Known 72-digit prime factors of Googolplex - 1

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  2. Number Theory
  3. Known 72-digit prime factors of Googolplex − 1

This is a list of known 72-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. 11 0203221602 5207456144 8409895092 4817472696 3043212890 6250000000 0000000001 (Dario Alpern, k=26021)
  2. 12 3405770864 3376827239 9902343750 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=424019)
  3. +129694419029057750551385771184564274499075700947656757821537291527196801 () (k=40529505946580547047308053495176335780961156546142736819230403602249)
  4. 13 4935020469 1290855407 7148437500 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=1159083)
  5. 15 8535832829 9520000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=2307)
  6. 16 7772160000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  7. 17 2053567411 0297563732 5300795055 2273541688 9190673828 1250000000 0000000001 (Phil Carmody, k=13)
  8. 18 1346365875 3566853931 7157410550 8625507354 7363281250 0000000000 0000000001 (Dario Alpern, k=13381)
  9. 19 2000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  10. 23 2830643653 8696289062 5000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  11. 40 9600000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  12. 57 3856549958 6629494420 3978012353 6729661282 1519374847 4121093750 0000000001 (Phil Carmody, k=111)
  13. 60 1680837813 4154178555 2679000304 0105148102 1568179130 5541992187 5000000001 (Dario Alpern, k=58191)
  14. 64 8433342576 0269165039 0625000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=557)
  15. 68 9280000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1077)
  16. 91 0949707031 2500000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=597)
  17. 96 6367641600 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=9)
  18. 96 9352280335 5793064899 3206101948 7719022436 0674619674 6826171875 0000000001 (Phil Carmody, k=3)