Known 279-digit prime factors of googolduplex − 1

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2. Number Theory
3. Known 279-digit prime factors of googolduplex − 1

This is a list of known 279-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. 216290960 5513009014 6624752284 8893204718 6344624460 6410395761 0313955228 7757396697 9980468750 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=23)
2. 323232272 4005210850 7617976743 0578026123 4560966979 3153327334 7842513059 7522431811 8100003141 0164544686 6942100823 1711515409 5023239806 1736202968 6615076171 3638256581 9549334063 3812371817 5427400307 5312392637 5206974423 1359504113 0531429138 2506652894 3352750502 5267601013 1835937500 0000000001 (Phil Carmody, k=199)
3. 491356638 6437161783 3093187255 8898693328 2022027307 3258399065 8213224378 4144520759 5825195312 5000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=209)
4. 584721565 2465820312 5000000000 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=981)