Known 90-digit prime factors of Googolplex - 10

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  2. Number Theory
  3. Known 90-digit prime factors of Googolplex − 10

This is a list of known 90-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. 1382943612 3846660477 6107052522 2214622011 0059305281 1323638331 3905965758 6047747241 2273927293 (Phil Carmody, k=14)
  2. 1408870973 0561923416 1706184675 8076586887 5987148353 7765528376 8771838483 5635545351 4165541547 (Phil Carmody, k=37)
  3. 1604274902 9466108797 2616558584 4925692338 1626016260 0021741357 2159907462 9009457675 6700323923 (Dario Alpern, k=2477)
  4. 1774106190 3697200000 0000017741 0619036972 0000000000 1774106190 3697200000 0000017741 0619036973 (Phil Carmody, k=54)
  5. 2019204486 5198658792 6013739073 6999420749 2871287128 9147917357 8069945921 3142451944 9870707879 (Phil Carmody, k=83)
  6. 2041750302 8345707110 7110731488 6101390567 7821782178 4219968124 6167489288 9288949310 3923172747 (Dario Alpern, k=2293)
  7. 2080524971 3246661386 1386159419 1110993852 7524752475 4555772496 0771413861 3861406943 8635746329 (Phil Carmody, k=156)
  8. 2091338799 1423473715 9862348428 8396434962 6755838489 5335500309 8179312205 3106509939 5152273453 (Phil Carmody, k=62)
  9. 2457104254 6808006482 5631176463 1770379466 0000000000 2457104254 6808006482 5631176463 1770379467 (Phil Carmody, k=1)
  10. 2903329638 0000000000 2903329638 0000000000 2903329638 0000000000 2903329638 0000000000 2903329639 (Phil Carmody, k=1)
  11. 2988166124 1621043050 4305013168 7692626840 0000000000 2988166124 1621043050 4305013168 7692626841 (Phil Carmody, k=140)
  12. 3090685452 0000000000 3090685452 0000000000 3090685452 0000000000 3090685452 0000000000 3090685453 (Dario Alpern, k=1382)
  13. 3358499074 2842076481 7232957103 2674504902 4881095847 8477403226 7723172329 2351861255 7555600751 (Phil Carmody, k=125)
  14. 3472918394 3633217417 6947569398 5063476481 6038433111 2565514717 2405215693 9090863713 0974956631 (Phil Carmody, k=5)
  15. 3688142225 2331876136 3632634070 3351013841 5449326966 6422539323 4511873141 4047768593 8871221493 (Phil Carmody, k=34)
  16. 3694506440 0819154275 5404989401 0661370600 4762058070 1067551630 3942903794 9357068669 4100687471 (Phil Carmody, k=145)
  17. 4367779816 1449042616 0970257882 1731089184 0001996639 4278097448 1310608979 3854902064 4662487997 (Phil Carmody, k=698)
  18. 4391188534 9727834201 6538200065 0126221396 0000000000 4391188534 9727834201 6538200065 0126221397 (Phil Carmody, k=806)
  19. 4620234257 5940783563 6040881888 5459942971 4397196095 0223038163 0337979658 1643685793 9857139067 (Phil Carmody, k=451)
  20. 4738334729 0352334569 5352265089 6023670338 6006222858 6625491348 7254216401 7842739457 7493196637 (Phil Carmody, k=326)
  21. 4950919855 5637565895 4371147933 2577325035 3269915157 5755146559 6836467259 0698410859 7366516079 (Dario Alpern, k=1091)
  22. 4985704069 8252470222 5602346587 0657287697 8580140420 6405563649 6832610642 7022206166 9237428119 (Phil Carmody, k=373)
  23. 7141748531 8469343450 7558095460 5013263244 7674414735 9099286675 9709921810 5168784134 5666496969 (Phil Carmody, k=4)