Known 49-digit prime factors of Googolplex - 1

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  2. Number Theory
  3. Known 49-digit prime factors of Googolplex − 1

This is a list of known 49-digit prime factors of googolplex − 1, i.e., 1010^100 − 1.

These numbers have the form 1 + 2k × 2m × 5n, where 0 ≤ m ≤ 100 and 0 ≤ n ≤ 100.

In the list you can see the prime factors and their corresponding value of k.

  1. 109951162 7776000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  2. 128013763 0436777527 7645824000 0000000000 0000000001 (Dario Alpern, k=173491)
  3. 134080942 9260930383 8720000000 0000000000 0000000001 (Dario Alpern, k=595439)
  4. 173494873 0468750000 0000000000 0000000000 0000000001 (Dario Alpern, k=142127)
  5. 186076164 2456054687 5000000000 0000000000 0000000001 (Dario Alpern, k=39023)
  6. 200561277 0443948259 3542448087 0400000000 0000000001 (Dario Alpern, k=414751)
  7. 210732433 7639202488 3200000000 0000000000 0000000001 (Dario Alpern, k=5849)
  8. 225404219 0671476096 2396651520 0000000000 0000000001 (Dario Alpern, k=3729)
  9. 264594746 1132891476 1543273925 7812500000 0000000001 (Dario Alpern, k=11637)
  10. 265659764 4090652465 8203125000 0000000000 0000000001 (Phil Carmody, k=1141)
  11. 271034240 7226562500 0000000000 0000000000 0000000001 (Phil Carmody, k=1421)
  12. 272848410 5318784713 7451171875 0000000000 0000000001 (Phil Carmody, k=3)
  13. 290024081 1398724360 9699362423 2709407806 3964843751 (Phil Carmody, k=107)
  14. 298403467 2779864100 0448000000 0000000000 0000000001 (Dario Alpern, k=207059)
  15. 309944152 8320312500 0000000000 0000000000 0000000001 (Phil Carmody, k=13)
  16. 338745117 1875000000 0000000000 0000000000 0000000001 (Phil Carmody, k=111)
  17. 366595642 7312266896 4788317680 3588867187 5000000001 (Phil Carmody, k=1651)
  18. 398786560 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1217)
  19. 450359962 7370496000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  20. 461168601 8427387904 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  21. 511333346 3668823242 1875000000 0000000000 0000000001 (Dario Alpern, k=6863)
  22. 581573041 5679307776 0000000000 0000000000 0000000001 (Dario Alpern, k=165293)
  23. 602286194 0066168602 6240000000 0000000000 0000000001 (Phil Carmody, k=653)
  24. 610670745 3727722167 9687500000 0000000000 0000000001 (Dario Alpern, k=2049071)
  25. 685635131 9584064185 6193542480 4687500000 0000000001 (Dario Alpern, k=3769319)
  26. 707324800 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=221039)
  27. 737869762 9483820646 4000000000 0000000000 0000000001 (Phil Carmody, k=1)
  28. 772774910 7289128005 5046081542 9687500000 0000000001 (Dario Alpern, k=33987)
  29. 849990908 0677673142 1921352089 6000000000 0000000001 (Dario Alpern, k=87887)
  30. 875318476 8000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=133563)
  31. 915527343 7500000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  32. 937500000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)