Known 86-digit prime factors of Googolplex + 10

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  2. Number Theory
  3. Known 86-digit prime factors of Googolplex + 10

This is a list of known 86-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. 101506 0236445544 5544554456 4606047909 0099009900 9901091605 0335455445 5445544555 4705057811 (Patrick Demichel, k=194735)
  2. 104098 4524871403 9649749950 3778200081 7029702970 2970401128 1554574374 2620046980 0807903053 (David Broadhurst, k=14)
  3. 111915 5290406201 7289004846 7076177042 8330876409 1669235506 3621282610 8958128437 5407053453 (Patrick Demichel, k=89002)
  4. 112163 8219866214 0170303523 1041458563 8181818181 8181706017 9961951967 8011514658 7140359619 (Patrick Demichel, k=623101)
  5. 113896 6190757864 7819636877 1576630025 7047877620 2952236276 3238635485 0771759256 8624507647 (Patrick Demichel, k=675397)
  6. 114915 4060083394 2751326283 4536383065 2825171509 8120851127 5952325335 5276148950 1111741761 (Phil Carmody, k=2720)
  7. 115400 6030837847 1908167154 7893924698 9391603208 3073529413 3070400324 0627410687 8008311223 (Patrick Demichel, k=1327399)
  8. 116539 2428835395 8658682389 3415380324 0665535466 6967834493 8325556191 0356266617 9181792583 (Norm Dresner, k=13409)
  9. 116940 6405574425 8695027278 8875832955 5955666205 3751235870 6275448455 6544518798 0690507131 (Patrick Demichel, k=487335)
  10. 117890 6311664700 4803668977 6247183594 0198019801 9802098088 6509684502 4605649175 6445203397 (David Broadhurst, k=26)
  11. 121196 7948021602 1602160217 2335701082 3762376237 6237744959 1710397839 7839783979 6098077321 (Patrick Demichel, k=852540)
  12. 125668 6266217279 7623914564 6843107357 6743911082 7182032426 0437853165 5056251498 1135863487 (David Broadhurst, k=1)
  13. 126800 9556572889 0144027112 2536068454 7432928551 2567198249 6989501440 2711098560 9968997007 (David Broadhurst, k=1)
  14. 129303 6872763161 8094188827 5763890981 6358423877 0882849500 7408654967 8838974547 6662006379 (David Broadhurst, k=79)
  15. 133917 1811198666 0394442528 5576579791 6879142787 8761548461 3433082736 7525208283 6729773939 (Patrick Demichel, k=1956389)
  16. 137085 1742016021 6021602161 5868733441 7623762376 2376374708 9365778397 8397839785 3492495819 (Phil Carmody, k=113)
  17. 140248 2785790002 4997901321 2559329908 8632549265 4767867184 5288990338 6742217665 3364056011 (Phil Carmody, k=1135)
  18. 141049 4495563592 5697056436 4318697866 8763059969 1237081080 3258623561 6933996467 3081757837 (Patrick Demichel, k=513422)
  19. 142618 3054997430 0266485312 5721227980 0009487975 9990654642 3064485406 0256997336 5730715957 (Patrick Demichel, k=56882)
  20. 150658 1972833396 1460115849 2581722619 9415670650 7303966207 6725705780 4808144442 9065023729 (David Broadhurst, k=8)
  21. 152428 0856531976 9023863364 8589551629 0134039795 8336511424 8573361395 3680819603 3731997651 (Patrick Demichel, k=2831925)
  22. 152540 7133947155 1930487967 4891279695 8566027714 7330199766 4971867184 5298038728 9877999247 (Patrick Demichel, k=365177)
  23. 157212 1701195347 0930173671 1454794015 1361694718 5376615042 4013063724 3996225551 1225208583 (Patrick Demichel, k=68357)
  24. 158086 6364326893 5740073104 8451263250 3050715705 6949442380 9415042599 2689357399 1501978957 (Phil Carmody, k=902)
  25. 159576 4021362326 1761217084 9493580773 2185967681 8206090468 3445315814 1470600852 5501944561 (Patrick Demichel, k=6520)
  26. 173592 3103282117 8638973577 8061910524 9854817345 7105639769 3365081044 5797517074 6772986503 (David Broadhurst, k=17)
  27. 174528 7014966167 7492233830 5054896018 0875458909 9124715618 7890425077 6616774920 5930354929 (Patrick Demichel, k=61176)
  28. 180606 4228416648 8221777215 5853515634 6319049057 3681131549 0547465706 1902728158 2172564693 (Patrick Demichel, k=289354)
  29. 181118 2473262166 5131929221 4713355611 9642572588 8618831779 4643077993 1267721173 7655409811 (Phil Carmody, k=2645)
  30. 189684 5684462437 5008391416 4419737070 1838438094 5484980959 4898555946 8801063435 2644668761 (Phil Carmody, k=420)
  31. 191013 6987938583 9784743947 0999385141 6682725092 9408726912 3444539033 2150406408 1652454979 (Phil Carmody, k=109)
  32. 191400 2621030864 7090527697 7555659368 2825328724 1311193100 7614656425 1591374731 5548553819 (Patrick Demichel, k=414061)
  33. 193151 8028113244 9020189192 1908532963 7695698992 2304494159 5723812237 1324490199 9604231957 (David Broadhurst, k=2)
  34. 200153 9326699634 1998514233 6428354710 7388582405 2611617748 6715282039 4609931828 3816937117 (Phil Carmody, k=346)
  35. 203110 9893438286 4503183072 5603175530 0000000000 0000203110 9893438286 4503183072 5603175531 (Phil Carmody, k=235)
  36. 206300 1118817622 1406382379 9223628810 3168596441 6831609858 4287414063 8237785938 2392225253 (David Broadhurst, k=2)
  37. 207589 6455885474 9716599488 4736398356 0000000000 0000207589 6455885474 9716599488 4736398357 (Phil Carmody, k=2642)
  38. 209222 7412556228 5687303955 7671722196 2983311425 7666471015 3902964042 0826486332 1003447127 (David Broadhurst, k=1)
  39. 217324 9205478490 4690307311 2733052559 6134289457 6308316513 0693422629 3863417064 9700938797 (Patrick Demichel, k=118858)
  40. 226393 4122056618 1422984258 6938947037 6486615531 1901158490 3813776889 6861295101 4410071979 (David Broadhurst, k=13)
  41. 228722 4750228616 8292554490 6823034290 2209880694 2307410972 2884969130 3641449856 7500827333 (Patrick Demichel, k=9974)
  42. 229603 6564524521 1236666449 4832829373 4181536986 9960054657 2255187812 1744901679 2557402251 (Phil Carmody, k=2875)
  43. 232036 5816170856 9674620785 9623940572 4608923107 5391308929 0425093964 5065697678 4232863681 (Phil Carmody, k=160)
  44. 232064 0095416773 7842427711 0006828201 2768102339 7867892856 2838061966 4353538695 4514502263 (Patrick Demichel, k=77881)
  45. 244232 1242545717 0144940474 2620775312 8104024891 4327792858 6030153244 3434902371 7346653419 (Phil Carmody, k=293)
  46. 245259 4289130808 8414513090 8178360473 1656379407 8747767614 5813463738 4755810540 1645349613 (Phil Carmody, k=626)
  47. 246948 7317030359 6964030362 1658903530 0000000000 0000246948 7317030359 6964030362 1658903531 (David Broadhurst, k=5)
  48. 250050 1568270121 9127075250 4786346173 5048641395 5048391345 3480371273 5921566145 0262295223 (Patrick Demichel, k=5309)
  49. 250423 5968769161 4790011273 6606016711 2694162698 6646531311 5614230507 4207127921 4294771847 (David Broadhurst, k=17)
  50. 270910 6922036212 1559274311 1767964027 2169724689 3174883254 0364285485 0909657440 3648508837 (David Broadhurst, k=2)
  51. 274554 2785367488 5782060057 8918995342 2530917875 7469356678 5316285364 3251142182 1449913219 (Patrick Demichel, k=100261)
  52. 288236 4058395725 8143550183 2771719564 8574284652 6873891636 3854992805 8767933697 9637870327 (Patrick Demichel, k=953247)
  53. 292882 8192827390 5175344418 6614494237 3922729684 2537855040 6313823326 5807447432 6989030049 (Patrick Demichel, k=120176)
  54. 295821 2479301658 6863950747 2419021258 3812255290 2457377795 6910642874 5872607331 8484867499 (Patrick Demichel, k=1047359)
  55. 296280 7530719548 7595880271 1779786593 1973844029 2175135301 7344200189 6807041483 1378462157 (David Broadhurst, k=2)
  56. 318610 2970252264 8348876358 1434382149 2110878891 2110560280 9140626626 3762002533 0676496743 (Patrick Demichel, k=24339)
  57. 331198 3796512670 2598833046 6885244101 5212059699 5058649695 5760373504 5222083907 7390892927 (Phil Carmody, k=117)
  58. 332899 3961889170 5903658098 2221486160 0000000000 0000332899 3961889170 5903658098 2221486161 (Patrick Demichel, k=9320)
  59. 352782 1498690212 3936933322 2215264561 8456180656 1544172125 9954870868 5480752666 0671445219 (Phil Carmody, k=291)
  60. 353100 0063530553 5379842212 0647816130 0240550239 9603995024 4677438385 8289572158 1096902197 (Phil Carmody, k=282)
  61. 359794 7994014833 5582994608 9382134893 4099638782 5900721012 2093653616 1483355826 3481773677 (Patrick Demichel, k=637718)
  62. 362859 0184014409 5056973174 5382319557 4150541833 5183775535 4083811663 0669663234 0000407689 (Patrick Demichel, k=311076)
  63. 363815 1706228103 9808977094 6207251673 4222654543 9497922765 9494178466 2588597456 6473826081 (Patrick Demichel, k=82960)
  64. 368369 7216146161 9124200659 0906707751 2101112546 7899255822 9317258708 7023088112 3007820299 (Patrick Demichel, k=2305301)
  65. 368569 3238953590 5082895505 4245308010 0000000000 0000368569 3238953590 5082895505 4245308011 (David Broadhurst, k=5)
  66. 377531 8692859970 3303247550 1609454164 1080804493 8919573037 9773664464 2222443056 2690258659 (Phil Carmody, k=751)
  67. 379531 3672527450 4685165707 9033304275 2773640702 0342982286 2049320422 8805606468 2345914117 (Patrick Demichel, k=74902)
  68. 388516 8471358678 5491805076 7938061707 6286971138 3713417378 4758329816 9204833938 4225032847 (John Gamble, k=16027)
  69. 408432 7465140944 6433886337 3582489650 8900518667 3519520542 5350148060 5432848861 9315038503 (Patrick Demichel, k=73449)
  70. 415253 5521678875 4702454453 7105523658 6814907433 3185507820 2336586308 7887547020 3920431093 (Paul Leyland, k=31462)
  71. 418445 4825112457 1374607911 5343444392 5966622851 5332942030 7805928084 1652972664 2006894253 (David Broadhurst, k=2)
  72. 440201 1631357031 1535212127 8713373800 0792079207 9208360993 2423436239 0743132919 9505453009 (Patrick Demichel, k=25208)
  73. 441724 7364513754 8814642424 8345879033 4851485148 5148956576 2215998903 3963157276 3197364183 (Phil Carmody, k=419)
  74. 446691 3387109475 2805496758 8133104700 9569757877 0430688814 2956867352 3235738881 7702862579 (David Broadhurst, k=1)
  75. 461677 5998696756 4735773848 0244102556 1514965053 8485496623 7513661810 3220808794 1759067611 (Patrick Demichel, k=2470555)
  76. 485867 8030424475 0393530611 8106374206 4455927692 5732408626 9694218925 2372104841 0024740129 (Patrick Demichel, k=1018288)
  77. 490044 7410358565 7371007973 0278884462 1514434267 8486055776 8924792833 5856573705 1793318731 (David Broadhurst, k=5)
  78. 491045 0657571653 5955266281 8734265077 8789906734 1210584310 9447478387 7165359547 7524171813 (Norm Dresner, k=11486)
  79. 513532 2718949400 2656920946 9784877499 3692169336 7320640163 9929862185 5260154348 9696244521 (Patrick Demichel, k=262420)
  80. 517512 6937188657 4632246709 9313652635 2937569733 1726943240 3610630675 3345360521 7765942801 (Patrick Demichel, k=1041400)
  81. 519642 7160256369 1930150517 0151484430 6511379854 8343529534 8275426274 4860113799 9706508971 (Patrick Demichel, k=430945)
  82. 526123 6339818648 1448664276 8529095990 5544554455 4455971668 1884373103 5904109821 4073650447 (David Broadhurst, k=7)
  83. 526195 6110590691 0039171080 0814823295 6712792996 3287733199 2823383687 3326378083 7527616293 (Phil Carmody, k=114)
  84. 536603 6840241985 3487639750 3502351731 2653362897 2652826293 5813120911 9165723146 9151011167 (Patrick Demichel, k=547741)
  85. 546505 5232358862 5813760927 9122144390 2764227642 2763681136 7531868779 6950466714 3642083253 (David Broadhurst, k=2)
  86. 551688 0213727026 8602587852 2779720064 3790951897 6390295619 0707728790 5580341966 1862264449 (Patrick Demichel, k=5696)
  87. 556153 2082219466 3800756968 4116467412 0000000000 0000556153 2082219466 3800756968 4116467413 (Phil Carmody, k=4694)
  88. 570377 3421708965 2778384159 7002461238 1980198019 8020372357 5401906985 0798186139 8982659259 (Patrick Demichel, k=791601)
  89. 602786 1156778311 2109810821 6840417567 3472364877 9447857709 3590486965 1402394693 7110034961 (Patrick Demichel, k=1499720)
  90. 603974 1397350152 8035373050 9269544820 4301552106 4300948132 2904201953 6266179055 5032007287 (David Broadhurst, k=27)
  91. 605171 2763889537 8721225703 0272417176 7675012909 2325592262 0438902447 1046212793 7947430087 (Patrick Demichel, k=5887)
  92. 658206 6893347408 0407247367 6940551040 2989207864 5015870980 3227121592 8695601360 0030046649 (Patrick Demichel, k=29036)
  93. 659650 1541120225 4205186340 3653710935 4275537150 5725122499 5816657375 9929649189 7929248087 (Patrick Demichel, k=1578763)
  94. 683638 5385550803 9094026772 3764921882 7422421017 0996924540 5417745368 8701272482 9519483797 (Patrick Demichel, k=123026)
  95. 691741 6009411873 7679678259 0939250809 8536585365 8535893624 2527173492 0856907106 7597334557 (David Broadhurst, k=2)
  96. 693227 3958484428 0561178458 8927742738 0000000000 0000693227 3958484428 0561178458 8927742739 (David Broadhurst, k=13)
  97. 701109 1495938728 2978260013 2420520239 6119762755 7967891981 4123080729 0322333133 7202701259 (Patrick Demichel, k=781163)
  98. 734884 1814532883 9441479345 2824751029 2729873752 7270861131 4544406636 6711605592 5554624783 (Patrick Demichel, k=1525479)
  99. 742581 7768924302 7889188796 9163346613 5458909912 4541832669 3227834215 2430278884 4622256527 (David Broadhurst, k=1)
  100. 756812 5175995729 7935555818 9281801578 1359801036 1359044223 6183805306 3424245217 2077999459 (David Broadhurst, k=1)
  101. 764992 0993993444 3687226115 8743781301 4759254867 4758489875 3765261423 1072028751 6015473567 (Patrick Demichel, k=52781)
  102. 783654 6786990471 4789808631 8384651649 1117667167 4507315751 7993508074 0305475352 3430872419 (Phil Carmody, k=4421)
  103. 784071 5856573705 1793612756 8446215139 4423094828 5577689243 0279668533 7370517928 2869309969 (David Broadhurst, k=8)
  104. 808906 8062334468 5517933033 9695058908 7966955333 3692727801 8192648148 7039006185 9832527213 (Patrick Demichel, k=23354)
  105. 822872 6298647250 5582108741 0108597735 9126470441 4236858878 6863363311 8550278987 7621617487 (Patrick Demichel, k=925871)
  106. 836175 8103693969 8727121612 5564128393 2665941544 7334894631 0769635514 6061180067 8230069939 (David Broadhurst, k=13)
  107. 836672 5187675352 8354261224 1637023476 0818977689 9181858982 6006653042 7535283534 2456001167 (David Broadhurst, k=7)
  108. 896460 2367021677 3088241173 2502900362 4687941259 5312955200 7054962936 8400299913 7190841623 (David Broadhurst, k=17)
  109. 940692 3996915496 7978503233 2465020726 5777277534 4859557252 3475609923 3010213019 0564721647 (Patrick Demichel, k=1934067)
  110. 958505 6582889828 9828982907 8748855657 8811881188 1189077317 5394771017 1017101719 7560736847 (Patrick Demichel, k=852727)
  111. 998319 4956157135 4886940317 1329262408 2794961814 2793963494 7838804678 7908021497 1465699407 (David Broadhurst, k=1)

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.