Modulo 4 Run 1 (mod 4) 3 (mod 4) 1,3,..(mod 4) 3,1,..(mod 4) --- --------- --------- ------------- ------------- 1 5 3 97 211 2 13 7 17 11 3 89 739 773 3 4 389 199 281 23 5 2593 883 317 47 6 12401 13127 409 167 7 77069 463 8009 131 8 262897 36551 6229 2011 9 11593 39607 233 17903 10 373649 183091 23633 25771 11 766261 4468903 228601 34499 12 3358169 6419299 1013 65867 13 12204889 241603 9341 49523 14 18256561 11739307 325217 90659 15 23048897 9177431 521 115979 16 12270077 95949311 51749 819583 17 297387757 105639091 505049 1865719 18 310523021 341118307 3773941 1391087 19 297779117 1800380579 5414081 2264839 20 3670889597 727334879 2556713 25123303 21 5344989829 9449915743 17123893 142003427 22 1481666377 1786054147 2569529 20855239 23 2572421893 22964264027 15090641 38907623 24 1113443017 54870713243 49008077 18246451 25 121117598053 79263248027 855234581 6160043 26 84676452781 454648144571 1756321181 1557431471 27 790457451349 722204126767 43679609 152226383 28 3498519134533 1749300591127 198572029 1450303451 29 689101181569 5070807638111 701575297 7152451231 30 3289884073409 8858854801319 7197633617 5552898499 31 0 6425403612031 12661191689 6639843979 32 0 113391385603 103272232741 61233611783 33 3278744415797 0 170951814773 9005520203 34 0 0 626798928989 99052377023 35 0 0 521204950769 380268915347 36 0 0 148638667361 946617613831 37 0 0 438921167921 0 38 0 0 0 929291719511 Jim Fougeron found some of the long congruent runs in http://www.primepuzzles.net/puzzles/puzz_256.htm The 32-run at 113391385603 was the first congruent run above 26. Modulo 6 Run 1 (mod 6) 5 (mod 6) 1,5,..(mod 6) 5,1,..(mod 6) --- --------- --------- ------------- ------------- 1 7 5 157 53 2 31 23 79 29 3 151 47 67 239 4 3049 251 37 137 5 7351 1889 1039 449 6 1741 7793 757 179 7 19471 43451 5569 5 8 118801 243161 2719 389 9 498259 726893 277 89 10 148531 759821 15667 2213 11 406951 2280857 11149 128903 12 2513803 1820111 10369 31469 13 2339041 10141499 8527 6761 14 89089369 40727657 113341 729269 15 51662593 19725473 780823 80447 16 73451737 136209239 151909 1303931 17 232301497 744771077 43777 1485353 18 450988159 400414121 2964553 7406639 19 1558562197 1057859471 4397803 1457333 20 2506152301 489144599 175573 1295219 21 1444257673 13160911739 6510079 809 22 28265029657 766319189 3954889 87902999 23 24061965043 38451670931 153544819 121930481 24 87996684091 119618704427 96050953 153576737 25 43553959717 21549657539 15186319 590121509 26 502429570231 141116164769 296080717 858510551 27 1820249525317 140432294381 98380549 3354061163 28 1892672756731 437339303279 131125681 77011289 29 4236406530997 1871100711071 2720227693 11048169689 30 2155866992887 3258583681877 52881047647 5696814287 31 1552841185921 5611314737339 25183752283 1572386903 32 0 24738041398529 4136299357 27799525007 33 0 0 95832732277 288413159 34 0 0 191765532499 62585146739 35 0 41173225034771 114058236679 348989218973 36 0 0 290614512109 405541876307 37 0 0 0 0 38 0 0 143014298809 0 Modulo 7 Run 1 (mod 7) 2 (mod 7) 3 (mod 7) 4 (mod 7) 5 (mod 7) 6 (mod 7) --- --------- --------- --------- --------- --------- --------- 1 29 2 3 11 5 13 2 113 317 773 3833 2357 293 3 37997 27197 5939 13339 106979 53731 4 575261 158867 341687 621527 637201 709547 5 12089267 894287 2617429 6760009 2809889 2993171 6 16292389 12883313 6996307 99641903 50503213 361718083 7 9984437 28648489 1232089337 49297819 345638333 279470351 8 1523792929 2428644899 4130894953 887048411 8295635297 3194228239 9 72027611573 62425749731 84834279799 137875952281 45914196389 19417691299 10 469100516641 288991234079 595178892367 208220255429 73838834753 314183482199 11 7384176068963 6201133988723 49722411511 3400274815627 3313036899877 2955453870529 12 0 0 2016473757721 0 0 0 Modulo 8 Run 1 (mod 8) 3 (mod 8) 5 (mod 8) 7 (mod 8) --- --------- --------- --------- --------- 1 17 3 5 7 2 89 491 389 359 3 2593 2243 2213 1823 4 20809 42299 45013 79063 5 208393 274123 73133 272863 6 2663897 4701443 1319861 989647 7 7336457 4310083 3250469 12955687 8 128910097 9065867 29662253 10604519 9 42453937 547580443 35677501 1062619847 10 1506473153 1885434347 101341613 309202951 11 24771906961 8674616939 13576124357 1383423311 12 123737745289 11312238283 12664911341 21120585463 13 201975758113 19201563659 124809839701 848540003159 14 152368449001 619849118491 132932904029 714231497663 15 4990160038937 4056100954547 1181960064853 534956098463 16 0 0 0 925195153703 Modulo 9 Run 1 (mod 9) 2 (mod 9) 4 (mod 9) 5 (mod 9) 7 (mod 9) 8 (mod 9) --- --------- --------- --------- --------- --------- --------- 1 19 2 13 5 7 17 2 523 5483 1381 1913 1069 1259 3 15823 25373 78241 20183 56131 22193 4 655453 182243 107509 74453 76543 132893 5 19256491 8606603 5321191 12859961 32820883 24143993 6 24084793 5379113 89121073 131695853 39874273 166539707 7 303392377 1734847733 561940843 18410243 399481171 285688421 8 3408167431 12196390601 1324001281 1248749069 716230591 881160173 9 17875882441 17619405959 34344033133 147779659553 10930792111 41142907853 10 179445819277 213529133423 1209605011789 435916100219 168445529647 283892437529 11 1563518842687 2732797330031 3877795268653 2113591441739 1379581580653 2133943155503 12 0 0 0 0 4016465016163 0 Modulo 10 Run 1 (mod 10) 3 (mod 10) 7 (mod 10) 9 (mod 10) --- ---------- ---------- ---------- ---------- 1 11 3 7 19 2 181 283 337 139 3 4831 6793 1627 3089 4 22501 22963 57427 18839 5 216401 752023 192637 123229 6 2229971 2707163 776257 2134519 7 3873011 58339093 15328637 12130109 8 91335901 44923183 70275277 23884639 9 36539311 961129823 244650317 363289219 10 196943081 1147752443 4075366567 9568590299 11 14293856441 6879806623 452942827 24037796539 12 363373386721 131145172583 73712513057 130426565719 13 381206903941 177746482483 319931193737 405033487139 14 154351758091 795537219143 2618698284817 3553144754209 15 0 4028596340953 0 4010803176619 16 0 6987191424553 0 0 Modulo 11 Run 1 (mod 11) 2 (mod 11) 3 (mod 11) 4 (mod 11) 5 (mod 11) --- ---------- ---------- ---------- ---------- ---------- 1 23 2 3 37 5 2 2311 10111 6427 1951 2557 3 452453 1066067 1503967 1023653 259033 4 5442361 2078221 52636411 11488261 6402181 5 2880836267 1322239547 145255861 396185431 236298529 6 4436243989 9429065747 12933776221 16535952019 13930111453 7 56675840497 55612826029 44742288583 195520526821 85272006649 8 1901256504247 4524017321287 4995900592103 9570670849997 1825518960479 9 0 0 0 0 3917068823123 Run 6 (mod 11) 7 (mod 11) 8 (mod 11) 9 (mod 11) 10 (mod 11) --- ---------- ---------- ---------- ---------- ----------- 1 17 7 19 31 43 2 3229 1129 15683 8017 3739 3 674603 444187 376307 466651 846757 4 13906261 24780961 1736281 12202507 16601881 5 222022037 258318287 140369941 222838097 267746797 6 11087576671 10550203099 1180181747 9725254999 6285546277 7 90331649557 81795872209 272006616241 288595010317 94043028529 8 0 492755092111 1204047928861 2217422600941 1328517155569 9 0 0 4682876776597 0 0 Modulo 12 The same value mod 12 means the same value both mod 4 and mod 6. Run 1 (mod 12) 5 (mod 12) 7 (mod 12) 11 (mod 12) --- ---------- ---------- ---------- ----------- 1 13 5 7 11 2 661 509 619 467 3 8317 4397 199 1499 4 12829 42509 32443 16763 5 586153 657197 407023 260339 6 1081417 647417 180799 2003387 7 10793941 1248869 4338787 7722419 8 7790917 13175609 84885631 20221283 9 682829881 234946997 472798219 927161471 10 1921572157 1039154933 1786054267 4284484931 11 370861009 7114719473 6024282871 7355362139 12 5637496849 183420597029 64791932287 84805717127 13 289391626057 32021552837 592175010019 478527373859 14 469257742237 1237381737257 6265824724519 2046207697631 15 628337233501 5760582040217 7816088451907 7302359785151 16 0 9194779588901 0 0 17 0 2904797643617 0 0OEIS shows that many of the above mod 12 values were first computed by Giovanni Resta.
By Jens Kruse Andersen. home
Last updated 6 February 2011.