Known 317-digit prime factors of googolduplex − 1

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2. Number Theory
3. Known 317-digit prime factors of googolduplex − 1

This is a list of known 317-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. 1675529 9953718434 1285422893 2465034759 2820275536 9186973024 9175715172 2172689016 8786488159 0421426433 2161816705 1326004965 0371564569 8947869531 2069896026 2198688590 0261243786 9572659110 4175895452 4993896484 3750000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=651)
2. 6807290 4753210672 7643794447 2573665357 0570259235 2326519324 0208295331 9818618904 6361011018 3614940064 7211274448 9893906058 7471550298 3576037407 8900407469 8414092661 7230321459 8335492668 8650067452 8462474252 5084156603 4078437818 6389576583 4367604420 9018271852 8901251175 9665358113 1249666213 9892578125 0000000000 0000000000 0000000001 (Phil Carmody, k=9)
3. 9956824 4445778267 3143050248 6048198784 9444034699 5386741296 1786583663 5181344566 1350589431 1717001141 7871311465 4328819597 1399545669 5556640625 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)