Known 295-digit prime factors of googolduplex − 1

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2. Number Theory
3. Known 295-digit prime factors of googolduplex − 1

This is a list of known 295-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. 13499 2236181719 4761463192 0938524482 7558567835 5888017454 5675679167 2529899622 6104963256 7366362428 9400075895 1733587309 7181320190 4296875000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=331)
2. 23563 6486334290 8745485970 5383934123 0862810344 5999735791 2535435762 4981052226 6423611100 8469843379 1933709304 8114351263 3016863206 0093300386 5073347607 1155723024 5708149062 2940733725 6986920692 7251070737 8387451171 8750000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
3. 39533 2422871144 6209130715 2692262571 2789123551 8388190331 2791611344 1555410911 3659847093 8907639185 8897089868 8031286384 4285264564 9671028073 7317040864 7661093481 9397868977 8305124491 4531707763 6718750000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
4. 44391 7792114270 5914443740 7610202149 6959830152 7217324271 7357971457 1256134782 6449216847 9831006031 3585804349 0418421966 1871235729 2224623961 3741636276 2451171875 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=187)