Known 88-digit prime factors of Googolplex + 10

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  2. Number Theory
  3. Known 88-digit prime factors of Googolplex + 10

This is a list of known 88-digit prime factors of googolplex + 10, i.e., 1010^100 + 10.

These numbers have the form 1 + 2k ∏i piei, where pi is a prime factor of 10100 − 1 and ei is zero or one.

The list of prime factors of 10100 − 1 is: 3, 3, 11, 41, 101, 251, 271, 3541, 5051, 9091, 21401, 25601, 27961, 60101, 7019801, 18 2521213001, 1410 3673319201, 7887 5943472201 and 168058 8011350901.

In the list you can see the prime factors, their discoverer and their corresponding value of k.

  1. 10122772 5475089599 0125904825 6443921599 8920424341 5723050573 0098721196 7439937842 6221522663 (Patrick Demichel, k=22669)
  2. 10546133 4066771856 3668495874 2269981049 9818275880 0192270253 3885047736 3850219994 2088256931 (Patrick Demichel, k=2357485)
  3. 10690762 2849726895 2743749077 7983637712 8759350453 1251340309 1609077348 3984398624 6742988167 (Phil Carmody, k=2401)
  4. 10972149 6700987229 7721459321 3265951505 2921579970 7153667505 2791822283 3584228080 7259000597 (Patrick Demichel, k=1336058)
  5. 11251362 4540909303 3047090809 2089154712 3977421167 6033830194 8518330470 9069669641 6066575881 (Phil Carmody, k=340)
  6. 11537483 0650083314 6811928935 2535998244 4398831673 9223960197 5898817652 4516223665 2191481223 (Phil Carmody, k=689)
  7. 12800222 3609562174 5397146758 7235002534 2054322554 9627834250 4845928289 5085390883 1849681823 (Patrick Demichel, k=1995427)
  8. 13497956 5952238202 0225384383 9568295467 4257425742 5756072214 0209663944 5967958641 3825721211 (Patrick Demichel, k=209595)
  9. 13714783 2986402321 0928098253 7132573986 0730564164 0716849380 7744161842 9802465910 3597990179 (Phil Carmody, k=4911)
  10. 13719344 5839878882 0588135909 8520724174 5320530923 4693188421 1160409805 5267604986 3841255099 (Phil Carmody, k=3141)
  11. 13876762 7787099581 8177977501 8747442937 5212637509 2124911072 6721139397 1469358228 6330922863 (Paul Leyland, k=30719)
  12. 13904716 3414210905 3406353531 2579576763 2315819606 7698085109 5730030512 1090533924 4895396371 (Phil Carmody, k=2365)
  13. 13994619 1132751232 0926440631 7849292569 0890001830 2538079076 9425957667 9256584888 9520313019 (David Broadhurst, k=1)
  14. 14338925 8324377602 4374047745 3650872090 0000000000 0014338925 8324377602 4374047745 3650872091 (Patrick Demichel, k=1592505)
  15. 14868981 9495131313 3132832619 5360690724 4523760145 3230913498 7799527388 1535313302 1540995687 (Patrick Demichel, k=24307)
  16. 15045028 6853153960 2271010780 4933393151 0420943456 9594101571 7274097417 1850067323 5354336609 (Phil Carmody, k=368)
  17. 15801813 4517729497 4031596635 0691117199 2619926199 2604124385 8102196701 8588329564 1928809001 (Paul Leyland, k=30500)
  18. 15940033 9064880278 1157301699 4664270926 9185113113 0830826920 8249993391 1972188586 3849384041 (David Broadhurst, k=20)
  19. 16264213 4305516637 8664319906 1773973364 7736477364 7720213151 3430960726 9072157458 5962504001 (Patrick Demichel, k=628000)
  20. 16467415 6354487176 6646927420 8732255529 6846695739 6830228324 0492208563 0199768318 8114440211 (Patrick Demichel, k=412495)
  21. 18641686 5564300094 8422162426 6439493519 2444724447 2426082760 6880424352 4022562020 6005230929 (Phil Carmody, k=18488)
  22. 18750614 6849802831 9015106748 5263473153 5267748135 5248997520 8417945303 6252641387 0004274983 (David Broadhurst, k=7)
  23. 19506046 9579264175 1840578418 1447887999 9109166236 8366122575 8010405087 9808499085 0222118047 (Patrick Demichel, k=71727)
  24. 19828633 0489435717 9571047883 5790029062 0000000000 0019828633 0489435717 9571047883 5790029063 (Phil Carmody, k=269)
  25. 20131590 5030073621 6874130482 0914594041 9455422528 0564709062 4485496149 7418707954 0370016571 (Patrick Demichel, k=41645)
  26. 22362132 9265630342 1934883914 0883111046 3056752441 6965609691 2322382783 8878131472 3939863489 (Phil Carmody, k=2336)
  27. 23128860 7777109351 1078499233 8125020922 9601004358 9577875498 1823895007 8522505125 1475983437 (David Broadhurst, k=2)
  28. 24929841 3178368019 6801967770 3817836236 0000000000 0024929841 3178368019 6801967770 3817836237 (Patrick Demichel, k=87926)
  29. 24971342 9760041131 3191264823 5231083638 3935456666 0208248142 2910319514 1142132844 2820389659 (Patrick Demichel, k=105981)
  30. 26202194 9011528522 1233862138 1826633758 6212328353 6483380172 2649024510 2510593866 7319173757 (David Broadhurst, k=62)
  31. 27988210 1895480796 9125025120 3937478745 6361151797 1179190616 8314368738 1849579051 9686660693 (Patrick Demichel, k=1220494)
  32. 28144773 8179390284 2934357407 5128682038 3556411967 6471732806 1735802251 9377945439 8685094007 (Patrick Demichel, k=309927)
  33. 28193433 4597760436 6012120489 5819703499 1126511265 1098317831 6528750828 5114390775 5306807767 (David Broadhurst, k=1)
  34. 31112785 6389203546 7395668857 6673567438 7750342503 2280770282 4139546049 9645326354 4423909943 (Patrick Demichel, k=27709)
  35. 34173858 7391224771 6378327866 1599640604 9850316684 9816142826 2459091913 3471988818 8250676081 (David Broadhurst, k=40)
  36. 36744450 6282674499 6248988711 5163981380 5386770553 4005059503 1281764315 5963963553 3708935659 (Patrick Demichel, k=527001)
  37. 38109305 8970402476 5197887568 0681951766 0000000000 0038109305 8970402476 5197887568 0681951767 (David Broadhurst, k=47)
  38. 40571854 8261116071 0179195508 2557158678 8933233018 1528796050 3675772027 2210172736 1926490931 (Patrick Demichel, k=71935)
  39. 40955507 2972232918 1782546635 0207412452 4258683987 5782271519 7230916905 7523862647 4466096441 (Patrick Demichel, k=9580)
  40. 43783423 5173928322 3535985675 4840467194 7558060441 1578022037 5651064389 7249166399 1442692849 (David Broadhurst, k=56)
  41. 44034313 1143158684 2140051833 6877516472 7732505068 6174526532 3999704950 1449026940 1133873059 (David Broadhurst, k=1)
  42. 45619725 8309245693 9265576170 0993862601 4696183970 5349435755 3005429664 4569392199 5690046573 (Phil Carmody, k=3254)
  43. 45957814 0375966835 4151594784 0047684387 2452197249 2406239435 2076230413 8300602465 2404512863 (Phil Carmody, k=289)
  44. 46487569 5727611495 7328641028 5938122344 9665376813 7213609383 1667426338 7668921358 6850233823 (Phil Carmody, k=4089)
  45. 49301622 6193195935 3291648016 0990534003 3698115592 6351186029 9891311527 9593532423 4688649597 (Patrick Demichel, k=309398)
  46. 49635881 9133524151 3880591286 0464511203 3172682375 3160427924 1819168503 8264101742 9823259253 (Paul Leyland, k=34234)
  47. 52071576 8585183309 0745599808 6407532303 7517284481 0697508517 6690391863 7702507687 1601920453 (John Gamble, k=16734)
  48. 52895742 3139714813 4027372040 5452821084 5130348696 5077452954 1990633883 1102976655 9677527613 (Patrick Demichel, k=1445054)
  49. 53429755 2586723940 9542977698 9918879065 6103891782 1720290539 6050227044 0640629984 3115997251 (Patrick Demichel, k=104125)
  50. 54495372 5860290556 0554877498 2654381724 3683761937 2155162978 9775662616 2252390415 0511451927 (Phil Carmody, k=1277)
  51. 56327001 9876254428 2445622322 1918728888 0000000000 0056327001 9876254428 2445622322 1918728889 (John Gamble, k=14436)
  52. 59563525 5090522881 7515930889 1568171976 5227756325 4831807200 0318279207 2288174563 6795928303 (Patrick Demichel, k=998047)
  53. 60159357 1990043592 4098461867 4838400689 7121771217 7061611860 5131727625 3023309350 2283370529 (David Broadhurst, k=16)
  54. 61449712 2169421453 0544752016 1770113608 6666666666 6605216954 4497245213 6121914650 4896553059 (David Broadhurst, k=13)
  55. 62019789 2872609850 9993673327 1078504880 8001144451 2060875338 0873754302 1992528875 9079649333 (Phil Carmody, k=254)
  56. 62925408 4637166487 5536034141 7004812859 2184788872 7878136535 6821955360 3351245268 9189601733 (David Broadhurst, k=2)
  57. 63295595 1506561246 1463777629 3185104422 5143535933 4721895456 1263187318 4942874518 7709767881 (Patrick Demichel, k=2277060)
  58. 66187006 1468692629 2007908032 6692707316 1270827449 8795359556 2739520079 0737080582 7963534767 (David Broadhurst, k=1)
  59. 68218498 8670737591 7274255004 0832931232 4322390642 4254172143 5651653050 7048135638 3489459411 (David Broadhurst, k=5)
  60. 68601124 7421821019 3699185144 2432036888 2433900760 5871275731 4693354641 6224755456 9882341961 (Patrick Demichel, k=658220)
  61. 71203586 3137632665 3147971161 5345394718 9322868463 0748335123 2460501128 3825102698 4668263183 (David Broadhurst, k=9)
  62. 71841921 7393237983 0014148202 8460743140 8197512978 3822882212 0286346708 5354679516 5792546731 (David Broadhurst, k=5)
  63. 80650782 1097338918 8562487935 2689923967 0288248337 0207597554 9190909418 1725760401 7598324371 (Phil Carmody, k=2565)
  64. 82065916 8841676010 7696376485 1675523116 0377911855 8941264265 7113925088 1605838159 5794022207 (Phil Carmody, k=19597)
  65. 83358740 0690621933 5628426727 5462828839 7821782178 2261576561 8512404111 7806644549 3284611019 (David Broadhurst, k=91)
  66. 84294020 9416359069 2373958369 4819737761 0168201645 4977988004 6873402663 3802954422 3319162757 (Patrick Demichel, k=562582)
  67. 85619904 0735415898 0918317979 3083579783 2884965170 0837357540 8158260418 3081277956 9688536447 (Patrick Demichel, k=1265207)
  68. 86726925 5527569861 0698355306 7436697481 0829409634 1818379919 7931321844 8338225642 1878767931 (Phil Carmody, k=235)
  69. 89695009 4386886372 2358793245 2815911516 0000000000 0089695009 4386886372 2358793245 2815911517 (Patrick Demichel, k=2275798)
  70. 90934639 9849113260 5743587037 8717501022 4205858159 5885076480 4054971420 1537728878 2923359183 (Patrick Demichel, k=42427)
  71. 92216168 3936024009 0075658363 0719888467 1588678293 3405619371 2104126937 5363238368 2714550023 (Phil Carmody, k=4979)
  72. 94251612 9361146431 4121799963 5697435262 0000000000 0094251612 9361146431 4121799963 5697435263 (Patrick Demichel, k=72467)
  73. 94683286 9251656148 4966371756 2903427512 3318778916 4621697285 7317777039 2925275407 5153838183 (Phil Carmody, k=699)
  74. 95001386 5510329844 2335255879 2725377820 2304433775 7790567610 7814763620 0030822103 5029811597 (David Broadhurst, k=2)

Phil Carmody is organizing a distributed computing project in order to find more factors of Googolplex + 10. If you like these pages I would appreciate that you donate some idle cycles of your computer. You will be cited as the discoverer of the factors you find.