Known 331-digit prime factors of googolduplex − 1

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2. Number Theory
3. Known 331-digit prime factors of googolduplex − 1

This is a list of known 331-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. 1 5764082100 5651365547 2008669822 7262512760 7426485960 3913547901 5629795509 3144257331 9475577911 7495492632 9215326856 4173459737 8785706468 6198074155 3037531071 1288809188 3693276509 6791982862 2941183114 3448763370 4293330083 6011767387 3901367187 5000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=431)
2. 1 5883677775 7491569783 5520376933 8552499799 7271548876 1878422715 2689107957 6777444150 9025709510 1526817682 6307047641 9114137076 6950696167 7420618410 0950762963 2882877353 7416739611 6149560685 0157389974 5773255852 9698741284 9688243490 9012028019 1076982104 2634323410 2919410588 5835597291 5887832641 6015625000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=21)
3. 2 9778100450 7027288720 7608775734 6297635636 9488542321 4741425339 0051239769 8113021277 9472786097 0035153049 8917346570 5087906485 4598254896 7003822326 6601562500 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=49)
4. 4 5479917724 6964340810 7052004048 3340359079 2497866436 3282238060 0956611422 4261762465 7286874112 8679654409 2355894717 5489605357 1109118456 5897905138 3025792955 7141629621 7996752636 5559853724 6066374929 0185898746 6307959034 2040779726 0703597341 8021512770 7924693822 8607177734 3750000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=7)