Known 198-digit prime factors of googolduplex − 1

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  3. Known 198-digit prime factors of googolduplex − 1

This is a list of known 198-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. 12315723 5472043288 1981240223 5607396821 7282424294 6922793783 2356250312 2817932862 6935604576 2774666903 0152573753 1744375384 8332000516 7076516272 5729169324 0404129028 3203125000 0000000000 0000000000 0000000001 (Phil Carmody, k=17)
  2. 12518570 7585700471 7684460650 7723283357 6155311283 0754463327 9006823846 8370228227 4908661592 8279190828 4766851438 5208400391 1716292289 9240129481 7682355642 3187255859 3750000000 0000000000 0000000000 0000000001 (Phil Carmody, k=27)
  3. 21619741 8757657214 5618359912 8581093668 1551942411 8541587418 2912453835 0615342153 2728879471 5115179783 4346022001 7109741484 3504058966 3843477822 0256722918 9660497935 8209597251 0614956263 4527683258 0566406251 (Phil Carmody, k=21)
  4. 22108591 5010417782 4098906076 8769022902 0569609329 5688034566 0680883631 5950160958 1326840705 9208889057 8599950010 7250214313 8808307453 3038897835 3575168966 9268671423 1967926025 3906250000 0000000000 0000000001 (Phil Carmody, k=1)
  5. 22710550 8578865946 5395598989 9133786495 4566185568 3673091554 9082965299 0214526653 2897949218 7500000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=483)
  6. 27141863 8493962205 8171809770 8545656132 6282098889 3508911132 8125000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=21)
  7. 29401439 4373278017 3447205997 3300128427 4417242214 4584672499 2353193385 0009600000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=213)
  8. 30879968 6215596682 2045969008 2959360000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=609)
  9. 33501588 9984351939 7710899131 0834001817 8319683680 0449436299 9423628934 8918944597 2442626953 1250000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=57)
  10. 49182693 8836395315 9694817519 4834677262 0550467417 9704846198 6452805644 4102909802 3518712113 3137196709 9611920724 2901659006 6913489279 6019280306 2626112703 0374400000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=601)
  11. 50769098 4030910923 9950709565 6916815858 8214796516 5679764106 1027477074 3647669487 1135937453 1361770133 8762950050 8352179391 7766860800 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  12. 59800124 7732236732 3738811511 7261993240 6080561770 8780346220 0099602341 6519165039 0625000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=621)
  13. 77141816 7727126177 1044833525 5209872606 8499271631 6824359901 1830724521 1326517164 7071838378 9062500000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=21)
  14. 87685633 4022506415 5869822158 2986198096 0092313698 3417929798 9843352811 6228798606 7804669645 7635576647 4633590520 4837506739 9399451772 9788640281 1855077743 5302734375 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=591)
  15. 88928324 5342588380 8530251648 6672313231 3113482232 1195318230 3424518077 2835634708 4800000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  16. 92730153 7671855346 4329338153 8690987834 1891194689 4477506132 5976472939 5335023907 3397493280 2068080210 9384084729 7840002897 5676239184 6223181346 4313745498 6572265625 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)