Known 333-digit prime factors of googolduplex − 1

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2. Number Theory
3. Known 333-digit prime factors of googolduplex − 1

This is a list of known 333-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. 122 7273366324 4316382739 4298874656 8910743803 8781248623 9127788727 9296776313 6804289641 1502447100 9332988069 2958928912 8296962829 1979652606 1797257018 7870602724 0863063276 3661149654 8213473545 2746099326 7595767974 8535156250 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
2. 126 1440656842 9038150834 8956155327 3389218911 3780918585 6025106366 1152398566 2532921064 7598675228 2232818457 1450905493 7628750274 3628366134 7357692654 1900920303 9248690957 9801476061 2115736648 7750550732 0165634155 2734375000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=803)