Known 22-digit prime factors of googolduplex − 1

  1. Alpertron
  2. Number Theory
  3. Known 22-digit prime factors of googolduplex − 1

This is a list of known 22-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. 10 2250000000 0000000001 (Phil Carmody, k=409)
  2. 15 6852205649 9200000001 (Phil Carmody, k=913)
  3. 15 6989853510 6012774401 (Dario Alpern, k=27887)
  4. 17 1798691840 0000000001 (Phil Carmody, k=1)
  5. 18 8922882080 0781250001 (Phil Carmody, k=1981)
  6. 20 4869940019 2000000001 (Phil Carmody, k=477)
  7. 23 2216855786 2912000001 (Phil Carmody, k=33)
  8. 24 1060000000 0000000001 (Dario Alpern, k=12053)
  9. 26 8553970253 8240000001 (Dario Alpern, k=2000883)
  10. 28 6720000000 0000000001 (Phil Carmody, k=7)
  11. 32 2122547200 0000000001 (Phil Carmody, k=3)
  12. 34 5937067114 4960000001 (Dario Alpern, k=322179)
  13. 35 4764298649 6000000001 (Phil Carmody, k=413)
  14. 40 2063641808 1051115521 (Dario Alpern, k=1428417)
  15. 43 0871119134 7200000001 (Phil Carmody, k=627)
  16. 44 0862874009 6000000001 (Dario Alpern, k=1051099)
  17. 46 4486400000 0000000001 (Phil Carmody, k=567)
  18. 51 1160500000 0000000001 (Dario Alpern, k=1022321)
  19. 51 2113320827 5538411521 (Dario Alpern, k=7107)
  20. 52 7765581332 4800000001 (Phil Carmody, k=3)
  21. 54 1563289600 0000000001 (Dario Alpern, k=20659)
  22. 56 2500000000 0000000001 (Phil Carmody, k=9)
  23. 61 0228953415 6800000001 (Phil Carmody, k=111)
  24. 61 3164062500 0000000001 (Dario Alpern, k=15697)
  25. 68 7194767360 0000000001 (Phil Carmody, k=1)
  26. 69 9968735121 8271682561 (Dario Alpern, k=4973577)
  27. 72 6395781120 0000000001 (Dario Alpern, k=138549)
  28. 73 5795360000 0000000001 (Dario Alpern, k=4598721)
  29. 78 6432000000 0000000001 (Phil Carmody, k=3)