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. 10534259 7778657691 5472818955 8776479904 9703664333 0306869926 7482322024 5769154622 8480144239 (Dario Alpern, k=1851)
  2. 10934907 4412949943 3124143810 8594674076 7714594523 2296340384 2127544466 5409549287 6309268601 (Phil Carmody, k=700)
  3. 11500802 0969050601 8630472520 2631112784 2274533096 1630351578 2128808507 1042780261 8970554559 (Dario Alpern, k=2601)
  4. 11838089 5385336510 2937505055 6726690363 6588534312 3423303777 1973870822 6348970743 3315224677 (Phil Carmody, k=2)
  5. 13195548 8612865236 4944908000 5390477593 3120131201 3106935652 4507265964 8175223200 7729653609 (Phil Carmody, k=4)
  6. 13439749 2263356682 9184335408 2003960000 6668903052 6655463303 4405546369 7484567644 4664943053 (Phil Carmody, k=34)
  7. 14161344 3426008130 4626095366 1172842390 5439141485 4575019858 8865149615 9186953880 6611983877 (Phil Carmody, k=2)
  8. 14248688 9922739153 0613273837 7974698426 0427816113 6348882451 4008065125 0998089793 5139340883 (Phil Carmody, k=377)
  9. 14368619 3490046227 8076097149 8301393444 0606060606 0591691986 7116014378 2529963456 2304667163 (Phil Carmody, k=47)
  10. 14661997 9304705387 6001765404 3133498434 6540525275 3474136722 5845230662 9461240128 9674023711 (Phil Carmody, k=5)
  11. 15510952 1035407493 6026275943 9571499048 2551526712 2142109395 8783020793 3928651829 0390442277 (Phil Carmody, k=458)
  12. 16427804 0404450281 1676729213 9359465927 3335216040 6681211763 3739666321 8341513173 2694681969 (Dario Alpern, k=1048)
  13. 16840590 3027279401 1325672366 2858424304 0991432663 1213365961 8908968924 8099478347 3955633471 (Phil Carmody, k=115)
  14. 18928326 4356146741 4785822154 7949030940 3961961855 6056966470 8318108597 0823860299 1910992797 (Phil Carmody, k=2)
  15. 20095862 7485835762 1264705948 3872936068 9075325668 1405827414 9557617396 0559623703 8190437409 (Phil Carmody, k=16)
  16. 23173343 6315297771 2269221679 6464902130 0975609756 0952436412 4660311984 8706388076 4510707627 (Phil Carmody, k=67)
  17. 25114383 0994055393 0110888988 0080143436 9108910891 0916203492 0102966284 1001978096 9189054329 (Phil Carmody, k=4)
  18. 26821976 8200967957 0012349435 6475349826 9274292742 9247470766 1073324785 9261943307 2798942917 (Phil Carmody, k=46)
  19. 28594864 8919041324 7580801527 2804493730 3762376237 6266218627 2681417562 3818425289 6566869969 (Phil Carmody, k=696)
  20. 28932610 1516531379 9276606338 1263116214 6138613861 3890318748 7655145241 3137992476 7401730077 (Phil Carmody, k=2)
  21. 30800670 1912350597 6126418200 0717131474 1066657243 8964143426 2979007841 5059760956 1783788719 (Phil Carmody, k=523)
  22. 31036343 0199203187 2540996502 3824701195 2222271402 7808764940 2421474590 0318725099 6046972599 (Phil Carmody, k=1)
  23. 31389625 7252124074 2769473680 5936697430 7783346877 6435993031 7738753759 1918290993 2329052479 (Phil Carmody, k=1)
  24. 33073486 7618393846 0660337689 3868671328 0000000000 0033073486 7618393846 0660337689 3868671329 (Phil Carmody, k=16)
  25. 44104594 2036029313 7531770245 2008808953 4600395368 5443709225 6636424682 2931374876 6609204323 (Phil Carmody, k=9)
  26. 45966085 9678598212 1324532924 8192430854 6882797503 3163168582 6561395715 4441735421 5075228359 (Phil Carmody, k=171)
  27. 49335355 1894340931 1924441292 9143398737 5158506118 0823010066 0500210653 8687367430 5398725209 (Dario Alpern, k=2876)
  28. 60045672 6628335122 6145387005 7555169896 4113224586 8030480259 5900209315 9073143434 2494004707 (Phil Carmody, k=197)
  29. 63235278 9510987923 1898515421 4971292813 3106197068 6957038210 2617184991 8792318352 8077489883 (Phil Carmody, k=11)
  30. 70187242 6091304144 6731558206 5827765057 7146024820 2924162422 3237328964 9585533386 2973789879 (Phil Carmody, k=21)
  31. 75743341 2430278884 4697257285 4661354581 6808811070 3266932270 9239089954 7888446215 1470165653 (Phil Carmody, k=34)