Known 100-digit prime factors of googolduplex − 1

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2. Number Theory
3. Known 100-digit prime factors of googolduplex − 1

This is a list of known 100-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. 1205203533 1942427066 5647156925 5871951891 6522453370 9462647603 2000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
2. 1334991897 4505688014 9688856635 5970071626 6903264729 0798121690 1004888887 3286129003 4376435130 4335360001 (Phil Carmody, k=1)
3. 1750450724 0172409230 0476449993 6024232000 6048463126 1321419023 7695744624 2644787200 0000000000 0000000001 (Phil Carmody, k=387)
4. 1759218604 4416000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
5. 2283596308 3295358096 9325755111 9192218212 3945984000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
6. 4452886059 8802566528 3203125000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=153)
7. 4497744949 9203348004 5279247860 8898818492 8894042968 7500000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=531)
8. 6972078301 2552617082 3186762956 8000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=11)
9. 7754818242 6846344519 1945648815 5901752179 4885396957 3974609375 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
10. 7834137500 1573479259 2681286152 7280844800 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=943)
11. 9536743164 0625000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
12. 9569221920 9256771691 2969724363 9593473420 1162601578 0440936274 6403043544 3714972696 6410287014 9475860481 (Phil Carmody, k=7)