Known 84-digit prime factors of Googolplex + 10

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  2. Number Theory
  3. Known 84-digit prime factors of Googolplex + 10

This is a list of known 84-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. 1040 3976430246 2861722397 9851803519 1825020920 8575639010 4071197094 8321272449 3244186049 (Phil Carmody, k=736)
  2. 1059 5579433929 9458280819 6193111521 9489564850 0510436209 5068998779 9968715969 5682676373 (Patrick Demichel, k=565514)
  3. 1105 3289350996 4506564294 6912018102 9406919229 0593081876 2696270225 5099645065 6318937333 (Patrick Demichel, k=1732234)
  4. 1120 4271299937 6372942131 0688866809 8560585605 8560584485 4289285668 2187643474 7871718797 (Phil Carmody, k=266)
  5. 1133 7818342741 1682711284 0855372635 5503200136 4496800997 3321542877 6179511147 6358572773 (Patrick Demichel, k=73582)
  6. 1163 8732468775 9398351676 3925757307 5204744422 4795256741 3937213198 4193607253 9130501731 (David Broadhurst, k=5)
  7. 1203 6851349013 3547828067 4732704705 0731707317 0731706113 3880358303 7183879249 5999002613 (Phil Carmody, k=294)
  8. 1208 9348393881 9413483829 1880384250 0570677790 8727241481 6307353657 5058830534 8723333663 (Patrick Demichel, k=152209)
  9. 1225 2320612476 0751534368 4686535682 1999141883 8000859341 4319754359 8752392484 6685677567 (Phil Carmody, k=191)
  10. 1265 5385651401 4459332201 1800954792 5454545454 5454544189 0068894053 0995213253 3653590663 (David Broadhurst, k=59)
  11. 1268 6066246438 8394640614 6332309896 5984399005 7114718750 1416213405 1505930532 5669564929 (Phil Carmody, k=256)
  12. 1375 3616355225 6753114985 7062161480 8256682566 8256681191 4640327341 1503567581 1194521087 (Patrick Demichel, k=385407)
  13. 1442 5807046959 2821222547 1846493874 3732290201 6267711240 9539337160 9088932345 5578784077 (Patrick Demichel, k=106426)
  14. 1466 3693384578 0363752056 6119421511 8821555694 1178445772 2514940272 1542196362 4940977207 (Phil Carmody, k=431)
  15. 1470 3527144971 8985845106 9379810033 2020496904 4435803129 9929266142 1613690160 1989315441 (Phil Carmody, k=1240)
  16. 1476 4104585745 4273384776 7420097126 6847473419 7434320372 9346428643 2160607951 0652322881 (Phil Carmody, k=160)
  17. 1513 9663021107 2094905745 7917222766 1277493651 8722507862 0940514759 0817412093 9194716419 (Paul Leyland, k=30411)
  18. 1524 1347069206 7401538940 5622691891 3980568233 4287848125 7336256265 1468923320 2347640419 (Phil Carmody, k=4039)
  19. 1533 9381228471 2073570318 6396940569 8613861386 1386140147 7995089857 3459708932 5010801957 (Patrick Demichel, k=354362)
  20. 1581 5700834501 1413404551 5711503794 9907106122 4308973664 2051133243 9898249995 8584550121 (David Broadhurst, k=20)
  21. 1586 5948859378 5135478762 2690708012 2222222222 2222220635 6273362843 7086743459 9531514211 (Phil Carmody, k=3355)
  22. 1628 3361878868 7171974187 5840987793 6731104402 1033891618 3887153820 2387815473 4834339717 (Paul Leyland, k=31222)
  23. 1631 7272451273 9908976211 6553338957 8702889210 1297112421 5975340484 1206087001 5256228169 (Phil Carmody, k=236)
  24. 1632 6746185999 4186081382 6127241066 3553733568 3553731935 6807547568 9367652185 7426492503 (Norm Dresner, k=13637)
  25. 1647 5902825312 2896155156 4281786540 0992934231 9007067415 6895759544 1903220924 5274720773 (Phil Carmody, k=2722)
  26. 1726 0072981908 2082502913 0615471745 0765658456 6998410940 1716313392 9611656517 2734044623 (Patrick Demichel, k=177469)
  27. 1744 4880306436 0371470964 1995295878 0455459100 0455457355 5575152664 0083988135 8460163223 (Patrick Demichel, k=224507)
  28. 1785 9852171911 2486787753 8081187902 6937849192 5193069125 1453697467 2432464176 9009925157 (Phil Carmody, k=466)
  29. 1900 4501638771 2693620224 3110812871 3224133614 6775868285 7725772385 9469486609 6334946487 (David Broadhurst, k=7)
  30. 1911 5843436974 6597875626 2289704347 9706357841 5393891986 0530078006 1627379084 8343377543 (Patrick Demichel, k=56849)
  31. 1943 5148252562 0760401725 8577897024 9803543572 9393476723 0155370118 8093345066 6137218373 (Paul Leyland, k=31274)
  32. 1959 7908867401 1142129154 8317488312 4402017733 5597984226 2310885134 6740111421 2719506047 (David Broadhurst, k=1)
  33. 1981 6937175671 0125480569 3302348843 9967378894 0032623087 6904554565 0158101675 3269727739 (Patrick Demichel, k=97371)
  34. 1989 3861758402 8556822050 0041361330 0592803945 9407198043 4454562348 7964018104 0634165277 (Patrick Demichel, k=238966)
  35. 2015 3149187017 3296012982 6905518509 1997745942 8002256072 5146932960 1298267039 8903264453 (Patrick Demichel, k=2262202)
  36. 2086 8919918113 9536692433 9847294789 6150279793 2723982885 6632752117 5657412060 4828881419 (Norm Dresner, k=13121)
  37. 2087 8815600000 0000000000 0208788156 0000000000 0000002087 8815600000 0000000000 0208788157 (David Broadhurst, k=2)
  38. 2092 9717162001 8064186708 0106529644 7996252010 6777547523 2683214847 7448177954 5166391247 (Patrick Demichel, k=1008253)
  39. 2096 9270588810 4547862746 3494816985 8407205560 3855439024 5550642903 1562745361 9677876877 (Patrick Demichel, k=439282)
  40. 2128 5091847560 0723176331 9055154631 1002868811 5481597982 5975862468 6157978484 0955956047 (Phil Carmody, k=3493)
  41. 2146 7277310193 8640960707 3594469787 6323185564 9295474432 6403942751 0944221960 5092156739 (Phil Carmody, k=571)
  42. 2158 7560394374 0946686893 1142469978 0384096359 9615905798 7944490734 0562590533 1526566339 (David Broadhurst, k=21)
  43. 2177 2437896743 7965836251 4575743671 3661828203 3661826026 1223931459 5695991951 9086084533 (David Broadhurst, k=2)
  44. 2245 3272688158 7998460169 7486857931 3469735371 3718319640 6934115573 8635146048 7798213173 (Patrick Demichel, k=1045646)
  45. 2264 9886126653 2123334159 6403813718 1337527471 3758298735 0606958580 0848359743 5434691757 (Patrick Demichel, k=6442)
  46. 2284 9382102683 9315454393 3085074179 6006410667 6006408382 6624307983 6690956274 2921336489 (Phil Carmody, k=1996)
  47. 2375 3065765163 7836434836 2401095821 4352813200 5647189174 7418578364 3483621635 6753909023 (Phil Carmody, k=1659)
  48. 2411 1757133885 3572005389 2541612826 5593151976 5159867507 3659189775 2462299595 8992074007 (Patrick Demichel, k=160973)
  49. 2491 7412451242 5594681206 3687782518 2769316408 4486434341 6907976450 6046163657 9995560687 (Patrick Demichel, k=1019667)
  50. 2499 9535029070 7510663954 9574161582 0000000000 0000002499 9535029070 7510663954 9574161583 (Patrick Demichel, k=1197481)
  51. 2563 9343837599 4701591015 5341970916 0570576274 0897288413 0017076327 9514010641 1857859601 (Patrick Demichel, k=48200)
  52. 2584 6927880289 6893515829 9167764773 4021673044 5978329540 0949553334 2871842785 3189437819 (David Broadhurst, k=1)
  53. 2657 5355246681 9150576579 3285990110 2514579387 0162749770 9102584259 3108601641 4895426489 (Patrick Demichel, k=2039228)
  54. 2668 3419510569 7331885604 3556436548 3350834483 1602663135 3489035257 7153377704 7796773703 (Phil Carmody, k=279)
  55. 2689 1619858599 2734661491 5525174797 8594588838 1405413851 0214447437 4140072653 4119763637 (Patrick Demichel, k=113606)
  56. 2745 9536391668 6700725332 5359829194 1059834923 6278955683 6503522936 2327237081 1317535611 (Patrick Demichel, k=1806235)
  57. 2746 0704780411 0270474134 4549587458 8311576839 1688425906 9016357250 1958897295 2861164299 (Patrick Demichel, k=25693)
  58. 2789 6097334176 5255159663 0903415320 4562227440 4562224650 8464893263 9307067777 3658812121 (Patrick Demichel, k=49540)
  59. 2842 4078227944 4475640167 6513653543 7591080438 1495460065 8612454087 3274802820 2989777493 (David Broadhurst, k=74)
  60. 2927 4161459806 0414400578 4130629067 8682217281 8271112385 1931919048 0038881734 3336886847 (Patrick Demichel, k=25977)
  61. 2933 5094511431 8588656121 8787636739 0643748989 7477435726 5501373364 5518576243 2639428237 (Norm Dresner, k=12026)
  62. 3281 3480340867 5330616367 1659003015 7974787571 9742963997 0628406213 8595113032 4296082727 (Patrick Demichel, k=1214817)
  63. 3305 8100024235 4370346732 9267281616 5940594059 4059409246 4040618294 8429752673 5207875677 (David Broadhurst, k=42)
  64. 3354 9958510812 3768416339 8762090946 0134433264 9607497368 2673090531 9558079735 1310235371 (Phil Carmody, k=745)
  65. 3372 0938959001 1866294178 8581605968 5391766268 2602918274 6524520414 4840213125 2587052731 (Phil Carmody, k=2155)
  66. 3422 6820258144 9972006165 4060501488 7018430343 6659861183 9321678174 7644033740 0129243597 (Patrick Demichel, k=26386)
  67. 3449 7953393416 6722709416 2828704249 1835374871 1835371421 3881981454 5112665454 9006670623 (Patrick Demichel, k=682591)
  68. 3531 9481647571 9336639235 2401288379 4022700741 7776409346 0401278867 7255849667 2977579459 (Patrick Demichel, k=67183)
  69. 3538 5090086585 4679183350 8536366908 6878773846 8448240250 9161836747 7250955677 0388030157 (Patrick Demichel, k=2358962)
  70. 3693 4900261991 6704481230 4485018619 7120799997 6222630382 7496281301 0652240013 9084949437 (John Gamble, k=17986)
  71. 3735 7199549198 4294830787 7150266042 6642378020 6642374284 9442828822 2347547232 9492111979 (Patrick Demichel, k=2536559)
  72. 3771 2661961088 3039523464 5038634468 6930693069 3069310701 9592654157 6108830395 1969327539 (Patrick Demichel, k=1026593)
  73. 3809 0438247011 9521916159 6414342629 4820720940 5179282868 5258967952 4701195219 1235063571 (David Broadhurst, k=15)
  74. 3852 4808274967 1215244897 8431338348 3551355218 7151631945 1914313136 2035697136 5746025293 (Phil Carmody, k=4342)
  75. 3896 1838798203 5879398557 7286286126 4437478419 3376076031 9118649220 0974612019 5426380903 (John Gamble, k=16589)
  76. 3964 3137550693 5963976579 1705182069 1033336218 8966667745 4170886912 4930640360 2738518289 (Patrick Demichel, k=323736)
  77. 4142 5243952580 1624135922 8233509892 5742999284 5376952945 3729335518 8822352258 6580292809 (David Broadhurst, k=4)
  78. 4162 0066839476 8924597079 7013789801 7897792336 8176672636 9623781545 1841721153 5306313293 (Patrick Demichel, k=744054)
  79. 4258 0033826166 0885882391 5897424377 4523498825 9419527463 5976519068 8996711803 7274735727 (David Broadhurst, k=11)
  80. 4288 5377939564 4942552802 6397747054 7755644090 3054444582 6441449545 7315083319 5381801419 (David Broadhurst, k=23)
  81. 4344 4479367512 4277182894 4309206126 5051653233 1454232876 9969283004 1046131647 9412938361 (David Broadhurst, k=20)
  82. 4531 7201058150 1473118731 2778877657 1778301667 3960043324 5493893685 5322011286 9397365013 (David Broadhurst, k=2)
  83. 4579 0656855495 8129296871 7548628988 5018729163 4050599460 6015011660 0688679965 3781721637 (David Broadhurst, k=2)
  84. 4790 1174864115 3343734678 7494917298 2384750187 7615254602 3559614303 0958984490 9879667487 (Phil Carmody, k=3997)
  85. 4796 6515570223 1477760322 1097105067 4455445544 5544559252 0971015767 7022314777 5552550613 (Phil Carmody, k=466)
  86. 4816 2071311317 5006863792 7963732030 6138613861 3861390954 8209925178 8868249931 4102345893 (Patrick Demichel, k=950054)
  87. 5045 5607197028 5557438743 7515240956 5854583169 4145421876 1461780197 9702855574 3369824127 (David Broadhurst, k=1)
  88. 5279 8614958991 4409826351 0536784286 3065449546 1038438450 6608810354 0635563264 5090163477 (Patrick Demichel, k=23262)
  89. 5412 0000000000 0000005412 0000000000 0000005412 0000000000 0000005412 0000000000 0000005413 (David Broadhurst, k=2)
  90. 5613 1305987786 2320930152 4297825495 0099009900 9900995712 1404997687 2221920251 4396835397 (David Broadhurst, k=86)
  91. 5698 4545700699 8079307470 6479727982 0182676542 8629556168 8644983995 4833942968 3969952133 (John Gamble, k=15754)
  92. 5717 3420003338 3408555993 3934553153 5484831556 6486189618 0069041813 3435779144 6531911957 (David Broadhurst, k=2)
  93. 5836 9199270484 9197877722 3098961680 8118879661 1881126175 7318150146 1078998061 1217841343 (Patrick Demichel, k=361211)
  94. 5879 3726602203 3426387464 4952464937 3206053200 6793952678 6932655404 0220334263 8158518139 (David Broadhurst, k=1)
  95. 5929 4523321048 2962122076 1071675335 9289641139 8014734811 9427674673 1785686394 3715973773 (Phil Carmody, k=142)
  96. 6094 5729317136 8700674710 1059743323 1749138083 6131602108 5621414572 2411013174 3039992371 (David Broadhurst, k=95)
  97. 6108 8619378638 9767055623 8556518925 5514247861 3051031832 2743066218 5446813865 7649367451 (Patrick Demichel, k=148525)
  98. 6222 0739982676 1901873502 7633147931 3901505668 6098500553 4641488344 8000367834 1534653601 (Patrick Demichel, k=1801200)
  99. 6232 5870871682 0709050390 7243423106 2969638162 2650906830 0764105125 6125129604 2100717049 (Phil Carmody, k=188)
  100. 6372 8701596730 4240201163 2931335607 6943811251 0607151012 7264016656 8811506133 2603554041 (Patrick Demichel, k=48180)
  101. 6518 3785525750 7518355314 9982721497 9389168522 3245056588 3111703142 5833712137 2827782477 (Patrick Demichel, k=804878)
  102. 6564 5114355984 1294709618 6101248975 5643564356 4356442208 0757920340 5651145262 1744813333 (Patrick Demichel, k=1814114)
  103. 7082 6255215322 5367675065 2395302461 7364314418 6257595793 7313811034 3190462358 7317061849 (Phil Carmody, k=276)
  104. 7116 9317709557 6396806000 8718836034 8899879539 4910713091 8248204228 3265715666 2193348277 (Patrick Demichel, k=1122642)
  105. 7170 6120203407 3170796592 6112142205 2830064884 7169942285 8950268292 0340731707 8942207091 (David Broadhurst, k=5)
  106. 7341 0961260999 7175939000 3558170612 3275910759 6724096581 4237171759 3900028240 6834081373 (Phil Carmody, k=1822)
  107. 7379 6495349871 7999289968 9113176976 6930693069 3069314310 3426042941 1068596899 6043870047 (David Broadhurst, k=7)
  108. 7433 2578180692 8230889007 0698057573 9307499043 2771508739 3924913692 2740131781 7324569613 (David Broadhurst, k=2)
  109. 7775 6465730584 9546460713 9659271243 7001101470 1317070728 7357782288 8595009000 0778773407 (David Broadhurst, k=11)
  110. 7988 7383878220 0093069994 1687063378 4702263867 5297744121 2086142087 5390806126 6389327247 (David Broadhurst, k=1)
  111. 8012 0508456261 4662107871 0714104510 7664694756 3282216624 7554644869 3640037084 4599992637 (Phil Carmody, k=1418)
  112. 8323 2501000000 0000000000 0832325010 0000000000 0000008323 2501000000 0000000000 0832325011 (Norm Dresner, k=12485)
  113. 8469 2437710600 3913226218 6851086254 4721829991 5278178477 7159540591 9191396227 1572916247 (Patrick Demichel, k=561113)
  114. 8488 5054717813 9458435702 0381454416 9008754589 0991253899 4063472403 0449681112 9390209007 (Phil Carmody, k=897)
  115. 8633 0832947347 2134966523 3552946321 9631656387 7040154003 4444072076 9201015033 6495567007 (Patrick Demichel, k=29641)
  116. 8820 7704847471 5540368331 3576152816 4254266149 5745742671 1959113621 1286102181 7830418967 (Patrick Demichel, k=42797)
  117. 8945 8194731658 9119261420 3655853726 6806649401 9940673320 9538466941 2607205839 4784135609 (Patrick Demichel, k=1343668)
  118. 9277 9331461123 6779470669 0969054438 2891838463 7108170814 2223299587 3887632205 3860892903 (David Broadhurst, k=9)
  119. 9574 2950651234 2088987686 7573031308 2359819804 4136587500 3684208580 4271854360 1060785757 (Patrick Demichel, k=159442)
  120. 9660 6565289534 8388374068 8176703990 5827240891 1815736440 5619598195 2754973546 3487647317 (David Broadhurst, k=2)
  121. 9911 5937528222 5295082776 1849400733 1840895696 7759795202 7831026550 0638231185 5025673317 (Patrick Demichel, k=674798)
  122. 9989 3763011571 3724330885 3218499296 6514339986 6514329997 2751328415 2790009101 3295840691 (Patrick Demichel, k=71155)

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.