Known 83-digit prime factors of Googolplex + 10

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  2. Number Theory
  3. Known 83-digit prime factors of Googolplex + 10

This is a list of known 83-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. 100 8067248915 2033119456 5371295214 3168316831 6831683269 1235565746 8864802624 8539612047 (Phil Carmody, k=403)
  2. 103 3642649393 3871421018 5880296648 0000000000 0000000103 3642649393 3871421018 5880296649 (Patrick Demichel, k=294636)
  3. 103 3704126470 1366089874 9459764303 8881629011 1385046743 0089029434 4826191063 8516040717 (Phil Carmody, k=302)
  4. 103 5870337940 5843951292 5525157855 2277227722 7722772380 8147565663 3566723569 7802385579 (Patrick Demichel, k=314891)
  5. 103 8309980788 7658642108 0432209241 9172209903 9172209800 0862229115 1513567795 8740000663 (Phil Carmody, k=277)
  6. 104 5567177482 0506226338 7974856510 5914273413 0953290176 9092481660 6835083194 1053290087 (Patrick Demichel, k=1195667)
  7. 105 5703318004 1178988819 6261919612 6641078483 2878170102 4032475679 3942067234 8031605019 (David Broadhurst, k=1)
  8. 105 5801147934 3127115357 1383718041 6966958486 3033041619 2768106420 6160156870 8350676529 (Patrick Demichel, k=158696)
  9. 105 7944833744 8427623011 7015303571 4512944362 2910393125 5769536646 9251528285 8558081049 (Phil Carmody, k=476)
  10. 107 2280474103 3465316328 3453025334 3823991242 1592915437 7200887656 7410467742 4992479853 (Patrick Demichel, k=184594)
  11. 109 3396389112 8645464961 6489662665 3539119343 9645353569 4881798867 9703274121 3698937249 (David Broadhurst, k=16)
  12. 113 4018570925 3472423909 0073222094 8962739711 5305409018 3668819996 1230537427 8722822259 (Patrick Demichel, k=2929591)
  13. 113 7796738450 9674007504 0424953196 2432568040 8818825560 5269488851 5437975294 5111726659 (Phil Carmody, k=1843)
  14. +11500490394117824585468796003575163076836624586334794818271756072956027758946488969 (k=56933120762959527650835623780075064736814973199677202070652257786911028509636084)
  15. 115 3593786448 8535931430 4477713511 6047349626 8158903296 3170694652 0658828554 9338560419 (David Broadhurst, k=23)
  16. 116 3307963372 4580774944 1771519258 3285353237 3060232743 9232224749 7526844791 3716721971 (Phil Carmody, k=265)
  17. 118 6339513986 7070052789 9413047021 6404992668 3595007450 2744506655 0665060121 5818039691 (David Broadhurst, k=5)
  18. 119 0678720762 6111747413 9613512734 1708928853 8195074241 9709241781 2228179991 3277136601 (Patrick Demichel, k=1210100)
  19. 120 4987353544 4351122792 7825364237 0851140890 9815284196 7776137944 1559779054 3742908129 (Phil Carmody, k=656)
  20. 122 2232799983 6545267076 0344824913 0893845292 5015949775 5671708954 7983983083 4644954133 (David Broadhurst, k=2)
  21. 123 2293728428 3386205957 3941013847 3333333333 3333333210 1039604904 9947127375 9392319487 (David Broadhurst, k=11)
  22. 123 5213774166 2402925479 8242429889 6393254688 3606745435 1607028854 6009670791 4635684579 (Patrick Demichel, k=124541)
  23. 125 0650058460 3462928168 5170210300 2272965987 3393973984 0260947559 7511176984 8451350167 (Phil Carmody, k=637)
  24. 125 3453403390 3174452421 8316016385 1832319509 2773926768 3782253739 3479202179 2885395179 (Phil Carmody, k=943)
  25. 125 3842779558 9832686124 6822531227 0075892562 5288721579 8886053015 4244394321 4340274819 (Patrick Demichel, k=396823)
  26. 125 7740582633 6608349473 7896826294 5868751641 2717702728 3409603326 5828504975 9661312481 (Patrick Demichel, k=566160)
  27. 126 8126770925 2259553992 1235247943 0284650611 3054435623 5037422757 9335441094 0666476927 (Patrick Demichel, k=1728607)
  28. 130 6352642704 8018254015 4547604755 3663366336 6336633794 0016009041 4354887678 8210971093 (David Broadhurst, k=62)
  29. 132 1770312453 8012222608 7983498510 9393487295 7600658478 3240704722 4369312495 7266562491 (Patrick Demichel, k=2047895)
  30. 133 7751085767 4790902747 5957333781 5634286376 5204668345 2993079840 8766567156 9389880729 (Patrick Demichel, k=824316)
  31. 135 6898734509 4462228692 1103694731 8510782876 1489217259 5409517385 5951445815 9614477609 (Patrick Demichel, k=57844)
  32. 136 3392085191 8052319131 3724601987 3354314938 6645685197 6746400130 4698004192 7078916927 (Patrick Demichel, k=6447)
  33. 138 8100145911 1187082415 1767560989 0631160355 0631160216 2531014443 9444077939 8863599367 (Patrick Demichel, k=82111)
  34. 141 5067768321 0894685296 3413236203 2866370564 7133629576 7934138885 8028314731 6279606769 (Patrick Demichel, k=229448)
  35. 141 5690322814 6058474671 1664513258 3682767574 0625947000 8958590077 2156068788 8593189973 (Patrick Demichel, k=178042)
  36. 143 3371555246 7128739098 2764072134 6176842737 1276444187 4159869163 7215434316 1420738731 (David Broadhurst, k=5)
  37. 147 4904064362 6445206915 9446154567 9450939647 8111148085 9228333040 7230177089 5087789651 (Patrick Demichel, k=100425)
  38. 147 8091710479 2253805623 9636983282 2112683059 4578602211 6760318699 5246948213 9793773291 (David Broadhurst, k=5)
  39. 154 8606481658 8447611996 5388951655 5541735497 0362452473 6497006826 2392928281 3738441213 (David Broadhurst, k=94)
  40. 154 9534555555 5555555555 5540060210 0000000000 0000000154 9534555555 5555555555 5540060211 (David Broadhurst, k=5)
  41. 156 2670973974 3251387848 3042478820 0117001243 3101177035 1003282175 7669755912 4716498561 (Phil Carmody, k=4160)
  42. 156 4993753866 0690562644 8397167098 8603401671 8948219921 8518537877 6920025650 7372775557 (Patrick Demichel, k=933478)
  43. 161 9532515512 4491848204 9281296939 3663366336 6336633825 3195881849 0828481868 2944663277 (Patrick Demichel, k=22862)
  44. 164 1719678482 9870542976 4605353295 0069293209 2654919653 6858820824 0808530474 3412860921 (Phil Carmody, k=4940)
  45. 164 4124902482 9468378383 3231073695 5775195261 5775195097 1650292778 6306816878 2544121567 (Norm Dresner, k=10211)
  46. 167 0222511531 4482177717 4495119303 5444577431 5858449294 8985642117 5133490827 2044698277 (Phil Carmody, k=686)
  47. 170 0623879669 8435966341 6587538016 2514943016 4015397746 9954017108 9668881098 0064195481 (Phil Carmody, k=260)
  48. 172 4408395109 8088837291 6058783416 8675515391 1324484781 3083910500 9413321900 4734298809 (David Broadhurst, k=4)
  49. 178 1224536269 1263182964 3275031818 3293134394 6005468407 7273508044 3021834225 7590860447 (David Broadhurst, k=1)
  50. 178 5051438523 8523852385 2403089038 2376237623 7623762554 7427676147 6147614761 4779326663 (Phil Carmody, k=3767)
  51. 179 0124380067 1121443922 6087789935 7502488621 2322972032 6474475217 3539422514 9003832409 (Patrick Demichel, k=714428)
  52. 181 3743492903 1232925768 8995654239 2797246400 7202753780 6540739303 8435679368 1792900641 (David Broadhurst, k=80)
  53. 181 9955607232 9593379237 1777806789 0316675170 9683325011 0272282403 9276704066 2094481961 (Patrick Demichel, k=142220)
  54. 183 7912692439 7890452510 8268915755 2490318724 4378303545 0681999929 7864930744 1421477077 (Patrick Demichel, k=1861982)
  55. 186 1576358811 7859741892 0260377806 1632174557 9482105078 5813091533 1351129953 5879814967 (David Broadhurst, k=1)
  56. 197 0060992305 4315183023 9991877578 0997226283 0962417784 1563217234 5007726864 0161225693 (David Broadhurst, k=14)
  57. 199 7625759255 2535029579 0681494142 0000000000 0000000199 7625759255 2535029579 0681494143 (David Broadhurst, k=1)
  58. 205 3709659481 2592828259 6160722384 6644702331 3355297874 0354361812 5948125928 2805424717 (Phil Carmody, k=2858)
  59. 206 8675561576 3842361576 3863048332 0000000000 0000000206 8675561576 3842361576 3863048333 (Patrick Demichel, k=178346)
  60. 215 6834620777 6978728222 2116319989 0808626300 9191373914 7643247078 6170101921 2924946291 (Phil Carmody, k=265)
  61. 217 8898332057 3415100972 6160782010 0000000000 0000000217 8898332057 3415100972 6160782011 (Patrick Demichel, k=219995)
  62. 219 0147069354 9680965704 7950497518 8887378849 1112621369 9034448204 0793586855 6837876369 (Patrick Demichel, k=270184)
  63. 220 4395269369 8712625319 3032388818 1765648459 5654361411 2958808047 5695084212 3608872373 (David Broadhurst, k=14)
  64. 221 7243976728 9976897005 1315711410 0000000000 0000000221 7243976728 9976897005 1315711411 (Patrick Demichel, k=225095)
  65. 226 2454905226 8888425698 1365582673 1174488255 1174488028 8719583028 2286062556 9808905583 (Phil Carmody, k=169)
  66. 226 6959531722 7145366573 3201381823 9015809707 4261791978 3424742061 2982087585 7818874543 (Phil Carmody, k=2119)
  67. 229 7333178048 1290286680 2893590927 8397148173 9899866458 2883605923 3527112318 3775211241 (Phil Carmody, k=1580)
  68. 237 5790932488 6161156444 2708374579 2912294832 7087705404 8703227321 3248861611 5620669413 (David Broadhurst, k=2)
  69. 238 6023589178 3817889388 4189252490 5987016623 8576657819 5182550951 4519724845 0004935449 (Phil Carmody, k=116)
  70. 238 6072715874 6593561881 7352694936 1412552471 6830699961 6801498250 8653606425 2667333807 (Patrick Demichel, k=235867)
  71. 239 1376790762 8119524362 7196065825 7124109968 9880057575 3078964542 0327573641 0457888693 (Phil Carmody, k=3714)
  72. 246 1335667276 9008376541 1742365194 1516456816 1436775295 1097124200 5974215733 1367717121 (Phil Carmody, k=640)
  73. 257 9841775638 0650834912 3798887304 6543986799 2926975669 7285165426 1319642321 9258747931 (David Broadhurst, k=5)
  74. 261 6342393754 0462332657 0706398289 7199626206 0768164761 3253447968 7738598750 4640148463 (Patrick Demichel, k=161221)
  75. 262 7138282315 2827405905 9671840138 1061156465 2422431152 7256728296 2819118318 3469703813 (David Broadhurst, k=2)
  76. 271 8075972335 7766364351 8518066020 8729100404 7340412160 6027118150 9970940021 8016470727 (Patrick Demichel, k=2632133)
  77. 275 7967764997 1151904086 2123751183 5939359170 0594143044 1410493495 4719707858 5332872921 (Patrick Demichel, k=42020)
  78. 278 7216767584 4043593375 5755747975 6893911629 6954065251 2120017370 5517792180 9195661409 (Phil Carmody, k=19664)
  79. 280 3027888446 2151394702 6135458167 3306773188 6693227091 6334661634 8844621513 9442231357 (David Broadhurst, k=26)
  80. 281 3593297045 8021411897 2844761112 8316831683 1683168598 1910128728 9704580214 1161592797 (Phil Carmody, k=346)
  81. 285 0510219632 9160488163 8762292403 8121707438 7151430931 0194760547 9647802547 8594789081 (Phil Carmody, k=4340)
  82. 285 4653716841 4114038803 3968201419 9957170909 4970487758 7450082730 2976910901 4836219619 (Phil Carmody, k=1871)
  83. 289 7648922263 9931250442 0015391588 7954369236 7954368947 0305446972 8023118794 7938977649 (Patrick Demichel, k=643416)
  84. 293 7353872846 9766435385 6385858161 7939226601 3594083539 7633906545 2893700555 1997491717 (David Broadhurst, k=2)
  85. 297 0767517343 8109086921 6518450409 5768494218 4048480837 8273253870 9959767093 0242053529 (Patrick Demichel, k=5396)
  86. 298 4292764858 0702858417 2517171872 0384072295 9615928002 4676837154 0318786121 2901244169 (John Gamble, k=16084)
  87. 301 1452778890 2692747399 1801597919 6245323763 4514141086 6176865798 1460079977 4113660613 (David Broadhurst, k=2)
  88. 305 2984706422 8975039236 5184857176 7128712871 2871287434 0113419294 1846326365 2313570049 (Phil Carmody, k=128)
  89. 309 1190827470 6680505930 3532570483 2872862385 9295926419 5982301257 9558087028 9140301249 (Patrick Demichel, k=1343008)
  90. 311 5614694046 6452205554 9515205572 0717427845 9282572465 6332121892 5734777709 0232633419 (Phil Carmody, k=599)
  91. 314 4358196239 5173967429 9507320711 3311450608 1677984158 2738114926 4193260070 6473452607 (David Broadhurst, k=7)
  92. 317 0360201101 2425732773 2408980133 8613861386 1386138930 8974062487 3811871387 1022841521 (David Broadhurst, k=40)
  93. 318 9038181554 8943869504 9522957326 0473509149 3334355523 5599045602 1800578690 8679648521 (Phil Carmody, k=18220)
  94. 319 2278066089 3971660930 1231723223 8957665920 1856297561 0527923487 2620357632 8556304837 (David Broadhurst, k=62)
  95. 331 0366225422 9050751741 2389443826 1951607985 8048392345 2317833408 7099143755 4341051813 (David Broadhurst, k=74)
  96. 331 4343583387 5107976448 2534361928 3001050811 7717247054 2581851403 8738140963 2642454339 (Patrick Demichel, k=288443)
  97. 332 5553210302 5492448034 8573339560 1028733479 8971266852 6581943782 4463714554 9602073041 (Patrick Demichel, k=653080)
  98. 335 6539699988 6817586019 0387047610 7581348540 7581348205 1041648552 0763762521 7194300931 (Patrick Demichel, k=25235)
  99. 337 5128443807 7810457474 0288758403 9999999999 9999999662 4871556192 2189542525 9711241597 (Patrick Demichel, k=280802)
  100. 351 1564183377 2388016962 4920822660 5973884555 0583910175 5592676008 7019114021 7163155329 (Phil Carmody, k=1856)
  101. 351 4794853013 3235061775 8306718522 7326732673 2673267678 2121585686 5908329102 5633451197 (Phil Carmody, k=3502)
  102. 354 1582503740 4135191563 9792759446 0000000000 0000000354 1582503740 4135191563 9792759447 (David Broadhurst, k=1)
  103. 354 7246318913 0277114030 9473266371 2673267326 7326733027 9919586239 7603846704 2146533699 (Norm Dresner, k=10603)
  104. 358 3810829955 9509646712 6916607540 1759843885 0799874257 0737819112 2768511955 2288513641 (Patrick Demichel, k=26140)
  105. 369 7021210052 5518132504 4964328471 8236535096 1763465273 5257745148 7281597408 3200863569 (Phil Carmody, k=296)
  106. 383 4085158730 8607551997 8916615242 7133578085 2866422298 1218736816 1473973912 6050193329 (David Broadhurst, k=56)
  107. 384 7472187845 1638595156 8016110735 2480282571 7500202505 7279011061 2475153550 4065765463 (Phil Carmody, k=227)
  108. 385 5024174777 7641527495 9641328483 8348389078 2658939007 8365833608 2637637784 5606329487 (Phil Carmody, k=211)
  109. 391 6137627054 8534018382 7276592476 3960396039 6039604352 0098023094 4573622343 1236988517 (David Broadhurst, k=2)
  110. 399 1284921779 6233424105 2709980919 1325319076 7937719344 1854550673 4734044623 7253372413 (Patrick Demichel, k=81982)
  111. 401 2283780756 5687541024 2252278776 8757348922 0750313581 2814311489 2625771210 6508870641 (Phil Carmody, k=1720)
  112. 414 8683448645 2429084688 0862761810 7564560397 2435440017 6248009042 4864524290 8427322209 (John Gamble, k=15248)
  113. 418 2563187528 4503106062 6115102005 1803139254 6998690446 1814130502 9422363924 2971341769 (Phil Carmody, k=2164)
  114. 433 6000583666 3530635646 3241959018 4550507570 8099991638 3264409852 9614722378 1453287357 (Phil Carmody, k=4802)
  115. 436 8477267483 0701652218 7694472613 1433753182 1433920005 5737046854 4616562120 4349769531 (Phil Carmody, k=4615)
  116. 456 9578598221 7400741901 0052641274 4514322910 0079557060 0586090952 3739991620 7627391397 (David Broadhurst, k=62)
  117. 468 8716835061 4274278353 8288525613 7440721004 2559279464 6157556065 6833557349 5729246619 (Patrick Demichel, k=110651)
  118. 489 8807534257 7240200808 2444143002 2410182277 7589818212 1217716535 4830018530 4854325281 (David Broadhurst, k=80)
  119. 499 2940379765 3419103030 7514564149 2192449970 7807550528 5132829736 1226653059 9707014121 (Patrick Demichel, k=45020)
  120. 500 1103850391 8561759467 5095882964 8867490688 1263443723 0735431116 1530612858 0829108167 (Patrick Demichel, k=539737)
  121. 505 1032828077 0593490592 5160840761 3092346794 6907653710 4125174871 7501143797 8253187557 (Patrick Demichel, k=633206)
  122. 516 2820919318 2572431488 5448537293 8217821782 1782178734 1038741100 4354609706 3666359077 (Patrick Demichel, k=357806)
  123. 524 5498710636 5639089731 0257429210 6295704217 4901281382 1832850154 6313985004 3926721223 (Phil Carmody, k=467)
  124. 539 7320720225 5653997308 6039000902 2268034598 0054484770 9640905874 5764250927 0307978263 (Paul Leyland, k=31699)
  125. 548 4277888005 7443704179 4202587795 0158196945 4318190147 2481613576 2250839002 4866979801 (David Broadhurst, k=100)
  126. 553 6203912424 2902169431 0717634101 9897061188 0768978189 1511712463 7960939612 0037592037 (Patrick Demichel, k=1488902)
  127. 575 3954810170 6329491102 2381712232 5006652188 3220958944 8111742161 8668682731 8778278053 (Patrick Demichel, k=59174)
  128. 577 6059462690 8328218431 2519300153 1043743032 5618542698 3693279099 8775964724 9908029127 (Phil Carmody, k=217)
  129. 618 1701886388 9011336123 8314329320 5068488251 4931512366 6770374640 3942847872 3382817573 (Phil Carmody, k=874)
  130. 618 5926369590 0617496377 0796570370 2890301799 7109698818 8816671389 7727194577 3686872171 (Patrick Demichel, k=111445)
  131. 642 8116443156 8618289507 8179524321 2933975690 7066024952 1050418847 5684313817 1113500013 (David Broadhurst, k=2)
  132. 649 5480804691 1461672303 1979545953 3763456242 6236544406 9244260933 7698216060 5743002197 (David Broadhurst, k=2)
  133. 661 7005836574 5976249225 1247426985 3688351632 6311649029 0694188207 2287897592 4935778619 (David Broadhurst, k=1)
  134. 673 5774536907 7769689387 0504839673 0663654334 9336346338 6438191242 7106035052 1168494009 (David Broadhurst, k=4)
  135. 692 8998976391 8071322277 2131066381 5710502990 4289497702 4709479382 2360819286 7841569373 (Patrick Demichel, k=84294)
  136. 698 5733194505 7487912701 7916968172 3552033397 6447967300 9285227903 3935879304 1469001571 (Patrick Demichel, k=68795)
  137. 704 4719880498 2859594347 4845305093 5174153797 2372721811 5233132939 4876402231 3547427847 (David Broadhurst, k=13)
  138. 714 8209169125 2895737947 8098173426 4280745540 9725350218 4230073682 1658359305 6995150967 (Patrick Demichel, k=6401)
  139. 717 3026741584 6977751934 8859332285 6518305937 5750739959 2665035695 4278808904 6468737527 (Patrick Demichel, k=2990577)
  140. 728 7282420410 8923785268 7890861459 7280195106 8255509554 2506309363 1702435134 9193213321 (Phil Carmody, k=1660)
  141. 730 8080239441 3347491945 7966207276 0000000000 0000000730 8080239441 3347491945 7966207277 (Phil Carmody, k=2846)
  142. 734 1149770111 0468843351 7922379434 2988900501 9762337767 2198659777 9581354271 5927754051 (Phil Carmody, k=475)
  143. 750 1215019750 7895060592 2401042157 2250245139 1772156739 6533233356 5151997295 9410955971 (Patrick Demichel, k=2526615)
  144. 806 0317175110 3472521410 6955978282 0983556135 9016444670 1300731246 2488965274 7939534419 (David Broadhurst, k=1)
  145. 810 3657109207 0920709207 0839672636 0000000000 0000000810 3657109207 0920709207 0839672637 (Paul Leyland, k=32282)
  146. 815 4917229313 7531770686 2549778486 0463146003 9536854811 5380375317 7068624682 3012924491 (Patrick Demichel, k=24895)
  147. 822 2079499509 1595814535 7900866874 0952730394 0952729571 8873230884 9356915858 3051863521 (Patrick Demichel, k=748720)
  148. 871 1351598213 4869799989 1627512519 8661829646 1849079771 0656844978 5146611330 3289297207 (Patrick Demichel, k=2034863)
  149. 903 4358336670 8078242197 5404793758 8735971290 3542423259 8530597394 4380239932 2340981837 (David Broadhurst, k=2)
  150. 939 5789431514 8214516524 8505762674 6443099627 0872420189 0494956059 9633016538 3683159569 (Phil Carmody, k=1976)
  151. 942 3248191983 3986182518 6028368688 4260219591 5739781350 7508411574 9725962927 0288588281 (Patrick Demichel, k=67060)
  152. 950 0533511300 6509925582 4708487258 7398873557 8116816512 2039021214 6784699753 4195693521 (Phil Carmody, k=520)
  153. 956 6835599070 6854937387 4827542302 9383269053 0616731903 6218868123 7471668334 4210811357 (Phil Carmody, k=19082)
  154. 972 3765981135 1348884212 2735888817 1548068100 5059831015 9917946126 7350776573 6097578131 (David Broadhurst, k=5)
  155. 977 0670115632 4071302098 0389275332 5307079217 7726976428 3654173157 6845561653 2599373597 (David Broadhurst, k=2)
  156. 989 1557295249 3958140349 1532848976 8978486310 7544222373 3915214965 7410784208 6130896299 (Phil Carmody, k=2461)
  157. 997 4659127985 3716765378 2164916633 0858935648 8499708136 3530873399 0568612413 9468958063 (Patrick Demichel, k=52837)

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.