Known 18-digit prime factors of Googolplex + 10

  1. Alpertron
  2. Number Theory
  3. Known 18-digit prime factors of Googolplex + 10

This is a list of known 18-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. 10005512 8505716009 (Phil Carmody, k=1116)
  2. 10070706 9199565201 (Patrick Demichel, k=1732600)
  3. 10121032 8665281103 (David Broadhurst, k=1)
  4. 10350944 2668384329 (Patrick Demichel, k=5884)
  5. 10390185 0164540539 (Phil Carmody, k=2851)
  6. 10716475 1690556253 (David Broadhurst, k=14)
  7. 10890353 1991843321 (David Broadhurst, k=20)
  8. 11035611 3559705927 (Patrick Demichel, k=288761)
  9. 11043747 4552301887 (David Broadhurst, k=1)
  10. 11199132 3706419863 (David Broadhurst, k=1)
  11. 11628202 1595786619 (David Broadhurst, k=13)
  12. 11774543 4391110247 (Phil Carmody, k=427)
  13. 11835834 8972381281 (Patrick Demichel, k=112560)
  14. 11846589 4487008423 (Patrick Demichel, k=1656229)
  15. 11851674 7619872009 (David Broadhurst, k=76)
  16. 11887315 4238859703 (Norm Dresner, k=13991)
  17. 12001200 1200120013 (David Broadhurst, k=2)
  18. 12135618 5612375173 (David Broadhurst, k=2)
  19. 12148270 5309359491 (David Broadhurst, k=5)
  20. 12228223 8139326847 (David Broadhurst, k=7)
  21. 12290179 2722120281 (Patrick Demichel, k=142580)
  22. 12369777 9987630223 (Phil Carmody, k=289)
  23. 12396950 2997557207 (David Broadhurst, k=1)
  24. 12446660 8106205487 (David Broadhurst, k=1)
  25. 12536732 1199584481 (David Broadhurst, k=80)
  26. 12642806 3736680677 (Phil Carmody, k=142)
  27. 12761500 2945977179 (David Broadhurst, k=1)
  28. 12934131 4128480011 (David Broadhurst, k=5)
  29. 13013911 5567941899 (David Broadhurst, k=1)
  30. 13086391 2851534287 (David Broadhurst, k=1)
  31. 13086659 4176843053 (David Broadhurst, k=2)
  32. 13158746 5014410491 (David Broadhurst, k=5)
  33. 13199698 1536615801 (David Broadhurst, k=100)
  34. 13244465 0676898801 (Patrick Demichel, k=286600)
  35. 13487343 7617688969 (Patrick Demichel, k=146876)
  36. 13568724 1078623623 (Patrick Demichel, k=29521)
  37. 13718185 1291434921 (David Broadhurst, k=20)
  38. 13974615 6376782211 (Phil Carmody, k=1535)
  39. 14425600 8491531899 (David Broadhurst, k=13)
  40. 14467579 2073803409 (Paul Leyland, k=38008)
  41. 14669185 1036417053 (David Broadhurst, k=2)
  42. 14700683 1717162091 (David Broadhurst, k=5)
  43. 14731730 7040995499 (David Broadhurst, k=1)
  44. 15056199 9647884841 (David Broadhurst, k=20)
  45. 15341864 6862399641 (David Broadhurst, k=20)
  46. 15410415 1302539129 (David Broadhurst, k=4)
  47. 15678916 8642654013 (Phil Carmody, k=214)
  48. 16338595 2370691041 (David Broadhurst, k=80)
  49. 16355229 3503579971 (John Gamble, k=16915)
  50. 16424464 2154953823 (David Broadhurst, k=49)
  51. 16817567 4779930401 (Phil Carmody, k=400)
  52. 16944314 0991559423 (Phil Carmody, k=247)
  53. 16974552 3592235779 (David Broadhurst, k=1)
  54. 17175572 5018671487 (David Broadhurst, k=7)
  55. 17590134 3399825859 (David Broadhurst, k=1)
  56. 17653340 9239784167 (David Broadhurst, k=1)
  57. 17759511 5055688609 (Phil Carmody, k=688)
  58. 17844196 8962445607 (Patrick Demichel, k=277187)
  59. 17987829 8144948173 (Phil Carmody, k=2814)
  60. 18133187 4350656459 (David Broadhurst, k=13)
  61. 18315377 4520339237 (David Broadhurst, k=2)
  62. 18434747 8038236729 (David Broadhurst, k=4)
  63. 18586326 0018586327 (David Broadhurst, k=11)
  64. 18632747 5922326663 (Phil Carmody, k=4949)
  65. 18759095 2903133761 (Phil Carmody, k=160)
  66. 19064787 0118074689 (Patrick Demichel, k=348704)
  67. 19152991 8193709899 (Phil Carmody, k=2161)
  68. 19211427 8635421539 (David Broadhurst, k=1)
  69. 19280028 4765101157 (David Broadhurst, k=26)
  70. 19287957 9809710333 (David Broadhurst, k=14)
  71. 19404289 3134343573 (Patrick Demichel, k=5774)
  72. 19590759 5321362651 (David Broadhurst, k=25)
  73. 19657383 5947361423 (Patrick Demichel, k=147841)
  74. 20414170 9491024049 (David Broadhurst, k=8)
  75. 20546478 6053851927 (David Broadhurst, k=7)
  76. 20575214 9808770641 (David Broadhurst, k=40)
  77. 20894299 9633926739 (David Broadhurst, k=1)
  78. 21486603 9978513397 (David Broadhurst, k=2)
  79. 21558398 9425681529 (David Broadhurst, k=4)
  80. +219135734428644361 (David Broadhurst using ECM) (k=44923274790620)
  81. 22110783 3165290677 (Patrick Demichel, k=106766)
  82. 22358956 0561457971 (Phil Carmody, k=1145)
  83. 22907466 3032098841 (David Broadhurst, k=20)
  84. 23240012 4161082373 (David Broadhurst, k=2)
  85. 23530652 2086835453 (Patrick Demichel, k=804442)
  86. 23543509 1108367811 (Patrick Demichel, k=441485)
  87. 23933515 7784888397 (Patrick Demichel, k=122402)
  88. 24320577 9797620499 (Patrick Demichel, k=254669)
  89. 24542242 4353013983 (Patrick Demichel, k=174809)
  90. 25022976 4163788837 (Phil Carmody, k=1106)
  91. 25314076 7322959407 (David Broadhurst, k=1)
  92. 25975536 6143102611 (Phil Carmody, k=3235)
  93. 26079416 8645039921 (David Broadhurst, k=40)
  94. 26127328 8491943047 (David Broadhurst, k=43)
  95. 26127890 3209104463 (David Broadhurst, k=97)
  96. 26202841 7481972241 (David Broadhurst, k=40)
  97. 26372194 5585276487 (David Broadhurst, k=77)
  98. 26446198 0630200373 (Phil Carmody, k=1994)
  99. 26663390 2703963917 (David Broadhurst, k=2)
  100. +267003239205288169 (David Broadhurst using ECM) (k=32890273368476)
  101. 27346562 0780734247 (Phil Carmody, k=223)
  102. 27450153 0661547647 (Phil Carmody, k=18687)
  103. 27589223 1474754291 (Patrick Demichel, k=1988505)
  104. 27683595 5744674129 (David Broadhurst, k=8)
  105. 28151969 1821039251 (Phil Carmody, k=2875)
  106. 28214601 4560039517 (David Broadhurst, k=62)
  107. 28482490 3853155117 (Phil Carmody, k=106)
  108. 28759970 3178926653 (Phil Carmody, k=3622)
  109. 28995786 8642381837 (Phil Carmody, k=1118)
  110. 29073018 0029073019 (David Broadhurst, k=13)
  111. 29238764 0236317931 (David Broadhurst, k=5)
  112. 29265702 6270797299 (Patrick Demichel, k=23161)
  113. 29402547 1444566739 (Patrick Demichel, k=100461)
  114. 29408373 6424066117 (David Broadhurst, k=2)
  115. 29578197 6205013929 (David Broadhurst, k=28)
  116. 29742687 5949998929 (David Broadhurst, k=56)
  117. 29964664 3339744447 (David Broadhurst, k=1)
  118. 30114062 0030114063 (David Broadhurst, k=1)
  119. 30938808 3348960727 (David Broadhurst, k=1)
  120. 31003514 3656767973 (David Broadhurst, k=2)
  121. 31008539 0922097649 (Phil Carmody, k=104)
  122. +315073697412756811 (k=116435217077885)
  123. 31566418 2372031769 (David Broadhurst, k=4)
  124. 31659070 7773218979 (David Broadhurst, k=1)
  125. 31665238 9774002019 (David Broadhurst, k=1)
  126. 32112622 8615337489 (David Broadhurst, k=56)
  127. 32291930 4205354583 (Phil Carmody, k=121)
  128. 32547742 6369181407 (David Broadhurst, k=1)
  129. 32569113 3171612499 (David Broadhurst, k=81)
  130. 32854146 8783634019 (David Broadhurst, k=1)
  131. 32966363 9117970601 (David Broadhurst, k=100)
  132. 33272064 1973116849 (David Broadhurst, k=8)
  133. 34584264 1712076499 (David Broadhurst, k=1)
  134. 35029872 7458205223 (David Broadhurst, k=1)
  135. 35099895 6405538409 (Patrick Demichel, k=82244)
  136. 35468540 0488131637 (Phil Carmody, k=406)
  137. 35788683 0313909447 (Patrick Demichel, k=94021)
  138. 35902360 7170554481 (Patrick Demichel, k=87080)
  139. 36220673 7601337521 (David Broadhurst, k=40)
  140. 36493832 1377647583 (David Broadhurst, k=1)
  141. 36724116 0036724117 (David Broadhurst, k=26)
  142. 37603140 1038098527 (Patrick Demichel, k=9401)
  143. 37691365 6315666499 (David Broadhurst, k=49)
  144. 37720673 4763664647 (David Broadhurst, k=31)
  145. 37721739 9707976739 (David Broadhurst, k=43)
  146. 37873447 9776724699 (Phil Carmody, k=2321)
  147. 37900228 2960726613 (Phil Carmody, k=874)
  148. 38276570 5295670091 (David Broadhurst, k=5)
  149. 38619620 8950290491 (David Broadhurst, k=5)
  150. 38741083 2482784133 (David Broadhurst, k=22)
  151. 38823011 5260511801 (Phil Carmody, k=3100)
  152. 39804130 6222822133 (David Broadhurst, k=26)
  153. 39946480 8151488503 (Patrick Demichel, k=55241)
  154. 39994499 7230417299 (David Broadhurst, k=1)
  155. 40106739 3914069167 (David Broadhurst, k=1)
  156. 40154265 3135513979 (David Broadhurst, k=1)
  157. 40934600 0875547293 (Phil Carmody, k=4562)
  158. 40961397 5674963093 (Phil Carmody, k=114)
  159. 41073138 0041073139 (David Broadhurst, k=1)
  160. 41455031 2153666921 (Phil Carmody, k=140)
  161. 41641593 8169740521 (David Broadhurst, k=20)
  162. 42692061 9189825641 (David Broadhurst, k=20)
  163. 42807386 5893474211 (Paul Leyland, k=30495)
  164. 42997246 2108781237 (David Broadhurst, k=2)
  165. 43315580 9208613303 (Phil Carmody, k=119)
  166. 44053662 1964415143 (David Broadhurst, k=1)
  167. 44586184 3063982731 (Phil Carmody, k=1435)
  168. 45277586 6621389081 (Phil Carmody, k=19180)
  169. 45322522 1030842327 (David Broadhurst, k=47)
  170. 45356576 7149537401 (Patrick Demichel, k=1172300)
  171. 45838011 3352639813 (Phil Carmody, k=114)
  172. 45985718 8478772659 (Patrick Demichel, k=43169)
  173. 46415898 8915900983 (Phil Carmody, k=1987)
  174. 46759174 5341520277 (Patrick Demichel, k=64886)
  175. 47431016 2347247477 (Phil Carmody, k=1762)
  176. 50037258 5641019653 (David Broadhurst, k=2)
  177. 50209946 9262296929 (David Broadhurst, k=16)
  178. 51300031 8848979881 (Patrick Demichel, k=1870340)
  179. 52014142 5794588401 (Patrick Demichel, k=1941400)
  180. +528409639473126379 (David Broadhurst using ECM) (k=29543198002523)
  181. 53575823 1146990729 (David Broadhurst, k=4)
  182. 54549446 9415875167 (David Broadhurst, k=1)
  183. 54765907 2397225933 (Phil Carmody, k=442)
  184. 55322225 4490132321 (Phil Carmody, k=240)
  185. 55732176 4048693447 (Phil Carmody, k=1171)
  186. 55758978 0055758979 (David Broadhurst, k=11)
  187. 56618570 3620975007 (Phil Carmody, k=493)
  188. 57059673 9942940327 (Patrick Demichel, k=8057)
  189. 57292921 2872000009 (David Broadhurst, k=4)
  190. 57967103 1961244413 (David Broadhurst, k=14)
  191. 58197525 2787330931 (David Broadhurst, k=5)
  192. 58296946 8943359983 (David Broadhurst, k=1)
  193. 58298231 3437636729 (David Broadhurst, k=28)
  194. 59018772 0059018773 (Phil Carmody, k=1082)
  195. 59081061 9662705927 (Phil Carmody, k=1753)
  196. 59408947 6814540477 (Phil Carmody, k=238)
  197. 59576333 8683858769 (Patrick Demichel, k=3031576)
  198. 59578027 6525810927 (David Broadhurst, k=1)
  199. 59887929 5722397167 (Patrick Demichel, k=1708621)
  200. 59951874 8968073903 (David Broadhurst, k=1)
  201. 60211100 0630671423 (Phil Carmody, k=557)
  202. 60450301 8251932823 (David Broadhurst, k=1)
  203. 60710145 4410834571 (Phil Carmody, k=2945)
  204. 62691688 1448830303 (David Broadhurst, k=1)
  205. 62768725 7367656971 (David Broadhurst, k=15)
  206. 63859395 2143067317 (David Broadhurst, k=2)
  207. 64846138 2837123367 (David Broadhurst, k=7)
  208. 64916220 7193629093 (David Broadhurst, k=2)
  209. 65258018 8812070927 (David Broadhurst, k=11)
  210. 65788061 5638555167 (David Broadhurst, k=13)
  211. 66128626 0150673543 (Phil Carmody, k=161)
  212. 66194283 8861858093 (Phil Carmody, k=4886)
  213. 66255137 2419069047 (Phil Carmody, k=1483)
  214. 66745902 0868063447 (David Broadhurst, k=1)
  215. 67255530 3231657823 (David Broadhurst, k=9)
  216. 67865335 1354994049 (Phil Carmody, k=576)
  217. 68255145 7733942743 (David Broadhurst, k=37)
  218. 70407751 4292735881 (Phil Carmody, k=2140)
  219. 71270365 2134820127 (David Broadhurst, k=1)
  220. 71930203 2525687733 (Patrick Demichel, k=691974)
  221. 72000720 0072000721 (David Broadhurst, k=40)
  222. 73597794 0532462813 (Patrick Demichel, k=47902)
  223. 74679964 8637232917 (David Broadhurst, k=2)
  224. 75469688 8182249253 (Phil Carmody, k=3082)
  225. 76409198 0868488407 (David Broadhurst, k=1)
  226. 76437391 5523575397 (Phil Carmody, k=442)
  227. 76997413 6460312081 (Phil Carmody, k=440)
  228. 79179213 9732416167 (David Broadhurst, k=1)
  229. 79540941 6284095423 (David Broadhurst, k=29)
  230. +799168560350388247 (David Broadhurst using ECM) (k=176885471525097)
  231. 80138565 3117583579 (Paul Leyland, k=38693)
  232. 80411987 6889284983 (Phil Carmody, k=247)
  233. 80609308 7906837287 (Patrick Demichel, k=1263307)
  234. 81219170 5043569489 (Phil Carmody, k=3816)
  235. 81357632 4282208819 (Phil Carmody, k=613)
  236. 81492409 6265710663 (David Broadhurst, k=7)
  237. 81645179 0094183853 (Patrick Demichel, k=776454)
  238. 82817394 1282515277 (David Broadhurst, k=2)
  239. 83013291 7900489477 (Patrick Demichel, k=234962)
  240. 83693822 8389548407 (David Broadhurst, k=1)
  241. 84755588 0876834797 (David Broadhurst, k=2)
  242. 84804589 6718467957 (Phil Carmody, k=1126)
  243. 87703201 3975120583 (David Broadhurst, k=1)
  244. 88004334 4790044447 (Phil Carmody, k=257)
  245. 88148399 8478000899 (Phil Carmody, k=3953)
  246. 90207368 9122468699 (David Broadhurst, k=1)
  247. 90394743 1338090973 (David Broadhurst, k=14)
  248. 90560799 9909439201 (Patrick Demichel, k=180400)
  249. 90895058 9906135053 (David Broadhurst, k=2)
  250. 92143246 2940396171 (David Broadhurst, k=15)
  251. 92832098 2801805623 (Patrick Demichel, k=98597)
  252. 94889599 5818594437 (Phil Carmody, k=3506)
  253. 97088724 2695448293 (David Broadhurst, k=2)
  254. 97347598 8423407129 (David Broadhurst, k=4)
  255. 98116872 4994134051 (Phil Carmody, k=2475)

Phil Carmody is organizing a distributed computing project in order to find more factors of Googolplex + 10. If you like these pages I would appreciate that you donate some idle cycles of your computer. You will be cited as the discoverer of the factors you find.