Known 314-digit prime factors of googolduplex − 1

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2. Number Theory
3. Known 314-digit prime factors of googolduplex − 1

This is a list of known 314-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. 1924 3905912663 8086522118 6256349066 9527469417 5367563506 2532594994 3554870215 1073385824 2758742562 7280026674 2706298828 1250000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=9)
2. 2590 8505665283 3338761590 5558840119 8713348001 0933088441 5507111041 0505775409 4872811739 1452251041 6864679681 6418818384 4899079098 5296840495 8400809590 1133117422 4324058741 3311004638 6718750000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
3. 8816 2076311671 5630976552 4029166842 5836399916 7579065641 1315637797 0881294459 1045379638 6718750000 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)