Known 28-digit prime factors of googolduplex − 1

  1. Alpertron
  2. Number Theory
  3. Known 28-digit prime factors of googolduplex − 1

This is a list of known 28-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. 14348901 6203837440 0000000001 (Dario Alpern, k=52201)
  2. 14448609 2800000000 0000000001 (Dario Alpern, k=1410997)
  3. 15867151 3824420079 1801856001 (Phil Carmody, k=21)
  4. 17462298 2740402221 6796875001 (Phil Carmody, k=3)
  5. 19384000 0000000000 0000000001 (Phil Carmody, k=2423)
  6. 19648000 0000000000 0000000001 (Phil Carmody, k=307)
  7. 20615843 0208000000 0000000001 (Phil Carmody, k=3)
  8. 22530555 7250976562 5000000001 (Phil Carmody, k=189)
  9. 23221685 5786291200 0000000001 (Phil Carmody, k=33)
  10. 26214400 0000000000 0000000001 (Phil Carmody, k=1)
  11. 26751431 2500000000 0000000001 (Dario Alpern, k=4280229)
  12. 27625000 0000000000 0000000001 (Phil Carmody, k=221)
  13. 28823037 6151711744 0000000001 (Phil Carmody, k=1)
  14. 29582320 0000000000 0000000001 (Dario Alpern, k=369779)
  15. 30301562 5000000000 0000000001 (Dario Alpern, k=19393)
  16. 37550926 2084960937 5000000001 (Phil Carmody, k=63)
  17. 41560519 4752000000 0000000001 (Dario Alpern, k=6193)
  18. 45035996 2737049600 0000000001 (Phil Carmody, k=1)
  19. 45455610 8175100569 6895221761 (Phil Carmody, k=47)
  20. 53144344 7727390720 0000000001 (Dario Alpern, k=96669)
  21. 58074653 1486511230 4687500001 (Dario Alpern, k=974331)
  22. 61993648 1280000000 0000000001 (Dario Alpern, k=236487)
  23. 70121046 1981586227 2000000001 (Phil Carmody, k=1557)
  24. 74883796 3353292800 0000000001 (Dario Alpern, k=6974097)
  25. 76553987 9058946392 0640000001 (Phil Carmody, k=83)
  26. 86147338 1519317626 9531250001 (Phil Carmody, k=37)
  27. 90702496 4952417894 4000000001 (Phil Carmody, k=1007)
  28. 91137695 3125000000 0000000001 (Dario Alpern, k=3733)
  29. 96000000 0000000000 0000000001 (Phil Carmody, k=3)
  30. 99643241 2672000000 0000000001 (Phil Carmody, k=29)