Known 85-digit prime factors of Googolplex + 10

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  2. Number Theory
  3. Known 85-digit prime factors of Googolplex + 10

This is a list of known 85-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. 10309 2503849771 0241623093 1382523809 7198531488 2801478820 9702381259 3043091604 8581055299 (Phil Carmody, k=1851)
  2. 10382 5885706275 4076922676 4066165132 4704463445 5295546937 0590169720 9372459230 8770628579 (David Broadhurst, k=1)
  3. 10407 0006360470 7523444834 4527259201 7782705099 7782694692 7776344629 0259260265 3255445899 (David Broadhurst, k=1)
  4. 10834 3288934223 2225915952 5816154368 3289117205 2111059531 2566098667 9494605158 1220404183 (Patrick Demichel, k=599797)
  5. 10957 2061055370 3614962217 6809866790 8888062338 7795198481 1576561512 0727465593 2822602597 (John Gamble, k=17846)
  6. 11236 7290786938 9364931190 0073146394 1782517766 5292802300 1794528569 2191749215 1906496087 (Patrick Demichel, k=1026581)
  7. 11352 9299568048 1005749710 5346247520 9963287207 0036724145 9262855255 1042462503 5309534729 (Norm Dresner, k=13436)
  8. 11446 7074875980 3352920355 4587762132 2097990673 7673871855 3283344999 5714456383 3742441451 (Patrick Demichel, k=6025)
  9. 11578 3844914978 6055564820 2836679091 8091422505 7122978184 3342304107 1693863949 8187049037 (Phil Carmody, k=142)
  10. 11591 5258673225 0500400754 4137295295 5577411394 4422600197 0836084619 4922989359 9714706691 (Phil Carmody, k=19605)
  11. 12229 6654121340 9641254815 3079143673 1100237388 8899774840 7754358729 8541017426 4179381063 (Patrick Demichel, k=550189)
  12. 12442 8158338281 3828138281 2583856698 0000000000 0000012442 8158338281 3828138281 2583856699 (Patrick Demichel, k=2478599)
  13. 12657 5464822178 8889670655 6268635942 1648830253 7264328232 3129096460 1597691828 3155113247 (Patrick Demichel, k=1924837)
  14. 12753 5870876140 5630953999 2605409496 9279939824 0684299814 2626731506 8022034624 1031120607 (Patrick Demichel, k=251247)
  15. 13013 9754006218 2959317507 8486633987 6480903091 1275133206 1289958590 7349795243 6135376453 (Patrick Demichel, k=8342)
  16. 13086 2291383055 6340016944 2351360141 8034453544 1965559542 0325836599 8305563400 0385813687 (Phil Carmody, k=4587)
  17. 13515 1501845262 8416207925 6810687305 6458627506 3541386008 7960472769 1957580419 3269314813 (Phil Carmody, k=1974)
  18. 13968 8873866937 2536357947 8691270592 9982929438 9982915470 1109062501 7446571491 1291658847 (Patrick Demichel, k=5677)
  19. 14150 6401586253 6883542736 5924782017 7747143880 8249442706 2139445763 2049994303 4306357939 (Phil Carmody, k=311)
  20. 14527 0886387998 0678852322 5575423151 2017738359 2017723832 1131350361 1338886036 6442315209 (Phil Carmody, k=1636)
  21. 14658 7547715127 1785510957 9649026610 3862944874 2247117870 2524285398 6512273409 7414236007 (Patrick Demichel, k=249191)
  22. 14664 3304853248 7945672704 3183220200 2620793247 7379221416 5925646496 5324879456 5804013449 (Patrick Demichel, k=131468)
  23. 14760 9612755263 0294778394 5338384631 5698447893 5698433132 6085692630 5403669499 0360063263 (Paul Leyland, k=39659)
  24. 14770 5460330369 9418347845 9928284999 2906689830 2464782985 9227571605 3230015447 4030628813 (David Broadhurst, k=2)
  25. 15480 0806194764 0988876334 3109526318 5853658536 5853643056 5047463772 4864782202 2744132219 (Patrick Demichel, k=320531)
  26. 16212 8441709542 0505566474 1410860212 8189801341 0300901431 1624172355 9628536535 0353540447 (David Broadhurst, k=1)
  27. 17046 1692789245 4222731337 5575852519 3895450920 6104566125 5588240166 0327280416 9471303441 (Patrick Demichel, k=2081480)
  28. 17595 2145203114 5667905176 0475297685 1816535945 2046978097 6562860505 3381160748 4548534851 (Patrick Demichel, k=1831475)
  29. 17654 6571634132 1789213571 4409397612 3259912838 8312726318 9140855026 8938276713 5527184201 (Patrick Demichel, k=149900)
  30. 17669 6525503003 4154248759 0444456306 2542239703 7457777965 9067742707 1612009055 2986696011 (Patrick Demichel, k=161945)
  31. 17724 6417107897 2492220308 9737122237 5036863714 5714423169 9795041394 2831568826 0595508529 (Patrick Demichel, k=1415576)
  32. 18011 9770104200 7382850589 8939301901 7802924418 2197093593 7573028618 9579926171 6742226321 (Patrick Demichel, k=1946840)
  33. 18050 3140974720 8074407097 5548806130 5546487841 4453530208 8687462562 2527919256 1095293973 (David Broadhurst, k=2)
  34. 18088 8496181988 4354963284 9689616544 3951549855 6048468233 2447731844 0403413429 3641166401 (Patrick Demichel, k=8800)
  35. 18622 0840449344 1262120804 7993973966 3300984107 5428289090 2763420029 3512269841 9140898437 (Patrick Demichel, k=41846)
  36. 19191 7584420596 0079402774 0338444751 8019801980 1980217211 5604222576 2059600793 8358246733 (Patrick Demichel, k=1715962)
  37. 19599 6728555980 0000177353 1373188694 4402177351 5597842248 1130733331 5598000001 5775366047 (David Broadhurst, k=41)
  38. 22295 6029030925 5013052740 0602961733 7388471396 2611550899 3417502321 7624581343 7991433131 (Patrick Demichel, k=66535)
  39. 22590 3334235382 5158616581 2972639733 7887353856 6487861135 8624222162 8045036796 0217284489 (Patrick Demichel, k=837956)
  40. 22861 7415654577 8513705657 0742465440 0000000000 0000022861 7415654577 8513705657 0742465441 (Norm Dresner, k=12880)
  41. 23600 3074158499 8585737648 3265835842 9976230318 9976206718 6902071819 1390492670 6710394477 (Patrick Demichel, k=872326)
  42. 24198 1220265137 4687841122 4611364276 4201494333 6020156792 5245389693 5296582891 4198126743 (Patrick Demichel, k=9929)
  43. 24389 1784297313 7302113087 8245182368 9581619377 6847482931 4879088050 8878199617 9140832179 (Patrick Demichel, k=78241)
  44. 25283 3590310600 7866395105 4570368684 8879719139 4485973936 4596450265 6840621823 8144685253 (David Broadhurst, k=2)
  45. 25632 2569724254 6089479598 3684166299 9996359263 8859924999 6749541364 4542397384 7810906091 (Phil Carmody, k=145)
  46. 25643 4198444781 2848371907 5458303815 3657676244 9876067639 3932891795 4776126853 3869977499 (Phil Carmody, k=173)
  47. 26988 4088440528 0359255952 6497739695 4640234186 9389761742 1848566575 1572603654 9979754441 (Patrick Demichel, k=128380)
  48. 28582 8358037443 7443744374 7232721024 1188118811 8811909770 9546156255 6255625562 8420839837 (Phil Carmody, k=322)
  49. 28874 9540373306 5276401960 3399855926 4547469633 8730707691 1899526606 2298956119 7482275063 (David Broadhurst, k=19)
  50. 29268 9054622237 8760844919 7169282035 2419987712 0529243733 1890410019 8113706245 1176264973 (David Broadhurst, k=34)
  51. 30364 2132575172 5770186580 7146712832 9900990099 0099040265 2033565271 5869196481 7047702933 (John Gamble, k=15034)
  52. 30446 6686883962 9179107272 4463169158 4507669979 5492360467 1194553942 4671437292 8970839139 (Phil Carmody, k=2651)
  53. 31208 7534360650 7191452250 6766963146 2992474546 2594036963 0039787202 3131699586 4193638891 (Phil Carmody, k=245)
  54. 31335 9374204484 2589819977 6047070487 9966416787 7887560405 9546940634 4543504352 8581664179 (Phil Carmody, k=313)
  55. 31587 9373669178 0205539857 4098841612 0000000000 0000031587 9373669178 0205539857 4098841613 (Patrick Demichel, k=160166)
  56. 31611 5991206737 0146384529 1338391350 2772277227 7227754383 8763483964 7374107301 4110668579 (Patrick Demichel, k=9001)
  57. 31785 6638733559 0990749340 1025817884 5843517174 5843485388 9204783615 4852767834 4817699291 (Patrick Demichel, k=698805)
  58. 32279 2192098011 0812316752 0487103499 1526715267 1526682987 9334617256 0714398515 1039611769 (Patrick Demichel, k=811748)
  59. 33998 9662213490 1072608622 5148814922 1441506700 4708404972 4209572094 8257344293 0954046361 (David Broadhurst, k=20)
  60. 34043 1804853587 1894155023 2028835381 7528077372 0098951230 3293430784 4933955057 5589424693 (Phil Carmody, k=2146)
  61. 35080 4335673934 3335060588 0374130951 4112797028 0913277552 5169490579 4029171930 8550587487 (Patrick Demichel, k=728761)
  62. 35133 4946943391 9550123422 3991173667 0970674260 6504492685 4007002678 4239577986 5154352237 (Phil Carmody, k=2146)
  63. 37089 5234099082 0903446959 2128579022 3081396637 2130034605 4858980852 6621903901 8071824881 (Patrick Demichel, k=112280)
  64. 38610 8404535861 0718726825 8768486833 9550733163 5311620550 2193967215 9808781669 2008176921 (Patrick Demichel, k=131020)
  65. 38920 0981781070 1984492765 1221382633 2299961731 0860091165 4851101048 2354203751 6281864157 (Patrick Demichel, k=49426)
  66. 39698 8985637335 8279454212 6905547479 4545871418 5454168280 3531508754 3733582794 1451418899 (David Broadhurst, k=1)
  67. 39706 4026800657 8680407297 7494116990 0203331301 9796708404 4230131959 8477075995 7697448293 (David Broadhurst, k=2)
  68. 40256 3138014429 9941479289 6150395639 2245087106 6707715998 8468740710 7219195464 0876805853 (Phil Carmody, k=3926)
  69. 40314 9230072470 8647005088 3112268669 2891536870 0311611546 2545562353 3249353511 3700349691 (Phil Carmody, k=1415)
  70. 42127 9871961829 8058915094 5535629258 3030303030 3030260902 3158341200 4971387935 7494673773 (David Broadhurst, k=82)
  71. 42940 7621741660 2002258340 2291817877 6168278362 3831764578 3790020022 5833979977 8460096241 (Phil Carmody, k=3880)
  72. 43046 1291554180 4525994264 3236055848 8885043510 0913505384 5261870814 1192605468 7960769249 (Patrick Demichel, k=42896)
  73. 45597 2323588625 8132189821 1221443902 7636856964 7636811367 5313268338 9504667143 6415413063 (David Broadhurst, k=37)
  74. 45740 2763336102 7927031000 6400539415 4203254868 0031828558 8341110529 5386643639 0011624437 (Patrick Demichel, k=7362)
  75. 45867 4253090650 2905185201 1471624338 0688472790 0688426922 6435382139 7783287588 9216848453 (David Broadhurst, k=2)
  76. 46390 5935331544 7613668455 7025390898 0768144591 9231901798 6703476136 6845523863 7793535491 (David Broadhurst, k=5)
  77. 46409 6998339070 9632927253 1693356820 3519273706 0197482051 9935254388 1911032988 5326170783 (Patrick Demichel, k=434619)
  78. 46660 1886458075 7537518440 3870089104 4783822219 4617814314 8557795340 1576858017 1072036853 (Patrick Demichel, k=9234)
  79. 46736 1524450603 8408282729 0251435359 3347898646 6652148089 4872349250 5060384082 3599334007 (David Broadhurst, k=1)
  80. 47384 6574863558 7904259724 7570173665 7951902662 8151058465 4086202450 6382304292 6397665253 (David Broadhurst, k=2)
  81. 47944 2275602095 3489321193 7940378636 2304433775 7695614168 4580035871 1184887418 0244812413 (David Broadhurst, k=2)
  82. 48608 9839279695 9927845457 1529948162 4990005591 0140573292 0085770204 0631255949 0660151089 (Patrick Demichel, k=3056456)
  83. 50534 6926704969 6779844448 2896873598 4248067104 5498576664 8643699379 9299052430 6768241481 (Patrick Demichel, k=77260)
  84. 50637 0346441416 8072121872 4657825110 3636363636 3636312999 3289922219 5564241763 8978538527 (Patrick Demichel, k=110927)
  85. 50703 4157135910 9578632517 1866887235 4249132720 5750917982 8406268631 5329499796 6116019957 (Patrick Demichel, k=54162)
  86. 50874 5249292075 0792492075 5879944568 0000000000 0000050874 5249292075 0792492075 5879944569 (Norm Dresner, k=11324)
  87. 51499 4036372022 8646582590 0410883359 9999999999 9999948500 5963627977 1353417409 9589116641 (Patrick Demichel, k=772880)
  88. 55925 3040902932 2206174891 0092669460 3626523122 6286055385 4622481778 8629152709 7593544771 (Patrick Demichel, k=625465)
  89. 55973 7550768260 4848346788 9050172048 0000000000 0000055973 7550768260 4848346788 9050172049 (Patrick Demichel, k=478936)
  90. 57961 0449275573 0651856628 1587616415 0586910126 9413147834 1036185700 0064946501 2174526543 (Patrick Demichel, k=1021469)
  91. 58556 5809350144 6714785906 5211646373 5961974547 6800194576 2119354929 6194527550 5556178369 (Patrick Demichel, k=120416)
  92. 58733 6153243029 7611737241 0234604562 1914713357 8085345375 8067956387 5697023883 2149317921 (John Gamble, k=15440)
  93. 60050 9775513488 5661064966 6621256038 5908685236 7980338333 2308470553 0128098357 7853166251 (Patrick Demichel, k=23125)
  94. 60354 0419865458 5744309300 1504527265 0527881780 3389288189 7733768666 0164866941 3848765379 (David Broadhurst, k=83)
  95. 64803 8276175403 2563702951 2348107797 6561454884 2781382918 3348636759 9725647012 0657453733 (Patrick Demichel, k=152066)
  96. 67657 6203201177 0671998622 5646964672 0862546495 6165132058 6659840154 7925296151 5864953011 (Patrick Demichel, k=663745)
  97. 75028 0923753237 1332464269 3144874825 2632273210 7367801817 3556026447 8700191058 5777148037 (Patrick Demichel, k=2454086)
  98. 76590 1974342108 0755253891 8531506692 4878048780 4877972190 2903706672 4122794888 6346542089 (Patrick Demichel, k=93436)
  99. 78078 1925233460 5565847355 8182131992 6835236407 3164841670 8760469867 8730610948 5017368401 (Norm Dresner, k=13800)
  100. 78857 8617208357 9870188693 2303130344 1831395206 3823348221 0305820314 5307820058 9687627413 (David Broadhurst, k=2)
  101. 85682 3825760211 6114615196 8371052895 3452536553 6161614217 8471397855 9489315779 0898216727 (Patrick Demichel, k=560027)
  102. 87003 5161657045 5434324417 2497151804 4012862177 0514770125 2118064255 1234776494 5367770093 (David Broadhurst, k=14)
  103. 87895 5211189961 0736101990 1369008140 2818916175 7181171719 8030106136 7917185814 4187924317 (Patrick Demichel, k=116306)
  104. 87942 7202323602 9837108977 8214192735 0441056776 4359004866 1844949764 2263025209 0282694571 (Patrick Demichel, k=3016085)
  105. 88564 9748133333 3333333332 4476835852 0000000000 0000088564 9748133333 3333333332 4476835853 (Patrick Demichel, k=239102)
  106. 89071 8186361258 3172953770 0585084357 6653386454 1832580250 8905272207 8181627903 2482644727 (Phil Carmody, k=167)
  107. 90005 6063757467 3802587801 2476870033 2464595055 0504497130 2201669106 1813858372 3931498533 (Phil Carmody, k=174)
  108. 90826 3406353295 8864970198 4724131018 4711218300 6065314763 9115199591 9304969147 4716843767 (John Gamble, k=17537)
  109. 91963 9336920939 0300529473 3968225398 9300484780 9330297961 6187572065 8177563830 5024329847 (John Gamble, k=17071)
  110. 93937 4434544554 4554455446 4839288899 9009900990 0990192947 3444445544 5544554456 3849189891 (Phil Carmody, k=665)
  111. 97682 4481928561 3216908415 2315271539 3877435752 6122661929 8359364313 9339472662 6192707293 (David Broadhurst, k=2)
  112. 98537 1035359519 8198939079 7970206925 2079207920 7920890616 3114567440 6119731159 0049414847 (David Broadhurst, k=27)
  113. 98789 2367067997 7346699208 2045788240 0093928212 0093829422 7726860214 2747229003 8048139973 (Patrick Demichel, k=1754374)
  114. 99418 5184728695 1379336728 3217852068 4719622255 3606958003 4232337604 8935818446 0613961207 (Patrick Demichel, k=1346491)

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.