583, 15835383623 110 29, 5479 111 111376852931 112 3, 5, 19 113 17, 101 114 367, 1223, 3023, 1539846827 115 173, 373729159129 116 7, 107, 18797, 258569, 13317821899 117 2003, 14087, 182773, 3950306411 118 117763, 29014213 119 13^4, 17351573, 24337069, 61789375937 120 7^3 121 3^5, 5, 13, 31, 3671, 5179, 281621, 1017817, 88924897 122 7, 9909649031 123 23, 10301, 347675833 124 7, 1483, 169787391959, 2756914593623 125 17, 1621, 465463, 4088417, 8168099, 19272271231 126 17, 113, 2971, 17569, 82613, 1132177, 3872129 127 36793, 28172887 128 5, 7, 23, 227, 18133, 54727, 153001 129 1423 130 3 131 797 132 133 11, 7845114637 134 1163, 1476751 135 11^3, 173, 941 136 283, 490661 137 5, 17, 4513, 631843, 2309378983 138 31573, 1307072704121 139 3, 265787 140 17, 263, 989347 141 142 433 143 1409, 90071 144 17, 90031, 182494597, 4870816651829 145 139, 4692139, 9245699483 146 5, 13, 31, 79 147 148 3^3, 17, 19, 241, 13619 149 59 150 39275311, 86224409, 689413717 151 11, 17, 257, 12402499 152 971, 171271 153 5^3, 41, 47, 419 154 83, 3393479 155 131, 1013, 3167809 156 1040803 157 3, 6491, 25427477, 170905747 158 838339427 159 59, 203286227 160 37, 2539, 55482547 161 13, 24623299777 162 5, 17, 37752418861, 1240117010507 163 17, 8627, 11161, 112501, 111405779257 164 31, 263, 13672663, 28892519 165 7, 47, 7307, 10820506512097 166 3, 53, 109, 197 167 24197, 10263089, 879796157 168 12329 169 7, 3555763, 280129489187 170 197, 92051, 149138057, 6983923403, 688450932677, 7276946929289 171 5, 7^3, 12239 172 173 7, 4242055123, 1769326777591 174 103, 35851, 1391627, 503579053 175 3^3, 17 176 13, 4021 177 7, 37, 53, 2667397361, 30676986113 178 5, 49823, 5402141272897 179 9067 180 11, 19, 42825111067 181 11 182 11, 41, 2801, 3559343, 7485706451 183 1319, 1483, 1207603, 177540533 184 3, 4177, 9629, 4047569 185 45355782763 186 26263, 444089, 3430633, 4144242503, 7139075131 187 5^3 188 139, 997 189 404054727617 190 4799, 1155282529 191 13, 14969, 15561319 192 193 3, 29, 4517 194 587, 4003 195 79, 18433 196 5, 73, 13577473537 197 1583, 87539 198 229 199 252737, 3169231399 200 227 201 647, 703867902289, 1346084590853 202 3^4, 72817, 557339, 1045729 203 5, 41, 4283, 348527 204 205 3181, 6211184971 206 43, 271, 1489 207 17, 79 208 14753, 8089693 209 11101991220583 210 229, 3137, 3301, 856950257 211 3, 11, 23, 2243, 7079 212 5, 19, 2341, 895133 213 5536514293, 11102234350993 214 7 215 25492931 216 13, 313 217 317, 546613, 12271583, 21703247 218 7, 13, 103 219 38159867 220 3, 7 221 5^4, 643 222 7^3 223 557, 773, 1699, 21893, 14670435433 224 41, 1559, 5939 225 617, 59887, 9435281, 172122949, 777577611439, 1134385910729 226 7, 6079, 762407 227 11, 607, 11161 228 5, 5042273, 131640617, 4612079713 229 3^3, 11, 67, 751, 5839 230 3631, 13763947, 1872544591363 231 67, 10106346118579 232 1609, 1744253911 233 28793, 158505661 234 7681 235 73, 5615713, 6813409, 284415947 236 29333, 73421, 11972894771 237 5 238 3 239 29, 248245147, 226298263141 240 709, 559556058431 241 242 79, 811, 22193 243 239, 5779, 137887129 244 67, 1562531, 145398167 245 13, 157, 258224651969 246 5, 919, 36451 247 3, 43, 103, 1952939 248 19, 7507, 11041777 249 199 250 607, 677, 145703, 4471289783 251 19, 23, 137, 104009, 72186019 252 293, 373, 5443, 775380797 253 5, 13, 19, 353 254 11, 133991931247 255 19, 2426233 256 3^3, 11, 61, 127, 501734306897 257 101, 36767, 38967659 258 61, 1789, 16433, 1618501 259 260 431, 18182387, 30713411, 1814501933, 4716042911 261 13, 53 262 5, 37, 23741 263 7, 19, 41, 2292461 264 23, 108559028999, 623466241919 265 3 266 17467, 56783521001 267 7, 43, 48247 268 157, 135197, 250504171717 269 7, 17, 683, 3853, 9691900516231 270 1039, 2131, 117281107 271 5, 7, 1931, 123433, 276599, 209223319 272 11, 29, 270037, 242596853 273 369181777, 2239724719, 2876777131 274 3, 867711191 275 7, 11681, 23741 276 277 23, 47, 467101 278 5^3, 911 279 2114207, 28023719, 35219994013 280 2816504239 281 282 71, 146093 283 3^4, 47, 1277, 425791 284 1019, 7343233307 285 286 61, 107, 313, 1223, 22067, 67710809 287 5, 37, 109, 29939857, 417310501 288 13, 163, 39359, 167749849 289 12809, 13577, 103520689 290 13, 19, 349 291 56895143 292 3, 19, 4032911, 248338589 293 41, 127, 4783 294 5437, 23059, 70435493, 74942188019, 122403459617 295 359, 27474131 296 5, 647161, 1142083, 84157313, 147342617, 240639968923 297 2203, 2979049 298 59, 6968327, 15483730513 299 43, 59, 22608811, 6379246051 300 16451, 7453915457, 689698873553, 1277106090707 301 3, 11, 139, 653, 2099, 2139521 302 11, 29, 140171 303 5, 11^3, 3659, 16666147627 304 914867, 71716327 305 29, 8179, 574007452819 306 4097452349, 5123513411, 37018092061 307 12377, 1358257 308 17^3, 1066283, 12033689, 845982659, 11035099247, 395014017641, 9064225665031 309 310 3^3, 9208187, 14114077, 809550601, 157115716291 311 1259 312 5^4, 7, 29, 18793, 23195264401 313 59, 181, 5867 314 307, 4651, 25931 315 13, 1206497 316 7, 73, 683, 73823, 399793651 317 23, 479, 563, 49663, 4553641 318 7, 409, 123323, 2606942171 319 3, 149, 3876857627 320 7, 907, 30841, 61064777, 1009723487, 33672813539 321 5, 1373, 958543 322 29, 3539 323 756677893 324 7^3 325 5232469337387 326 31, 98561, 187123 327 313, 967 328 3, 5, 10597 329 330 13 331 8162711 332 11, 43, 439, 59497, 341311, 55979453791 333 11117 334 335 37, 257, 769, 109169, 516253 336 61, 713206139, 1286050773883 337 3^3, 5, 281, 27253, 606617197 338 160103717 339 1559, 6137400559 340 1951 341 342 21727 343 131, 62039, 123657671 344 181, 631, 10067, 810737 345 13^3, 155879509 346 3, 5^3, 152249, 1189387, 263097379, 5916086653 347 881, 2267, 482123, 2077831474027 348 11 349 33563, 158519 350 11, 113, 1907963, 1143803478967 351 21481 352 29137, 506357, 172951900829 353 5, 1777, 1357028641 354 23759676653 355 3, 223331, 1216529 356 6449, 7793, 79633, 1183739 357 173, 4421, 86939, 151299235147 358 863, 8429 359 17053, 1309207 360 13, 21191, 226427, 5548157, 5011672048373 361 7^3, 373, 389734306669, 1413511130477 362 5 363 364 3^6 365 7, 127, 179 366 71 367 7, 1093351697 368 653, 7027, 98715677, 1694245079 369 7, 67, 167, 17278981 370 17, 31, 4019, 109178341891 371 5, 13417, 452773, 5774475251, 1171163184743 372 1109, 3187, 31183, 3139771 373 3, 7, 229, 521, 1459, 1733, 12658733, 16405492517 374 239, 541, 5273, 133718839063 375 11, 60149, 12360570283, 3836591535613 376 2746101529, 210597418519 377 11, 20950913 378 5, 3907, 562760381, 2686334549 379 257, 397, 15971 380 283, 466528317833 381 61, 11071, 277177 382 3, 661, 124793, 145547 383 393407449 384 5087 385 13 386 260029069, 865540074911 387 5, 13, 426469, 1337250620137 388 3023, 11034629 389 43, 263, 489913, 634222159 390 2885527, 92693389 391 3^3, 61, 54686771, 1860448231 392 8017, 19037 393 11, 4909 394 6872251 395 173, 3613, 10613, 20731, 57507259 396 5, 41, 419, 6269, 182286268247 397 398 107, 173, 157571, 7936141, 62786819, 6316025327 399 3626230477 400 3, 23, 292839600293 401 402 17, 769 403 5^4, 38281 404 1616594849 405 23, 6329 406 11353 407 814725809 408 1201, 3328531, 15807749, 11282166659, 327531638393 409 3, 61, 293, 971, 261973067413 410 7, 1913 411 151, 449411 412 5, 1367 413 101, 1223607109 414 7, 13, 17, 521, 3011 415 17, 647, 877, 1284841, 1041435347, 65687316613, 339667268561 416 7, 3527, 19759, 1547931373 417 67, 2422052838641 418 3^3, 7, 383, 2731, 21997, 3798121 419 113, 11317, 125591, 1379157029, 13887930593 420 29, 71, 1223 421 5, 51827, 1249631578717 422 7, 11, 13, 31, 8009, 109714452139 423 11, 43, 43051 424 11, 23, 18049 425 347, 9080722847473 426 17, 227, 445051249, 11655068219953 427 3, 29443, 1117609 428 5, 305119, 327289 429 17, 19, 739, 416014778029 430 13, 23, 1157475947 431 19, 48672818933 432 16650067037, 39513838009 433 17, 173, 1069, 23293 434 435 1291, 46027, 354721093, 973026028577 436 3 437 5^3, 17, 25243, 392037594877 438 13339, 919834369 439 31, 41 440 17, 683, 145632679, 287612364751 441 31, 719 442 139, 16057, 4516177 443 2851, 1950919 444 43, 10061, 11677, 3114971, 30060151211 445 3^4, 929, 6803, 122045003 446 5, 269, 409, 23663 447 1709 448 83, 161053 449 47, 89, 317, 10301, 56777978399 450 13693 451 17, 31, 263, 2621 452 17, 1824341 453 5, 11 454 3, 43237, 249099581 455 456 23, 37747, 967451, 81436181, 238325543 457 13, 27539, 34555063, 13071293359 458 19, 1103, 1573669, 23262073613 459 7, 13, 89, 12409601, 40285829 460 47, 97, 173, 4021, 528087761, 569337199 461 283, 487 462 5, 89, 407219, 8609663 463 3, 7^3, 193, 100193, 353567, 117637057 464 17, 37, 761, 172058297, 688591531 465 7, 283, 463, 289577, 172212123847 466 19 467 7, 877, 1117 468 19, 495434851 469 11, 1787, 3581, 4363, 37799 470 19, 107, 20569369 471 5^3, 7, 11^3, 25033, 32917 472 3^3, 47, 67 473 19, 691, 580591269703 474 4539383, 441807559 475 40067558767, 2030471492243 476 47, 3709, 6037 477 38917 478 5, 301813, 698263, 69108241, 167076149, 567610567 479 480 31, 83, 9551 481 3, 263, 1033, 43729183, 16342676923 482 73 483 484 13 485 401, 13151, 20315069, 563629901 486 54181, 39115509911 487 5, 8167, 49711, 3889457390729 488 23, 3741599 489 792434887 490 3, 7138603 491 85619, 145062913, 153563974423 492 8821, 1801265021, 507183010457 493 211 494 41, 101, 1831, 17539, 33563, 1480301 495 3989, 7607, 29128129 496 5, 11, 17, 67, 821522213 497 89, 99679, 329138561 498 11, 23, 37, 53, 613, 1231, 3911 499 3^3, 13, 41, 109, 1351381433 500 139, 593, 5690203, 25044990577 501 11136859, 17975011 502 921749, 41243570141 503 5, 71, 149, 769, 3547, 27107, 502829, 5447587, 12977871443 504 241, 180023, 854263 505 29401 506 53359, 164789 507 64170859 508 3, 7, 4157, 4637, 8269, 44443228507, 3294039176489 509 19, 31, 167 510 2614130353 511 43 512 5, 7, 127, 10111 513 127, 136142371153, 155278064713, 916178079991 514 7^3, 11, 13, 3881069, 6178181 515 85331, 1432774157, 332936488067 516 7, 1367, 8423 517 3 518 29, 1249, 5479, 41171561939 519 31, 107, 1481, 13219 520 7, 59, 88581263 521 5, 31, 189242239, 238893749 522 79 523 87151, 410292053 524 525 73, 101 526 3^4, 23, 4493, 498787, 2699297, 153058441, 81010796381 527 709 528 5^3, 29 529 13, 41, 61, 557, 683, 69821, 3701293, 101473303, 602884483 530 233 531 23 532 61, 117373 533 317, 709, 62495053, 522215957, 11498439471877 534 461, 20887457, 1123280699 535 3, 29, 5641, 18869, 20574863, 89134527103 536 4923917599, 2633306585713, 10845992853133 537 5 538 29, 31, 83, 48051967 539 1259, 21139 540 446839 541 19, 241 542 2389, 176777 543 11 544 3, 11, 1283 545 11, 139, 331, 41397961291, 78408415913 546 5 547 6856249, 14611699, 4073785931 548 167, 179, 937, 554797 549 550 193 551 20981 552 28012541, 2794033050563 553 3^3, 5, 61, 1146731 554 13, 191, 6577, 162954257 555 811, 675942089 556 13 557 7, 41, 3853363747 558 17, 127 559 23, 26921, 3550681, 38599651 560 687965833, 717154888019, 6968709252079 561 7, 149, 984341, 3108031, 371190797, 4819264757 562 3, 5^3, 8117 563 7, 59, 1163, 1170523, 59264549 564 101, 124753 565 7^3 566 197, 14281, 3975197, 372710977 567 568 29, 97 569 7, 23, 47, 127, 2089, 23284710937 570 8237, 704029, 3029016437, 7803229163 571 3, 5, 79, 97711, 2941363 572 9697, 5349691, 46646429 573 19 574 11^3, 15764887 575 4397 576 181, 323273 577 578 5, 30297315091 579 1597, 3119763759841 580 3^3, 251, 1171, 9791, 2961976705169 581 37, 252151, 210235657, 413723231 582 547, 3593, 11399, 94343801, 7600668015529 583 13, 8179, 16761933943, 1076995015717 584 79, 36629, 78139, 264437, 61254253, 3107503031 585 586 313, 160367 587 5, 71, 2129, 5147, 27017 588 662261, 79238053429 589 3, 41, 127 590 11, 31, 16239371 591 13, 167 592 11, 71711 593 139, 133669, 6994159 594 181, 4249409, 69539473 595 175211900441 596 5^3, 617 597 17, 8317, 34261, 1462337, 1409540555809 598 3 599 13, 163, 1609, 241847, 240028601 600 16545527 601 23, 29, 275449 602 49856441, 4296222379, 136607763707 603 5, 5171 604 174583069, 3708344844353 605 37^3 606 7, 304886261, 27819387289 607 3^5, 167, 9493777048307 608 87103, 195527 609 19, 2357, 342899, 1372027, 2018342790929 610 7, 73, 167, 193, 46643 611 69833 612 5, 7, 19 613 71, 4933, 1103749, 5309128929443 614 7, 19, 37, 4135953097 615 241, 719 616 3, 19, 54647, 2113426706683 617 11, 73, 173, 11340841, 524782374541 618 7, 83, 6917, 31259, 4299709 619 11 620 83, 1279 621 5, 227^3, 788267 622 623 2454847 624 19, 1750159 625 3, 173, 1350203 626 13, 43, 199, 7880903, 4466664490909 627 23, 6317 628 5, 13, 1748333, 78899454869 629 73, 70907076263 630 3521406407 631 92791 632 633 23, 359, 1358701219, 106368238477 634 3^3, 31, 631, 161717, 972113, 2893217456009 635 11, 349, 1954427, 4637077358621 636 637 5, 83^3, 406995037, 77709781997 638 37, 109, 504076009, 5404096543 639 640 37, 53, 97, 27197, 254857, 1042783068319 641 642 4909 643 3, 432961, 109677284419 644 53, 2441, 1275823 645 1979, 96907, 22258021 646 5, 101, 523, 13670707 647 29, 3967, 350345059 648 10056229241 649 227320911611, 10417307739907 650 651 19, 41, 1297905707431 652 3, 23, 211, 367 653 5^3, 13, 19, 979655167 654 89, 5995802237, 7789251677 655 7 656 299491051 657 23, 743069, 6408257917 658 2531, 835123 659 7, 17, 37, 683, 1256115359329 660 98467, 50684987, 14558291257 661 3^3, 7, 2267, 66499 662 5 663 7, 5517380309263 664 11, 227 665 11^3, 38351 666 11, 79 667 7^3, 73, 7000101336457 668 13, 59, 6151, 86420305483, 678837772049 669 61, 1283, 1405099, 159601837, 29818623287 670 3, 37, 241 671 5, 37, 4287851, 1658026219 672 12973, 2643898427, 390318115531 673 674 317 675 283, 89273 676 2887 677 118043, 52049449, 17465830391 678 5 679 3, 3940237201 680 61, 6110045797 681 682 73, 11059, 119891, 322319, 1573984283, 2727714443 683 13, 11689 684 37 685 59, 71, 2663 686 293 687 5^3, 349337, 769467423479 688 3^4, 1913, 2221231, 550905527923 689 101, 107, 2281, 237711045569 690 103, 383, 179143 691 17, 47, 22189, 438645631 692 61, 16417361 693 127, 59797, 386853067, 82624216783 694 145687 695 11, 113, 179, 337, 12923 696 5, 197, 1740400433 697 3, 37, 5657, 251263, 22431386569 698 13, 37, 137, 729931 699 67, 367, 43719679 700 701 181, 259379, 1112589719 702 5931943281421 703 5, 17, 3187, 22877, 1561697891869 704 7^3, 17, 969679 705 41, 28703, 627349 706 3, 587341, 158647033 707 708 7 709 37, 41, 4003, 2247559 710 7, 163, 70583, 116389469179 711 11 712 5, 7 713 11 714 80687, 32761163 715 3^3, 17, 79, 569, 5026993 716 7, 67, 1409, 3798631, 63547474493 717 5857, 24393821 718 17, 43, 127, 833947 719 33517343 720 79, 58987373, 1174711799221 721 5^3, 89, 1721, 12265126831 722 17, 149, 9613, 25564237 723 13, 5275056613 724 3, 73, 4128816579809 725 13, 53, 463, 1069, 25031, 1144948919 726 17, 73, 694322150177 727 43, 1033, 108926644109 728 5, 37, 173, 11579, 32413 729 17, 313, 1811, 33345661, 172558204933 730 29, 37, 997, 483367, 2687910504751 731 79, 4437733, 293352840601 732 53, 200363, 1153337, 3701360956217 733 3, 33107 734 4057, 29879, 27573023, 220172117521 735 419, 1031, 4771549, 16969019 736 97, 15971, 1837387736549 737 5, 5413701149 738 11, 61 739 740 11, 17, 23, 11239, 56643720073 741 17, 5913426151, 742406450839 742 3^3, 1223 743 498205373 744 71777917423, 4597714335853 745 101848850969 746 5 747 19371749 748 749 29, 229 750 4712977, 19521409 751 3, 29, 353 752 13, 337, 17387, 162792941, 4442443146601 753 5, 7, 17^3, 103^3, 85667, 7886533 754 37^3, 4556154049 755 47, 53, 181, 347411 756 11^3, 153059 757 7, 43, 1627 758 10651, 599231 759 7 760 3, 13 761 7, 137, 2678027227 762 5, 173, 9671183 763 37 764 39769, 7844838261629 765 7, 97, 40609 766 659, 434293, 33487771 767 47, 157 768 13, 89, 101, 217380803 769 3^4, 1123 770 203591, 16964627 771 5, 1153, 290367167 772 29, 1795951, 9161171 773 1689860966747 774 613, 65203 775 59, 79, 811, 1193021 776 2748601 777 461 778 3, 5^3, 167, 2251, 76168171 779 491, 1129, 19441789, 106355563, 204337391 780 23, 55697 781 257, 65089, 492673, 40035521 782 107, 173 783 3209, 11851481, 678700937 784 29, 61 785 11, 17, 571 786 11, 4001, 5737, 24785267707 787 3, 5, 11, 37, 47, 521, 79349, 463654823, 5758879799 788 59, 68507, 976497503143 789 326581391 790 19, 691, 22433, 102453517939 791 47, 73 792 19 793 23 794 463, 79999, 251663 795 13, 109, 137, 13033, 7954361 796 3^3, 5, 31, 930467, 1028089 797 13^3, 59 798 1187, 2671, 220933, 1354663, 64498393, 77704709 799 2711, 1304302388663 800 4177, 107873, 5984773 801 802 7, 47777, 443147 803 5 804 69859, 1127587 805 3, 59 806 7^3, 23, 109937, 594862869883 807 117841 808 7, 1332849953 809 3500789 810 7, 277 811 137, 523079203 812 5^3 813 144589 814 3, 7, 31, 6221, 21611, 785591, 102655909 815 816 11, 191 817 71 818 3329 819 19, 6053 820 29, 103, 443 821 5, 83, 1321, 17483, 4881491 822 13 823 3^3, 8761, 201629413 824 53, 797273 825 239, 115151 826 39023 827 19, 853, 180077, 1050594287 828 5, 10939, 74363, 3000878401 829 19, 352819, 2789042449 830 9149800081 831 19, 10211, 47563, 72047 832 3, 11, 43, 839 833 2447 834 11, 19, 179, 379, 22410427631, 32909294281 835 836 29837, 178351 837 5, 13, 233, 15054791, 2044907519 838 59, 6481 839 31, 50363 840 41, 6131, 37670891 841 3, 1373, 1601 842 40949, 5546069 843 331 844 1151483 845 846 5^4, 23, 5748243233 847 17, 739, 24923 848 67, 139 849 751, 1549, 8803, 55399 850 3^5, 6907, 25884228763 851 7, 23633, 20315742701, 345194602913 852 13, 6329, 91439576471, 555520753789 853 5, 439, 306463, 1537177 854 1289, 1867, 20611, 1831153 855 7, 5003699, 2594162089 856 1114909723, 2821215913 857 7^3, 1289, 3217, 706396492363, 1134648724883, 3192914290147 858 3169, 374909 859 3, 7, 11^3, 107, 374819, 452904061 860 861 11, 29, 797 862 5, 47, 17921, 7516879 863 7, 677, 1663 864 101, 185917, 1390938630359, 6062887489201 865 43, 61, 13009 866 7681 867 13, 43, 113, 571, 3008591801 868 3 869 870 19, 37, 673, 19642399921 871 5, 740671, 9751111, 22437120037 872 71, 659, 4259, 18607481677 873 193, 311, 419, 1481, 26189, 45757, 2431279 874 1327, 21929, 36835049, 49641077 875 97, 463, 8789041, 7274227777381 876 225883992461 877 3^3, 11, 5333, 10420949921 878 5, 47, 1811 879 547 880 47660971 881 882 461, 1523567, 104204701 883 133669 884 113, 137, 227, 347, 1770427, 9177131316803 885 83, 71951486617 886 3, 17, 167 887 5, 103, 1777 888 21821, 36530537, 260809416157, 11836130643457 889 1553 890 3727, 122526881 891 281, 431, 463, 6287, 9323, 11171, 11488171 892 13, 709 893 894 13, 193, 101467 895 3, 8263, 109211429009 896 5, 71, 86561, 19943299 897 29, 25931, 7371173, 25651103 898 77477, 16781183, 3236190731 899 222931 900 7, 1429, 37049 901 9070194079 902 19, 31, 448381597799 903 5^3, 31, 47 904 3^3, 7, 37 905 31 906 7, 11, 397, 2487208351 907 11, 2467, 30871 908 7^3, 11 909 29^3, 88591, 592722853, 19847682901 910 59, 3191, 736083469307 911 5801 912 5, 7, 43403, 8127857, 148948381 913 3, 521^3, 572204387 914 97, 2843 915 3739 916 3047731 917 31, 36451 918 5722573 919 31, 727, 28573, 210290775221 920 921 5, 13^3, 560293 922 3, 151 923 421, 10963201 924 43, 705620261, 7514041403893 925 40497841 926 79, 151, 199, 654541 927 2969, 98561 928 5, 197, 7558202369, 12072985543 929 13, 23 930 29, 191, 1523 931 3^4, 71, 1721, 3823, 64958874053, 155264790283 932 29^3 933 34283, 70381, 303271 934 19, 23, 657368814491, 1224740697023, 2499317937827 935 79, 373921631, 78788384573 936 2297, 4079 937 5^4, 11, 13, 946615183 938 1097, 1279, 186379241, 2685084937, 16892529431 939 940 3, 3881 941 101, 881, 20509, 476299 942 59, 190207 943 10966324807 944 2027, 2053 945 191, 85469, 9469043294933 946 5, 2089 947 97, 6547 948 17, 283, 23911, 574645219 949 3, 7, 103, 35062463, 58204507, 3128717057 950 951 29, 739, 24329, 38603 952 271, 1123483 953 5, 7, 11, 23, 71, 409, 433, 210299, 10575751005041 954 170263 955 7, 11, 1163766306223 956 21943, 19772243 957 7, 191, 3299, 7590581, 64979339, 4329619667 958 3^3, 569, 1515227101 959 23, 4734841 960 97, 1439, 10883, 39239 961 7, 16253 962 5, 65651, 18772739 963 67, 3966939661 964 13, 106451 965 113 966 13, 2927, 78793697, 293320903 967 3, 5959361 968 181, 2083 969 1415039 970 19^3, 124183, 357649, 3964628170861 971 5^3, 41 972 433 973 19, 63017407777, 552524295209 974 53, 181, 311, 98929, 33721969, 2946957263, 118854316033 975 19, 41, 2095459 976 3 977 19, 149, 1451, 1523 978 5, 61, 307, 4857277, 15705589 979 73 980 11, 17, 67, 312601 981 43, 147989201 982 11, 3243061 983 43 984 167 985 3^3, 19, 23^3, 67, 14153, 76853893 986 987 5, 6577, 13493093 988 157 989 641135233 990 173, 349, 3299 991 13 992 17^3, 5657, 60920988451 993 17, 4283353 994 3, 17729, 1134357971 995 3829600711 996 5, 816227 997 67, 32130277 998 7, 11 999 409, 21613, 204107, 73562057 1000 20419173917 1001 324619, 11113814531, 6189477415223 1002 7, 31, 83, 742301921833 1003 3, 5, 1722323, 86440531, 1355930027 1004 7, 17, 31, 107 1005 53, 769, 1276621, 806886119387 1006 7, 13, 2417, 6899 1007 17, 89, 5812464392017 1008 98669 1009 134191, 56247187 1010 7^3, 173, 3469, 13908749837 1011 17, 11287 1012 3^4, 5, 19, 47, 3907801, 2037927389, 410283092777 1013 2676154778399 1014 19, 929, 709139, 100791227, 1909367843, 907679162881 1015 17, 47, 420919, 34461263, 3197051691277 1016 31, 43, 3613906693 1017 23, 1787, 4133, 7213 1018 17, 31, 17957, 7931408963501 1019 31 1020 16231, 22708597 1021 3, 5, 13, 97, 701, 1579, 112826390947 1022 20789 1023 769, 626852340577 1024 2267557769, 1616862242221 1025 101, 797, 3709, 9127 1026 271, 23623, 57389, 166467758603 1027 11^3, 23, 2203, 8269, 1874706913 1028 5^5, 11, 57880817, 184205599 1029 11, 17, 41 Vergleich zu meinen berechneten Erwartungswerten (expectation values) bei P^2 Fehler = (Ist - Erwartungswert) / Wurzel(Erwartungswert) Error = (effective - expectation) / Sqrt(expectation) Untere Basen von 1 bis 1029 von bis Erwartungswert Ist Fehler 10^2 10^3 403.2 378 -1.3 10^3 10^4 293.0 300 +0.4 10^4 10^5 228.6 253 +1.6 10^5 10^6 187.3 173 -1.0 10^6 10^7 158.6 155 -0.3 10^7 10^8 137.4 142 +0.4 10^8 10^9 121.2 131 +0.9 10^9 10^10 108.4 129 +2.0 10^10 10^11 98.1 100 +0.2 10^11 10^12 89.5 104 +1.5 10^12 1.2E+13 88.6 96 +0.8 New 21.04.2015 Update 07.10.2022 Richard Fischer