Known 394-digit prime factors of googolduplex − 1

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2. Number Theory
3. Known 394-digit prime factors of googolduplex − 1

This is a list of known 394-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. 2735 8781612862 0865034049 6920528090 3541645870 3142995882 7793690501 8658284359 2965155106 6065130084 6295836305 3495700485 6870711365 3867097353 5577328624 5765737819 1525758286 9640111548 3321910185 9339157672 2888756053 0641731429 4518704672 9351365914 2482776260 3374439214 0855911772 1850230505 8844361856 0413589365 9283073464 7583179706 1354120111 0928500345 1763174098 2324117794 6329116821 2890625000 0000000000 0000000001 (Phil Carmody, k=601)
2. 8390 6333226002 3258620233 5979895800 5670485304 7642545775 6055458124 8570631832 0388309305 3196751700 4812787817 0055366281 5614135089 3191071284 6549304693 5433291095 2779164183 9135862904 9682104583 5497396708 0912737366 0696904111 0909944181 6207051003 5647675878 6255850847 5916167351 8992254356 8156285812 0722675406 4543362745 8278397394 9231138417 2484878263 2761867716 9084548950 1953125000 0000000000 0000000000 0000000001 (Phil Carmody, k=9)