Known 26-digit prime factors of googolduplex − 1

  1. Alpertron
  2. Number Theory
  3. Known 26-digit prime factors of googolduplex − 1

This is a list of known 26-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. 105717 7600000000 0000000001 (Phil Carmody, k=2581)
  2. 107099 2020185722 9127680001 (Dario Alpern, k=14863)
  3. 115010 6754839740 4160000001 (Phil Carmody, k=2043)
  4. 135271 2192000000 0000000001 (Dario Alpern, k=82563)
  5. 135936 6511525510 5126400001 (Dario Alpern, k=3773)
  6. 147906 4551516050 2759587841 (Dario Alpern, k=320721)
  7. 148579 0248960000 0000000001 (Phil Carmody, k=1107)
  8. 155500 0000000000 0000000001 (Phil Carmody, k=311)
  9. 168254 4000000000 0000000001 (Dario Alpern, k=105159)
  10. 190271 4987373343 5392000001 (Dario Alpern, k=4326273)
  11. +19721061166646717498359681 () (k=30814158072885496091187)
  12. 213927 4444800000 0000000001 (Dario Alpern, k=2611419)
  13. 244140 6250000000 0000000001 (Phil Carmody, k=1)
  14. 248839 1988567123 6747919361 (Dario Alpern, k=8431)
  15. 249941 2787200000 0000000001 (Dario Alpern, k=3051041)
  16. 254689 0303373671 4048765953 (Dario Alpern, k=21573)
  17. 295543 6706542968 7500000001 (Dario Alpern, k=3099)
  18. 348687 1719360351 5625000001 (Phil Carmody, k=117)
  19. 355784 3705622691 8400000001 (Phil Carmody, k=79)
  20. 368058 0277370880 0000000001 (Dario Alpern, k=1371123)
  21. 369419 4142583193 6000000001 (Dario Alpern, k=67197)
  22. 386498 8684654235 8398437501 (Phil Carmody, k=83)
  23. 425012 9834582680 6923264001 (Phil Carmody, k=9)
  24. 428809 5348326400 0000000001 (Phil Carmody, k=39)
  25. 450359 9627370496 0000000001 (Phil Carmody, k=1)
  26. 496693 3827315302 4000000001 (Dario Alpern, k=22587)
  27. 503316 4800000000 0000000001 (Phil Carmody, k=3)
  28. 506176 8559427391 4814464001 (Dario Alpern, k=1404923)
  29. 521627 4261474609 3750000001 (Dario Alpern, k=273483)
  30. 544823 7061500549 3164062501 (Phil Carmody, k=117)
  31. 563714 4576000000 0000000001 (Phil Carmody, k=21)
  32. 662500 0000000000 0000000001 (Phil Carmody, k=53)
  33. 702120 7809448242 1875000001 (Dario Alpern, k=736227)
  34. 720575 9403792793 6000000001 (Phil Carmody, k=1)
  35. 734003 2000000000 0000000001 (Phil Carmody, k=7)
  36. 779198 8551616668 7011718751 (Dario Alpern, k=1045823)
  37. 780345 0163200000 0000000001 (Dario Alpern, k=148839)
  38. 795271 0937500000 0000000001 (Dario Alpern, k=1017947)
  39. 824633 7208320000 0000000001 (Phil Carmody, k=3)