Known 367-digit prime factors of googolduplex − 1

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2. Number Theory
3. Known 367-digit prime factors of googolduplex − 1

This is a list of known 367-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. 4959119 3747872604 2911856632 7512947647 2819702597 9597814385 3763159689 0953170455 2304156700 9009542777 2689131825 4261080864 1525576729 3727160260 8621417295 1549624024 4278214776 3947011322 2807694937 2098658931 0959029372 3666854434 8762124274 6912350166 5009458222 7727688877 8230808790 8145211031 2966397032 1416854858 3984375000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=11)
2. 6393585 7199852256 8176953922 3333000991 9341215335 4003001117 2110185554 5700571033 1678205953 7372280337 2908501177 1028918597 0423983653 2452756705 1411129907 8762418197 2445940346 9747692876 6049853338 3878963639 7986759774 8807384050 4512190818 7866210937 5000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=179)