Known 85-digit prime factors of googolduplex − 1

  1. Alpertron
  2. Number Theory
  3. Known 85-digit prime factors of googolduplex − 1

This is a list of known 85-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. 10351 9633412361 1450195312 5000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=1389417)
  2. 10871 6359680000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=81)
  3. 11847 2708867193 9354394085 0332344442 0500520960 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=17)
  4. 14379 8828125000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=589)
  5. 17593 9224862720 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=2097359)
  6. 20873 4975058246 6326047743 2303198866 3695976693 7600000000 0000000000 0000000000 0000000001 (Phil Carmody, k=117)
  7. 24870 5508004464 6521058032 1417775609 2964302657 2979367811 3818080454 9017600000 0000000001 (Phil Carmody, k=369)
  8. 25317 0080989178 2168167507 0792923554 9323264000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=93)
  9. 26843 5456000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  10. 27033 6000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=33)
  11. 29497 1466064453 1250000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=3093)
  12. 30140 7974666844 1906117132 5022324696 2633538714 7264555096 6262817382 8125000000 0000000001 (Phil Carmody, k=597)
  13. 30329 9400005444 6976900039 1972897084 5078417874 7535814404 1241561530 3680000000 0000000001 (Phil Carmody, k=9)
  14. 34972 0252756924 3102334439 7544860839 8437500000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=63)
  15. 36016 8037506465 5785068796 5467815287 8530621226 2698779604 8974354317 3120000000 0000000001 (Phil Carmody, k=171)
  16. 37282 0068150758 7432861328 1250000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1281)
  17. 42633 3095345995 9493656583 6178488098 0849266052 2460937500 0000000000 0000000000 0000000001 (Dario Alpern, k=3145783)
  18. 43520 7425653061 3638460636 1389160156 2500000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=49)
  19. 45496 7496278016 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=847443)
  20. 46074 1276049937 6918033913 7111605814 1395166042 3774023617 3761052672 0000000000 0000000001 (Phil Carmody, k=7)
  21. 49319 2672729492 1875000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=10343)
  22. 50771 9814777374 2675781250 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=13629)
  23. 52314 9661930402 8838297600 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=709)
  24. 57277 5247207123 1727722703 7631709184 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=353)
  25. 63940 6966332270 0267141121 1431337382 1099470487 5520000000 0000000000 0000000000 0000000001 (Phil Carmody, k=7)
  26. 65765 5645870358 2710401597 4400000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=17)
  27. 71134 7070136980 6192815303 8024902343 7500000000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=250283)