Known 73-digit prime factors of Googolplex - 1

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  2. Number Theory
  3. Known 73-digit prime factors of Googolplex − 1

This is a list of known 73-digit prime factors of googolplex − 1, i.e., 1010^100 − 1.

These numbers have the form 1 + 2k × 2m × 5n, where 0 ≤ m ≤ 100 and 0 ≤ n ≤ 100.

In the list you can see the prime factors and their corresponding value of k.

  1. 106 9004800000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=20879)
  2. 110 7148800000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=2703)
  3. 145 5191522836 6851806640 6250000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  4. 157 4218750000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=403)
  5. 211 7582368135 7508476708 0625169910 4905128479 0039062500 0000000000 0000000001 (Phil Carmody, k=1)
  6. 222 3212511363 0720000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1011)
  7. 323 3257317791 5899904000 0000000000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=918947)
  8. 402 3406499457 9266105745 3187822829 9319744110 1074218750 0000000000 0000000001 (Phil Carmody, k=19)
  9. 409 2000718304 5670196008 8139458093 7922000885 0097656250 0000000000 0000000001 (Dario Alpern, k=7548409)
  10. 417 5533616784 7989514712 0259935036 3016128540 0390625000 0000000000 0000000001 (Dario Alpern, k=3081)
  11. 440 4571325722 3617631552 7700353413 8202667236 3281250000 0000000000 0000000001 (Phil Carmody, k=13)
  12. 517 8602998979 4431817047 1371398644 3224257527 6177376508 7127685546 8750000001 (Dario Alpern, k=16027)
  13. 555 1115123125 7827021181 5834045410 1562500000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  14. 805 3063680000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  15. 894 0696716308 5937500000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)