Known 315-digit prime factors of googolduplex − 1

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2. Number Theory
3. Known 315-digit prime factors of googolduplex − 1

This is a list of known 315-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. 15192 9083932156 7799595718 7631299131 4467535453 3379191194 6047647985 3264131690 3169785445 2990290834 2617601488 4421278106 0747374795 0280085206 0317993164 0625000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
2. 18231 4900718588 1359514862 5157558957 7361042544 0055029433 5257177582 3916958028 3803742534 3588349001 1141121786 1305533727 2896849754 0336102247 2381591796 8750000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)