Known 167-digit prime factors of googolduplex − 1

  1. Alpertron
  2. Number Theory
  3. Known 167-digit prime factors of googolduplex − 1

This is a list of known 167-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. 1405910 5607947488 6962829328 3651869330 8967803494 6934894784 3986116441 1992439598 3995947470 0214407465 8928593502 8457297527 9726002583 1423419686 5281516099 4020363704 7296000001 (Phil Carmody, k=1)
  2. 1454323 1313385469 1769421367 7672096287 6224903025 2141868242 6227349603 6927407198 8496081541 6262967373 6266647006 6645505138 8269363200 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=11)
  3. 1471195 7192312533 0402401314 6064296816 2739895572 9625808896 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  4. 1504828 4986507122 0396828153 2256923499 3629805684 5453015626 0930177210 0476634491 7063517777 7065791861 0309120000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=43)
  5. 1509203 0001002782 2781702653 6711158742 0936869073 1631658113 3781718422 8675694475 6938702422 4092145907 1385600000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=69)
  6. 1588186 7761018131 3575310468 8774328678 8463592529 2968750000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  7. 1713633 5372924804 6875000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=23)
  8. 2276565 1080770262 5498374442 2058811218 7215705145 1422600146 6967667662 7784592248 5370880000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  9. 2867200 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=7)
  10. 3094850 0982134506 8724781056 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  11. 3637978 8070917129 5166015625 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  12. 3982729 7778311306 9257220099 4419279513 9777613879 8154696518 4714633465 4072537826 4540235772 4686800456 7148524586 1731527838 8559818267 8222656250 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  13. 4019004 6320322368 7965246209 0214648608 1181334055 8747556013 0725927233 0636206927 1548236425 5157998261 3953622760 5501129523 2000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=51)
  14. 5724716 7826726528 5661823995 3965391771 4853481653 5119947576 1152000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=57)
  15. 6250000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  16. 6509656 7944564245 3195919538 4016107345 9600761867 1992320930 5083548400 3552518678 2952504028 2705179230 8078762748 0308368203 4092471990 7604867330 5194824934 0057373046 8750000001 (Phil Carmody, k=351)
  17. 6735367 0694323330 2827415189 7221734334 6142961378 6472271886 4082480244 2045752875 6850384965 5598969548 0093359947 2045898437 5000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=63)
  18. 8218214 4000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=627)
  19. 8296081 1566519819 5536142796 7639867291 3778576014 9154340246 6453643302 8414936080 0719189615 9721990771 4958832072 1225288824 3965760214 9898919401 5435582032 2514534400 0000000001 (Phil Carmody, k=99)
  20. 8997827 5890863927 6562107701 5371963717 7393942366 0383326620 1511145223 6751613429 7574063808 1372207781 7142998418 2126704179 0246416532 1109885993 7801703036 1730327710 2694400001 (Phil Carmody, k=1)