Known 56-digit prime factors of googolduplex − 1

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

This is a list of known 56-digit prime factors of googolduplex − 1, i.e., 1010^(10^100) − 1.

These numbers have the form 1 + 2k × 2m × 5n, where 0 ≤ m ≤ 10100 and 0 ≤ m ≤ 10100.

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

  1. 107999 7746575244 1467343432 3647777996 8000000000 0000000001 (Phil Carmody, k=13)
  2. 112243 3257470133 4411804299 5152610535 9095756193 0055680001 (Phil Carmody, k=3)
  3. 157673 2375364860 4643038925 8099584118 4602521600 0000000001 (Phil Carmody, k=181)
  4. 184467 4407370955 1616000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  5. 184774 3988037109 3750000000 0000000000 0000000000 0000000001 (Phil Carmody, k=31)
  6. 197020 0937500000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=6304643)
  7. 215885 0616056382 9358800666 6240000000 0000000000 0000000001 (Dario Alpern, k=571443)
  8. 237790 0603251621 8880000000 0000000000 0000000000 0000000001 (Phil Carmody, k=33)
  9. 254126 1619200000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=1551063)
  10. 254287 7197265625 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=3333)
  11. 279859 6857728208 3202817375 4224553704 2617797851 5625000001 (Phil Carmody, k=413)
  12. 304527 2827148437 5000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=7983)
  13. 366640 0516522116 9590950012 2070312500 0000000000 0000000001 (Phil Carmody, k=129)
  14. 386784 1247233151 2776679549 7720813181 9597243351 0400000001 (Phil Carmody, k=271)
  15. 426319 1900274298 1309874831 3600000000 0000000000 0000000001 (Dario Alpern, k=451383)
  16. 565164 8096443039 7440000000 0000000000 0000000000 0000000001 (Dario Alpern, k=321259)
  17. 602134 0351084089 6571093402 2553600000 0000000000 0000000001 (Phil Carmody, k=19)
  18. 606294 8198614917 5747355987 9822145533 9353907658 7520000001 (Phil Carmody, k=531)
  19. 659421 7010339231 0882337303 3810952192 0000000000 0000000001 (Phil Carmody, k=127)
  20. 672530 4731020991 4733854720 0000000000 0000000000 0000000001 (Dario Alpern, k=729159)
  21. 867361 7379884035 4720596224 0695953369 1406250000 0000000001 (Phil Carmody, k=1)
  22. 909494 7017729282 3791503906 2500000000 0000000000 0000000001 (Phil Carmody, k=1)