Known 316-digit prime factors of googolduplex − 1

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3. Known 316-digit prime factors of googolduplex − 1

This is a list of known 316-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. 122727 3366324431 6382739429 8874656891 0743803878 1248623912 7788727929 6776313680 4289641150 2447100933 2988069295 8928912829 6962829197 9652606179 7257018787 0602724086 3063276366 1149654821 3473545274 6099326759 5767974853 5156250000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
2. 176402 4708660849 1264527540 6831997804 0018029940 8693321406 5487874482 5863103051 5060367225 2884734916 7335778474 8077392578 1250000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=33)
3. 221591 4868268576 5873821433 8299924002 5083667292 8135628884 2454697113 6712845667 4686230827 4206215496 8984742006 8030400587 8498422861 2746615801 0380872638 9922333745 4987966193 3539566818 6479494383 2306721167 0738416556 1005157481 0754869029 4087487123 0762313536 8779337603 3843273376 0782866738 7366294860 8398437500 0000000000 0000000001 (Phil Carmody, k=3)
4. 300164 0055279321 2822867352 9025801187 5622535558 7117246119 6897276951 6072692514 8436645225 3221835277 9409542563 3713603019 7143554687 5000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=23)
5. 339023 4336218199 8569974198 8935430602 7960037850 3332505128 8911808735 1090616743 8484793258 0979561469 8642020648 4291302982 7129748518 2262074956 0153027800 5415028842 3972474319 2589832046 7595580599 3438017410 5621926371 6381588594 0933556132 2334371575 0189737507 5931929276 0111778928 2447745335 9577339142 5609588623 0468750000 0000000001 (Phil Carmody, k=47)
6. 578736 2657661494 5029150031 7898735362 2187481819 9500101373 5669201246 4837171492 6042841398 1571793556 2133789062 5000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=413)