Known 22-digit prime factors of Googolplex - 10

  1. Alpertron
  2. Number Theory
  3. Known 22-digit prime factors of Googolplex − 10

This is a list of known 22-digit prime factors of googolplex − 10, i.e., 1010^100 − 10.

These numbers have the form 1 + 2k ∏i piei, where pi is a prime factor of 10100 − 1 and ei is zero or one.

The list of prime factors of 10100 − 1 is: 3, 3, 11, 41, 101, 251, 271, 3541, 5051, 9091, 21401, 25601, 27961, 60101, 7019801, 18 2521213001, 1410 3673319201, 7887 5943472201 and 168058 8011350901.

In the list you can see the prime factors, their discoverer and their corresponding value of k.

  1. 10 0498616366 5335925279 (Phil Carmody, k=1)
  2. 10 1844857521 5157319557 (Phil Carmody, k=886)
  3. 10 2068492039 2918758079 (Phil Carmody, k=1)
  4. 10 4836423299 5114376199 (Phil Carmody, k=13)
  5. 10 5115065054 0913754107 (Phil Carmody, k=1)
  6. 10 6231366908 2671675759 (Phil Carmody, k=1)
  7. 10 7205314393 2306880719 (Phil Carmody, k=81)
  8. 10 7522968016 4709979563 (Phil Carmody, k=667)
  9. 10 8923928349 0112047151 (Phil Carmody, k=325)
  10. 11 0309917634 8045887209 (Phil Carmody, k=4)
  11. 11 3377422450 6376575079 (Dario Alpern, k=2423)
  12. 11 4293341694 6785741813 (Phil Carmody, k=2)
  13. 11 4521262044 3036113519 (Phil Carmody, k=1)
  14. 11 5389877924 9168476481 (Phil Carmody, k=160)
  15. 11 5802013527 2478310163 (Phil Carmody, k=17)
  16. 11 5885613837 1217524877 (Phil Carmody, k=2)
  17. 11 6434060471 6411467973 (Phil Carmody, k=2)
  18. 11 6834822893 6834822883 (Phil Carmody, k=1)
  19. 11 7035269937 9036906107 (Phil Carmody, k=551)
  20. 11 7530160362 3186111431 (Phil Carmody, k=135)
  21. 11 7829050534 2321007319 (Phil Carmody, k=1)
  22. 11 8240649425 0967042641 (Phil Carmody, k=40)
  23. 12 0147873494 7698911441 (Phil Carmody, k=680)
  24. 12 1942946336 0559435133 (Phil Carmody, k=2)
  25. 12 2232471421 4453531791 (Phil Carmody, k=5)
  26. 12 3103995774 3103995763 (Dario Alpern, k=1777)
  27. 12 3188322491 9028972397 (Phil Carmody, k=2)
  28. 12 3838250482 5513170293 (Phil Carmody, k=494)
  29. 12 4255842558 4255842547 (Phil Carmody, k=1)
  30. 12 6295922164 6352403373 (Phil Carmody, k=2)
  31. 12 6597076075 9066955077 (Phil Carmody, k=2)
  32. 12 7708393573 8193884907 (Phil Carmody, k=1)
  33. 12 9274788344 1995645281 (Phil Carmody, k=560)
  34. 12 9510295767 1784517169 (Phil Carmody, k=8)
  35. 13 0853770494 2479562827 (Phil Carmody, k=1)
  36. 13 3184958436 3023483649 (Phil Carmody, k=128)
  37. 13 3357561777 2067419733 (Phil Carmody, k=2)
  38. 13 5119062773 4719835603 (Phil Carmody, k=49)
  39. 13 5180182670 0218462213 (Phil Carmody, k=266)
  40. 13 6582592471 9644565867 (Phil Carmody, k=13)
  41. 13 7710597466 8127228521 (Phil Carmody, k=620)
  42. 13 7967847814 9089568201 (Phil Carmody, k=100)
  43. 13 8340043236 5207628591 (Phil Carmody, k=5)
  44. 13 9481051236 9658967067 (Phil Carmody, k=1)
  45. 14 0479702996 4810154769 (Phil Carmody, k=8)
  46. 14 0565768885 3491880769 (Phil Carmody, k=416)
  47. 14 1840058093 9256070227 (Phil Carmody, k=623)
  48. 14 3984472746 3984472733 (Phil Carmody, k=74)
  49. 14 4355337122 6563153679 (Phil Carmody, k=1)
  50. 15 0379150078 7606872837 (Phil Carmody, k=2)
  51. 15 5084600017 1503898311 (Phil Carmody, k=35)
  52. 15 6338824575 9044554609 (Phil Carmody, k=8)
  53. 15 7293445555 5115227719 (Dario Alpern, k=2509)
  54. 15 8192574504 4464252049 (Phil Carmody, k=56)
  55. 15 8751088199 1985528243 (Dario Alpern, k=2709)
  56. 15 9017672515 7187289519 (Phil Carmody, k=173)
  57. 15 9550361691 9550361677 (Phil Carmody, k=2)
  58. 16 0792202039 4376827641 (Phil Carmody, k=20)
  59. 16 1512241241 3636157813 (Phil Carmody, k=374)
  60. 16 1830783156 0607650921 (Phil Carmody, k=20)
  61. 16 2514207979 2393541083 (Phil Carmody, k=289)
  62. 16 2830136597 8611403347 (Phil Carmody, k=1)
  63. 16 2984631644 3990063169 (Phil Carmody, k=96)
  64. 16 3393940619 1481408119 (Phil Carmody, k=1)
  65. 16 4142882367 1929629397 (Phil Carmody, k=2)
  66. 16 6855831721 7904100707 (Phil Carmody, k=1)
  67. 16 6924587325 4998520557 (Dario Alpern, k=2386)
  68. 16 7665030466 9046735733 (Phil Carmody, k=2)
  69. 16 8359943005 3706477643 (Phil Carmody, k=9)
  70. 16 9076739193 3867698013 (Phil Carmody, k=2)
  71. 16 9465078471 1058726751 (Phil Carmody, k=375)
  72. 16 9676058984 5715662929 (Phil Carmody, k=8)
  73. 17 0952650273 9162962889 (Phil Carmody, k=4)
  74. 17 1476556195 3977989243 (Phil Carmody, k=619)
  75. 17 3969423637 4270658747 (Phil Carmody, k=223)
  76. 17 6408298493 0836463483 (Phil Carmody, k=17)
  77. 17 6731714192 9013543243 (Phil Carmody, k=1)
  78. 17 6745185024 5931932639 (Phil Carmody, k=1)
  79. 17 9468004440 6204517169 (Phil Carmody, k=8)
  80. 18 3359516316 3307150333 (Phil Carmody, k=2)
  81. 18 5354927819 5054039889 (Dario Alpern, k=2504)
  82. 18 5603190068 6462398201 (Phil Carmody, k=700)
  83. 19 2721175172 1536877081 (Phil Carmody, k=60)
  84. 19 3501850716 9129350013 (Phil Carmody, k=2)
  85. 19 9423946474 0948049787 (Phil Carmody, k=7)
  86. 19 9468771889 1002393437 (Phil Carmody, k=2)
  87. 20 0307681581 3025651733 (Phil Carmody, k=2)
  88. 20 1671545925 9836214587 (Phil Carmody, k=7)
  89. 20 2340202601 2788948671 (Phil Carmody, k=65)
  90. 20 3734048766 3510634323 (Phil Carmody, k=1)
  91. 20 5010824516 0450430077 (Phil Carmody, k=2)
  92. 20 5057968298 0325485517 (Phil Carmody, k=38)
  93. 20 7582184782 5012289253 (Phil Carmody, k=34)
  94. 20 9143123499 5025390893 (Phil Carmody, k=314)
  95. 21 0074358357 6821403559 (Dario Alpern, k=1703)
  96. 21 0090403651 1885109907 (Phil Carmody, k=1)
  97. 21 2784722296 5947490361 (Phil Carmody, k=20)
  98. 21 4505813907 8848436797 (Phil Carmody, k=2)
  99. 21 8108809184 8354726159 (Phil Carmody, k=1)
  100. 21 8519038895 8664547919 (Phil Carmody, k=1)
  101. 21 9130612863 6020902267 (Phil Carmody, k=1)
  102. 22 4343608498 8497719893 (Phil Carmody, k=234)
  103. 22 8675007009 3143174787 (Phil Carmody, k=7)
  104. 23 6018519066 9637488323 (Phil Carmody, k=79)
  105. 23 7639621345 3712928521 (Phil Carmody, k=140)
  106. 24 1308395111 6555919841 (Phil Carmody, k=80)
  107. 24 2227375264 8825136409 (Phil Carmody, k=4)
  108. 24 2393331321 4482437413 (Phil Carmody, k=2)
  109. 24 2667390738 7030648843 (Phil Carmody, k=9)
  110. 24 2772879483 7868672363 (Phil Carmody, k=1)
  111. 24 2818555734 5608759969 (Phil Carmody, k=16)
  112. 24 5117458749 1538828323 (Phil Carmody, k=299)
  113. 24 5357728211 1603023191 (Dario Alpern, k=2055)
  114. 24 5786632322 0880034321 (Phil Carmody, k=520)
  115. 24 6720437069 6531595427 (Phil Carmody, k=1)
  116. 24 7292924414 3926587757 (Phil Carmody, k=2)
  117. 24 7927236349 5152629471 (Phil Carmody, k=15)
  118. 24 8167350013 9763501773 (Phil Carmody, k=2)
  119. 25 8045856970 3357999569 (Phil Carmody, k=248)
  120. 25 8966189493 6784983009 (Phil Carmody, k=368)
  121. 26 5569191330 1266713717 (Dario Alpern, k=1082)
  122. 26 5859314315 1149539961 (Phil Carmody, k=20)
  123. 26 6830527862 9159632013 (Phil Carmody, k=722)
  124. 26 7996310310 7562467409 (Phil Carmody, k=8)
  125. 26 8112155290 2443005799 (Phil Carmody, k=53)
  126. 27 3114463646 2232489797 (Phil Carmody, k=2)
  127. 28 0125451496 0022313831 (Phil Carmody, k=5)
  128. 28 2620960351 2155825187 (Phil Carmody, k=31)
  129. 28 2755638224 8300192653 (Phil Carmody, k=834)
  130. 28 7999768489 7200838809 (Dario Alpern, k=1564)
  131. 29 1892525585 9219258231 (Phil Carmody, k=5)
  132. 29 3115116575 5012454519 (Phil Carmody, k=1)
  133. 30 1173135750 1609155071 (Phil Carmody, k=35)
  134. 30 1404903593 8889972053 (Phil Carmody, k=94)
  135. 30 3758280250 5059595733 (Phil Carmody, k=2)
  136. 30 4870865594 8715558987 (Phil Carmody, k=313)
  137. 30 5857003935 6822730213 (Phil Carmody, k=454)
  138. 30 7780090853 2339243717 (Phil Carmody, k=42)
  139. 32 0135610896 7458428999 (Phil Carmody, k=1)
  140. 32 0678945654 0518393561 (Phil Carmody, k=20)
  141. 32 1600638792 5185574493 (Phil Carmody, k=46)
  142. 32 1698452130 2808569763 (Phil Carmody, k=601)
  143. 32 2821839756 7042973759 (Phil Carmody, k=21)
  144. 32 6290228342 0414447849 (Phil Carmody, k=28)
  145. 32 6970391135 7585816929 (Phil Carmody, k=16)
  146. 32 6978182815 2415756547 (Phil Carmody, k=1)
  147. 33 1753105469 9245684387 (Phil Carmody, k=1)
  148. 33 3274282225 7836828853 (Dario Alpern, k=1166)
  149. 33 6426289785 4613242591 (Phil Carmody, k=5)
  150. 33 7521613689 5479483547 (Phil Carmody, k=103)
  151. 33 8458652850 5058255013 (Phil Carmody, k=74)
  152. 34 0903330106 6893972627 (Phil Carmody, k=7)
  153. 34 2273844043 5134617803 (Dario Alpern, k=1899)
  154. 34 3791172638 4582401973 (Phil Carmody, k=2)
  155. 34 9370236657 5396782797 (Phil Carmody, k=2)
  156. 34 9449387694 2191808037 (Phil Carmody, k=2)
  157. 35 0583876681 9217330387 (Phil Carmody, k=1)
  158. 35 3994149935 2145000693 (Phil Carmody, k=2)
  159. 35 6778397232 5293248683 (Phil Carmody, k=7)
  160. 35 8187615865 9344942107 (Phil Carmody, k=1)
  161. 36 1157147550 0604634797 (Phil Carmody, k=2)
  162. 36 5128378364 8204954933 (Phil Carmody, k=122)
  163. 36 5963617562 6907566969 (Phil Carmody, k=4)
  164. 36 7230749565 7213694843 (Phil Carmody, k=11)
  165. 37 5701975784 3968685037 (Phil Carmody, k=2)
  166. 37 7382392788 6032241321 (Phil Carmody, k=340)
  167. 38 6919227156 6802552439 (Phil Carmody, k=173)
  168. 38 8670807099 1380954947 (Phil Carmody, k=1)
  169. 39 8062580625 8062580587 (Phil Carmody, k=31)
  170. 40 0333039169 9214338083 (Phil Carmody, k=529)
  171. 40 1170523260 9738567609 (Phil Carmody, k=116)
  172. 40 3059791104 9941519187 (Phil Carmody, k=1)
  173. 40 4480166646 0464482761 (Phil Carmody, k=20)
  174. 41 0889304914 7292513227 (Phil Carmody, k=7)
  175. 41 1618161023 8104553763 (Phil Carmody, k=7)
  176. 41 2467730387 8552634321 (Phil Carmody, k=40)
  177. 41 5198280031 7126694239 (Phil Carmody, k=1)
  178. 41 7504906650 3090899267 (Phil Carmody, k=117)
  179. 42 3005358990 7474924799 (Phil Carmody, k=959)
  180. 42 7401595855 6091506441 (Phil Carmody, k=580)
  181. 43 5014895848 9331122449 (Phil Carmody, k=8)
  182. 44 2337473959 8994245849 (Phil Carmody, k=4)
  183. 44 6747996475 6033508999 (Phil Carmody, k=143)
  184. 44 6891316786 7721392933 (Phil Carmody, k=14)
  185. 45 5637420375 7589393599 (Phil Carmody, k=1)
  186. 45 6458627506 3541372449 (Phil Carmody, k=16)
  187. 46 8815762698 6801881079 (Phil Carmody, k=1)
  188. 46 9606040020 2278660599 (Phil Carmody, k=1)
  189. 47 2313906823 4199857759 (Phil Carmody, k=23)
  190. 47 9396249939 9396249893 (Phil Carmody, k=14)
  191. 48 0090894542 9018888489 (Phil Carmody, k=4)
  192. 48 2863697259 4417482121 (Phil Carmody, k=20)
  193. 49 3537012211 7062422213 (Phil Carmody, k=2)
  194. 50 5601002766 7172803043 (Phil Carmody, k=219)
  195. 50 8432848754 0703686213 (Phil Carmody, k=2)
  196. 51 0699506058 0411605003 (Phil Carmody, k=1)
  197. 51 0814984121 6451809827 (Phil Carmody, k=1)
  198. 51 2116268936 3205377797 (Phil Carmody, k=2)
  199. 51 4431817652 2537879267 (Phil Carmody, k=1)
  200. 52 0064026461 9448168609 (Phil Carmody, k=496)
  201. 53 0569105691 0569105639 (Phil Carmody, k=13)
  202. 53 5947986277 4669161157 (Phil Carmody, k=2)
  203. 53 7292432382 1556764439 (Phil Carmody, k=1)
  204. 54 1995401132 7785456561 (Phil Carmody, k=680)
  205. 54 4506213718 4139642041 (Phil Carmody, k=20)
  206. 54 7329591240 6853822427 (Phil Carmody, k=463)
  207. 54 8375137258 9829044729 (Phil Carmody, k=68)
  208. 55 3151274988 5650568919 (Phil Carmody, k=53)
  209. 55 8184971401 0086347307 (Dario Alpern, k=1967)
  210. 56 3431111757 2372088827 (Phil Carmody, k=7)
  211. 56 9930136925 1316275483 (Phil Carmody, k=1)
  212. 57 9592118179 4374420147 (Phil Carmody, k=7)
  213. 58 4781128225 4405863587 (Phil Carmody, k=1)
  214. 58 6845239003 5449806281 (Phil Carmody, k=260)
  215. 59 3486057196 9659298439 (Phil Carmody, k=1)
  216. 59 6576835900 0594135751 (Phil Carmody, k=125)
  217. 60 1993588186 7491498333 (Phil Carmody, k=2)
  218. 60 8875835742 7762876039 (Phil Carmody, k=1)
  219. 60 9303697656 9303697597 (Phil Carmody, k=2)
  220. 63 4309218423 4309218361 (Phil Carmody, k=20)
  221. 64 0532414561 3288723587 (Phil Carmody, k=11)
  222. 64 4740942905 4728862333 (Phil Carmody, k=894)
  223. 65 2928457139 6480448707 (Phil Carmody, k=47)
  224. 65 9993400065 9993400067 (Phil Carmody, k=1)
  225. 66 5573168303 5364422747 (Phil Carmody, k=1)
  226. 66 5803620238 2314460877 (Phil Carmody, k=2)
  227. 66 6633132463 3233066067 (Phil Carmody, k=1)
  228. 66 8561504253 2344196587 (Phil Carmody, k=77)
  229. 67 5943606744 8189234517 (Phil Carmody, k=202)
  230. 68 0790369277 8943433317 (Phil Carmody, k=2)
  231. 68 7021441011 0897901119 (Phil Carmody, k=49)
  232. 69 3262254662 9394073933 (Phil Carmody, k=2)
  233. 69 6700181588 1650676569 (Phil Carmody, k=4)
  234. 70 5827055701 5926065533 (Phil Carmody, k=234)
  235. 71 2582515609 1068571387 (Phil Carmody, k=1)
  236. 71 6375231731 8689884213 (Phil Carmody, k=2)
  237. 71 8819735997 0549878723 (Dario Alpern, k=1079)
  238. 71 9973229386 5952912853 (Phil Carmody, k=2)
  239. 72 8150917551 2032684213 (Dario Alpern, k=1234)
  240. 73 3503086075 8018101791 (Phil Carmody, k=295)
  241. 74 7436739322 1060233199 (Phil Carmody, k=1)
  242. 75 3468828865 3389419551 (Phil Carmody, k=725)
  243. 75 4581070699 5944398117 (Phil Carmody, k=706)
  244. 75 8183553816 1846010041 (Dario Alpern, k=1340)
  245. 76 3888758271 9062759563 (Phil Carmody, k=1)
  246. 76 6994644156 8928314997 (Phil Carmody, k=2)
  247. 77 7341614198 2761909893 (Phil Carmody, k=2)
  248. 77 7763493250 5237219839 (Dario Alpern, k=1801)
  249. 78 2329913474 7064325839 (Phil Carmody, k=13)
  250. 79 1906553316 1734310197 (Phil Carmody, k=2)
  251. 80 0223506807 4011526373 (Dario Alpern, k=1014)
  252. 81 1832650800 3696275479 (Phil Carmody, k=821)
  253. 82 3059096510 8456054923 (Phil Carmody, k=7)
  254. 82 8241164575 6441082083 (Phil Carmody, k=1)
  255. 83 3007104649 9242217761 (Phil Carmody, k=80)
  256. 83 4370841906 7255174271 (Phil Carmody, k=395)
  257. 84 3501151018 8014000413 (Phil Carmody, k=82)
  258. 84 4489989791 3509496797 (Phil Carmody, k=146)
  259. 85 4089644857 5188251467 (Phil Carmody, k=1)
  260. 85 7267343625 8342412387 (Phil Carmody, k=7)
  261. 86 1293130835 6842646147 (Phil Carmody, k=1)
  262. 86 6269324079 0074801283 (Phil Carmody, k=31)
  263. 88 0890954836 6111125609 (Dario Alpern, k=1116)
  264. 90 0726229553 9273770357 (Phil Carmody, k=822)
  265. 93 1145114222 6365460791 (Phil Carmody, k=105)
  266. 94 3742532682 3023934889 (Phil Carmody, k=4)
  267. 96 4068166814 4960123373 (Phil Carmody, k=2)
  268. 97 2607689178 4358789031 (Phil Carmody, k=185)
  269. 97 4720980750 2036305239 (Phil Carmody, k=1)
  270. 98 6003375912 0451249043 (Phil Carmody, k=7)
  271. 99 5877307704 7594037521 (Phil Carmody, k=40)
  272. 99 8812156244 3701618519 (Phil Carmody, k=1)