# Known 112-digit prime factors of googolduplex − 1

1. Alpertron
2. Number Theory
3. Known 112-digit prime factors of googolduplex − 1

This is a list of known 112-digit prime factors of googolduplex − 1, i.e., 1010^(10^100) − 1.

These numbers have the form 1 + 2k × 2m × 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. 10 1111322080 3298822854 3884198570 8684223250 3365313078 8025009678 6767244338 9892578125 0000000000 0000000000 0000000001 (Phil Carmody, k=21)
2. 13 2956768231 5534482061 2150995063 3920802605 0579431932 5295856760 9139200000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=101)
3. 14 2940113059 9901609689 9836292622 5074422749 7317034858 4261546420 7483455538 7496948242 1875000000 0000000000 0000000001 (Phil Carmody, k=19)
4. 14 2962266571 2490250240 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=31)
5. 15 2676512362 6603892185 9566352593 6206201057 1475104371 4878971091 4975614741 7065221816 3013458251 9531250000 0000000001 (Phil Carmody, k=133)
6. 16 4214663788 0645004988 7456054178 7046634405 6963136541 9200278143 9518334892 5022492892 3671541269 8686122894 2871093751 (Phil Carmody, k=3)
7. 22 6182198744 9685048476 5081423788 0467771901 7490744590 7592773437 5000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=7)
8. 24 2483200000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=37)
9. 27 3691106313 4408341647 9093423631 1744390676 1605227569 8667130239 9197224820 8370821487 2785902116 4476871490 4785156251 (Phil Carmody, k=1)
10. 33 1321580192 8249582729 2599741877 0216462746 7027457896 6200351715 0878906250 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=21)
11. 34 1757925747 3456131832 0347298712 8338336432 7235770644 4319152665 7251555156 1249024880 0367393390 9852160000 0000000001 (Phil Carmody, k=1)
12. 37 0779555881 5619874816 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=201)
13. 38 5356877030 6091678857 3721175136 3686823341 5884800000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=27)
14. 42 3104724007 2963948199 6675907136 3934190392 4711915520 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=579)
15. 46 0430732079 7904083353 6000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=39)
16. 50 8657511686 5084121294 8257889434 0560893283 5093582980 3347587585 4492187500 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=403)
17. 51 6987882845 6422967946 3043254372 6783478632 5693130493 1640625000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
18. 52 4067512165 4696438260 8937940723 6495390539 7760000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=47)
19. 57 9525837247 3100601033 2158024367 7273191414 7181752030 1826388683 4023979286 5280000000 0000000000 0000000000 0000000001 (Phil Carmody, k=41)
20. 71 1306451482 2403103129 6000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=241)
21. 73 5597859615 6266520120 0657303214 8408136994 7786481290 4448000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
22. 76 3301452252 3883602321 7993317727 0688568755 7389159025 9814810439 3780163350 5864581120 0000000000 0000000000 0000000001 (Phil Carmody, k=103)
23. 86 2028741737 0624828265 7020277204 8915785540 7562282762 2400000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=9)
24. 95 3674316406 2500000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)