Known 359-digit prime factors of googolduplex − 1

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2. Number Theory
3. Known 359-digit prime factors of googolduplex − 1

This is a list of known 359-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. 135140608 9248593123 9899700202 1712163462 0438511541 4990016532 9019782094 6414242487 5394326551 8138026248 0493537347 5467582277 7456364818 5150925491 1237913654 6283164500 0164300462 6840290917 5743935491 8680328962 7973064149 3763970939 1446479674 0475593429 9607789143 5751296474 5284052762 8627524387 3979673796 9665336293 3060626982 4954779323 8889425992 9656982421 8750000000 0000000001 (Phil Carmody, k=27)
2. 566962593 2484053377 8722809213 4571178292 8914362472 2019215549 9322693182 3882469499 7973406095 7309181517 5804743968 7157754068 9324117714 4661522187 2935853671 5346106647 3116627526 7251039900 0268832094 1024861067 8370485335 3039648845 4840680713 7906506308 3263150996 2758321159 1187739575 3037944814 4230991601 9439697265 6250000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=393)
3. 761382551 1946947669 8220736674 9163064047 0856549103 2867448181 8096371843 0093667898 4217972222 8716735285 8688993773 1732526875 3980621402 7330880108 3421190730 2853933531 6149499207 0852006479 7646200473 1420522858 4815423421 3315414839 1641243259 0703485146 8324632151 0523557662 9638671875 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)