Known 29-digit prime factors of googolduplex − 1

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  2. Number Theory
  3. Known 29-digit prime factors of googolduplex − 1

This is a list of known 29-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. 104857600 0000000000 0000000001 (Phil Carmody, k=1)
  2. 109375000 0000000000 0000000001 (Phil Carmody, k=7)
  3. 109951162 7776000000 0000000001 (Phil Carmody, k=1)
  4. 114688000 0000000000 0000000001 (Phil Carmody, k=7)
  5. 118125000 0000000000 0000000001 (Phil Carmody, k=189)
  6. 121111318 4690475463 8671875001 (Dario Alpern, k=8127643)
  7. 154952650 2191602335 7440000001 (Phil Carmody, k=21)
  8. 165355205 5358886718 7500000001 (Dario Alpern, k=13871)
  9. 175460065 5604940800 0000000001 (Dario Alpern, k=7979)
  10. 181715726 8524169921 8750000001 (Dario Alpern, k=762171)
  11. 196426833 8549628926 6368512001 (Dario Alpern, k=8319)
  12. 196761088 8575785097 3896704001 (Dario Alpern, k=266661)
  13. 208514457 6000000000 0000000001 (Dario Alpern, k=1018137)
  14. 223825100 8000000000 0000000001 (Dario Alpern, k=34153)
  15. 237390585 2437019348 1445312501 (Dario Alpern, k=1274481)
  16. 250899757 3654609920 0000000001 (Dario Alpern, k=7131)
  17. 281056000 0000000000 0000000001 (Dario Alpern, k=8783)
  18. 285568000 0000000000 0000000001 (Phil Carmody, k=2231)
  19. 300000000 0000000000 0000000001 (Phil Carmody, k=3)
  20. 310062279 0328320000 0000000001 (Phil Carmody, k=141)
  21. 389667906 0462328872 9600000001 (Dario Alpern, k=2768757)
  22. 418750000 0000000000 0000000001 (Phil Carmody, k=67)
  23. 487457946 7773437500 0000000001 (Dario Alpern, k=7986511)
  24. 532163627 8435840000 0000000001 (Phil Carmody, k=121)
  25. 667540997 0135040000 0000000001 (Dario Alpern, k=4857)
  26. 671088640 0000000000 0000000001 (Phil Carmody, k=1)
  27. 788129934 7898368000 0000000001 (Phil Carmody, k=7)
  28. 894069671 6308593750 0000000001 (Phil Carmody, k=3)