Known 358-digit prime factors of googolduplex − 1

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2. Number Theory
3. Known 358-digit prime factors of googolduplex − 1

This is a list of known 358-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. 10955122 6699797440 8554468762 8429303173 6011546127 7838896022 8943762033 2968674171 5917979872 6128241879 2422567458 7007752284 5955670289 5626009390 1879271000 7109617689 3923442715 0352183607 2086179450 5021080681 2174268998 2056617736 8164062500 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=117)
2. 11443267 0700219050 5975826936 2414642529 6627287234 5995680248 6072121837 2237272536 7136626603 6625017271 6739854941 4640178047 4461960438 3078889237 4802842238 3738628915 6314690474 3548161894 1668678826 4049974088 5349236983 1553947083 5022761718 8465956132 8589916229 2480468750 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=43)
3. 14138189 1800574524 7291582323 0360473851 7686206759 9841474752 1261457498 8631335985 4166660508 1906027516 0225582886 8610757981 0117923605 5980231904 4008564269 3433814742 4889437376 4440235419 2152415635 0642442703 2470703125 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=9)