Known 255-digit prime factors of googolduplex − 1

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2. Number Theory
3. Known 255-digit prime factors of googolduplex − 1

This is a list of known 255-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. 19223 6240646217 0983924710 5108573478 3993134635 4867110569 5744000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=49)
2. 22095 3981085611 1628870197 8769690985 7846802911 6451340148 5393920000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=11)
3. 38690 0351268231 1192173085 6345345790 0785996816 3267454060 4906191546 3552912781 6767321971 2353615555 8512549912 5187687875 0492914538 0432818071 2118756545 6921220174 9905943870 5444335937 5000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=7)
4. 45350 8408267641 7553648566 9408766061 2376581162 4028080405 3429735368 7969906035 1296833461 5573511420 4781620653 9381599876 4170916660 7262293524 6272390941 1579370498 6572265625 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=313)
5. 48699 4043545932 1626624000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=33)