Known 82-digit prime factors of googolduplex − 1

  1. Alpertron
  2. Number Theory
  3. Known 82-digit prime factors of googolduplex − 1

This is a list of known 82-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 6989710659 2625614863 2175053373 4400000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=211)
  2. 12 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  3. 13 1698835543 1623237651 7044764572 9695467235 3933126533 1200000000 0000000000 0000000001 (Phil Carmody, k=11)
  4. 17 0530256582 4240446090 6982421875 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  5. 19 5300000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1953)
  6. 20 4636307898 9088535308 8378906250 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=9)
  7. 22 9949392860 3624226525 4259109497 0703125000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=2589)
  8. 24 1040706638 8485413312 9431385117 4390378330 4490674189 2529520640 0000000000 0000000001 (Phil Carmody, k=3)
  9. 25 1456570479 8428683388 8460800000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=13)
  10. 28 1925493490 7582188928 6679287562 2400000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=139)
  11. 29 8932812500 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=191317)
  12. 30 1710059607 9718689892 9957097021 7120524939 2646798966 7840000000 0000000000 0000000001 (Phil Carmody, k=63)
  13. 32 1130730858 8409732381 1434312613 6405686117 9904000000 0000000000 0000000000 0000000001 (Phil Carmody, k=9)
  14. 32 7836460201 0697126388 5498046875 0000000000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=18023)
  15. 36 6576158212 5588305742 5304084293 8777600000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=353)
  16. 38 7602074835 7580623023 3588922547 7749409654 2798770889 0893792736 0408568463 3600000001 (Phil Carmody, k=351)
  17. 41 5675507848 0218109150 8490321478 1981707637 1715145456 1856352156 1340906898 9808640001 (Phil Carmody, k=919)
  18. 42 6467750003 2121315598 4878540039 0625000000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=3001)
  19. 44 0439717670 9798070453 3043588480 5139743113 2160000000 0000000000 0000000000 0000000001 (Phil Carmody, k=79)
  20. 46 3711082674 9910044682 7265949673 7647586558 8840676978 4667498209 6286515200 0000000001 (Phil Carmody, k=43)
  21. 47 0407680000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=183753)
  22. 47 3316543132 6070832470 3713916967 1737803923 8610654138 0286216735 8398437500 0000000001 (Phil Carmody, k=3)
  23. 52 8414954676 1525399754 7349570558 4761203288 0306817952 2062963076 0884633600 0000000001 (Phil Carmody, k=49)
  24. 53 1667660800 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=5192067)
  25. 65 8201822928 4824168619 8767302294 0201993094 3462534319 4533944360 9600000000 0000000001 (Phil Carmody, k=1)
  26. 69 1752902764 1081856000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  27. 73 9097595214 8437500000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=31)
  28. 82 2476800000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=251)
  29. 94 1565260308 0021145753 6841348114 9962415353 3166696051 7693440000 0000000000 0000000001 (Phil Carmody, k=3)
  30. 99 3013381958 0078125000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=833)