Known 293-digit prime factors of googolduplex − 1

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2. Number Theory
3. Known 293-digit prime factors of googolduplex − 1

This is a list of known 293-digit prime factors of googolduplex − 1, i.e., 10^{10^(10^100)} − 1.

These numbers have the form 1 + 2k × 2^m × 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. 158 8186776101 8131357531 0468877432 8678846359 2529296875 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
2. 322 1225472000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
3. 749 0682167507 5173234493 5906217388 2511864037 3420706933 0613944872 6176613242 6783994391 7861615606 2823413508 8860650102 7203142268 0539871863 8899273796 3077409204 6283345192 6642759123 6654501619 1077266398 6790576018 3930397033 6914062500 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)