Known 347-digit prime factors of googolduplex − 1

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2. Number Theory
3. Known 347-digit prime factors of googolduplex − 1

This is a list of known 347-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. 1796271 9326289082 5202448070 1016763707 4671909321 7041821971 9757962671 4762867139 3235170395 9229308818 4709841783 3574681278 9188951798 2813104924 0338723594 1257321202 0299637454 5179670294 2920400865 0405054016 2350216605 0475920285 3599917173 3611717744 9683823646 0327500942 9614852615 9910552291 1656862561 3581389188 7664794921 8750000000 0000000000 0000000000 0000000001 (Phil Carmody, k=51)
2. 2828807 3753000879 5709754581 4158389826 1548085504 4189020252 4264336060 1791292744 8154464578 7413319538 0063351826 5800356517 7460399790 6508264433 9454169326 3563189617 2049044695 5308304731 2839028030 4049961522 7090527299 6383706382 4121890713 5614982281 5747592969 9787853266 4572048815 8985972404 4799804687 5000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=187)
3. 4804999 4284394422 1863100451 6327543589 7615591521 4755200587 8365147807 8094728621 7791798277 3978240933 2639770216 8016625147 6531781860 2138699573 0177348041 0534512515 5561397349 7843210343 7359784373 0441967252 0105708947 5333830077 8362541499 5216909988 6208276947 3271157207 9832321876 0128978644 8852610623 8921434179 3175488959 3776169931 5160512924 1943359375 0000000001 (Phil Carmody, k=3)
4. 6933116 6283147514 4911840120 8644681079 5944112484 7538262036 6692907442 6425009276 8308145128 1409704231 1460666281 7986829300 4129649861 9878377188 4621017543 2100948370 7878226499 4103456956 5090350806 7131042480 4687500000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=431)