Known 285-digit prime factors of googolduplex − 1

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2. Number Theory
3. Known 285-digit prime factors of googolduplex − 1

This is a list of known 285-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. 14045 0290640765 9498146754 8241576029 7097450700 1638254994 9011466361 5811498300 2199894845 9905292617 7939003291 6137189426 0058917526 0122597447 9361383680 7701422586 7812722362 4551733568 7271905358 2698744975 2323300344 8694944381 7138671875 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
2. 26101 2178719940 9810684117 6437026190 2228046570 3227586619 1034545821 8788929783 8994490889 1584507415 4731264570 7279443740 8447265625 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)