Known 56-digit prime factors of Googolplex - 1

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  2. Number Theory
  3. Known 56-digit prime factors of Googolplex − 1

This is a list of known 56-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. 184467 4407370955 1616000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  2. 184774 3988037109 3750000000 0000000000 0000000000 0000000001 (Phil Carmody, k=31)
  3. 197020 0937500000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=6304643)
  4. 215885 0616056382 9358800666 6240000000 0000000000 0000000001 (Dario Alpern, k=571443)
  5. 237790 0603251621 8880000000 0000000000 0000000000 0000000001 (Phil Carmody, k=33)
  6. 254126 1619200000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=1551063)
  7. 254287 7197265625 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=3333)
  8. 279859 6857728208 3202817375 4224553704 2617797851 5625000001 (Phil Carmody, k=413)
  9. 304527 2827148437 5000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=7983)
  10. 366640 0516522116 9590950012 2070312500 0000000000 0000000001 (Phil Carmody, k=129)
  11. 426319 1900274298 1309874831 3600000000 0000000000 0000000001 (Dario Alpern, k=451383)
  12. 565164 8096443039 7440000000 0000000000 0000000000 0000000001 (Dario Alpern, k=321259)
  13. 672530 4731020991 4733854720 0000000000 0000000000 0000000001 (Dario Alpern, k=729159)
  14. 867361 7379884035 4720596224 0695953369 1406250000 0000000001 (Phil Carmody, k=1)
  15. 909494 7017729282 3791503906 2500000000 0000000000 0000000001 (Phil Carmody, k=1)