Known 351-digit prime factors of googolduplex − 1

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2. Number Theory
3. Known 351-digit prime factors of googolduplex − 1

This is a list of known 351-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. 1 2411657087 0920650643 8178817968 2757671462 5525105163 7472388828 0227008854 3956530835 1738489656 0857831783 0903244237 3671206846 3683530658 7704827612 4902935234 3988326867 8075891920 5122277667 4682986025 0868610440 2330688809 0392580970 8710655951 5404611692 2914866353 9774588571 1628943681 7169189453 1250000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=641)
2. 3 0174867129 8520595304 9668567526 1001329530 4238633218 8465607932 2261209501 5879378883 6583182777 7108541582 7384326349 2907434533 0622291964 2954550297 2751654602 5088787889 5700587286 5089062323 4168157933 4907725709 0584680554 4570088386 5356445312 5000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=33)
3. 7 2611098403 4247176153 3807437411 9097141941 6098509148 2872789555 5150207806 5268316118 4117529189 2694023692 0260789220 1664626636 3203182481 1065684160 4346344975 0321725045 6762238224 5255134560 0719497026 6392026756 4337103017 0003398815 5483556658 7780489619 4899764161 3345876976 3819873332 9772949218 7500000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)