Known 19-digit prime factors of Googolplex + 10

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  2. Number Theory
  3. Known 19-digit prime factors of Googolplex + 10

This is a list of known 19-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. 102462834 0621757567 (David Broadhurst, k=1)
  2. 102601827 2686390609 (David Broadhurst, k=8)
  3. 103312295 6814933157 (David Broadhurst, k=2)
  4. 103636203 9625111651 (David Broadhurst, k=25)
  5. 106310778 0316202539 (David Broadhurst, k=1)
  6. 108371777 5299973771 (David Broadhurst, k=15)
  7. 108583250 0150784889 (Norm Dresner, k=10356)
  8. 108741793 2550184797 (Phil Carmody, k=166)
  9. 110405450 8837412411 (Patrick Demichel, k=252055)
  10. 111950496 3774888373 (David Broadhurst, k=2)
  11. 112795922 1131357491 (David Broadhurst, k=5)
  12. 113881690 8386833303 (Patrick Demichel, k=1447399)
  13. 115354705 1176158211 (Patrick Demichel, k=6045)
  14. 115864681 5957448841 (Patrick Demichel, k=7820)
  15. 116089627 0967399539 (Phil Carmody, k=4121)
  16. 120343660 4029704139 (David Broadhurst, k=1)
  17. 120565562 0912644771 (Phil Carmody, k=165)
  18. 122563325 9794248889 (Phil Carmody, k=3188)
  19. 123914830 5074409881 (Phil Carmody, k=2540)
  20. 124450526 6001010729 (Phil Carmody, k=156)
  21. 124969620 2130052931 (Phil Carmody, k=215)
  22. 126356418 0126356419 (David Broadhurst, k=1)
  23. 126413386 0407701047 (Phil Carmody, k=4597)
  24. 126489653 5320664819 (David Broadhurst, k=13)
  25. 127135924 8245947807 (David Broadhurst, k=1)
  26. 130077025 4415377521 (David Broadhurst, k=40)
  27. 131203312 7588426809 (Patrick Demichel, k=24636)
  28. 133325239 7294612677 (David Broadhurst, k=42)
  29. 133982321 0560415533 (David Broadhurst, k=14)
  30. 134002467 4589448013 (Phil Carmody, k=3194)
  31. 136621646 5202248771 (David Broadhurst, k=15)
  32. 136704896 6023879207 (David Broadhurst, k=1)
  33. 138094827 5217358343 (Phil Carmody, k=281)
  34. 139046678 8678798477 (David Broadhurst, k=46)
  35. 139365152 0054961877 (Patrick Demichel, k=40302)
  36. 141581418 9777117769 (David Broadhurst, k=68)
  37. 142521328 4600997091 (Phil Carmody, k=905)
  38. 143186120 8336262419 (David Broadhurst, k=13)
  39. 143288513 1608374459 (David Broadhurst, k=21)
  40. 143878697 8862506849 (David Broadhurst, k=16)
  41. 143917699 0836987007 (David Broadhurst, k=1)
  42. 145057215 6284052649 (David Broadhurst, k=28)
  43. 145927818 8874162383 (David Broadhurst, k=1)
  44. 151260758 7712617881 (Phil Carmody, k=340)
  45. 155905636 4692579213 (David Broadhurst, k=2)
  46. 155987618 0548110877 (David Broadhurst, k=2)
  47. 159074450 2186330823 (David Broadhurst, k=1)
  48. 161079601 1521903607 (David Broadhurst, k=83)
  49. 162540399 7615237379 (Phil Carmody, k=259)
  50. 164198673 9051518641 (David Broadhurst, k=40)
  51. 164402407 4566274677 (David Broadhurst, k=2)
  52. 166035257 1521481619 (Phil Carmody, k=1301)
  53. 166960829 2660606693 (Phil Carmody, k=254)
  54. 167574427 8731288173 (Patrick Demichel, k=924354)
  55. 167579829 5010382447 (David Broadhurst, k=1)
  56. 168802021 7541420877 (Patrick Demichel, k=6562)
  57. 169708980 9364659091 (David Broadhurst, k=5)
  58. 169893285 6681547957 (Phil Carmody, k=2142)
  59. 170976566 9606192329 (Paul Leyland, k=35828)
  60. 176235925 6088505493 (David Broadhurst, k=2)
  61. 176293319 7359123197 (Patrick Demichel, k=324686)
  62. 178311237 0769725517 (David Broadhurst, k=2)
  63. 179934657 7210318819 (Phil Carmody, k=241)
  64. 181365233 3059302361 (David Broadhurst, k=20)
  65. 182757574 5464674063 (Patrick Demichel, k=67119)
  66. 183372728 4665112121 (Patrick Demichel, k=599020)
  67. 183572980 2580654663 (Patrick Demichel, k=445337)
  68. 184228088 3496481447 (David Broadhurst, k=27)
  69. 185847614 3759487103 (Patrick Demichel, k=71039)
  70. 187153352 6549586743 (David Broadhurst, k=1)
  71. 195813765 6295296601 (Phil Carmody, k=2700)
  72. 199796291 0694006967 (David Broadhurst, k=27)
  73. 200237706 2604190339 (David Broadhurst, k=1)
  74. 200548824 4840101583 (Norm Dresner, k=13877)
  75. 201848085 0026536717 (David Broadhurst, k=2)
  76. 202803362 3596816453 (David Broadhurst, k=2)
  77. 204093942 7292271931 (David Broadhurst, k=5)
  78. 204122737 9795877263 (David Broadhurst, k=19)
  79. 210864228 2905018423 (Patrick Demichel, k=23167)
  80. 211120594 2261588013 (David Broadhurst, k=82)
  81. 213270269 9683671721 (Patrick Demichel, k=370540)
  82. 214809754 7347641451 (Patrick Demichel, k=26275)
  83. 214960458 0214960459 (Phil Carmody, k=173)
  84. 217597585 7964220597 (David Broadhurst, k=2)
  85. 219933227 9780066773 (Patrick Demichel, k=438114)
  86. 221525081 6535715219 (David Broadhurst, k=13)
  87. 221718666 6591905531 (Phil Carmody, k=1765)
  88. 223542538 8874163047 (Phil Carmody, k=4497)
  89. 224674180 1732608969 (Patrick Demichel, k=2083628)
  90. 229716505 2261044767 (David Broadhurst, k=1)
  91. 229873966 6599394327 (Phil Carmody, k=3717)
  92. 230847836 3289277939 (David Broadhurst, k=1)
  93. 231383044 7796205477 (David Broadhurst, k=2)
  94. 239000889 4354365373 (Patrick Demichel, k=29234)
  95. 240939627 6450032899 (Patrick Demichel, k=112133)
  96. 244814816 4864978613 (David Broadhurst, k=2)
  97. 247818974 6697974299 (David Broadhurst, k=1)
  98. 249224540 0944407049 (David Broadhurst, k=36)
  99. 249673417 3326813041 (Phil Carmody, k=4520)
  100. 252175959 9280419367 (David Broadhurst, k=61)
  101. 253114566 5736186517 (Patrick Demichel, k=403422)
  102. 254978787 4116364927 (David Broadhurst, k=57)
  103. 255243789 0273702091 (Paul Leyland, k=34765)
  104. 258277448 4066660613 (David Broadhurst, k=2)
  105. 258889626 4110648251 (Patrick Demichel, k=800375)
  106. 264919480 8779770967 (David Broadhurst, k=13)
  107. +2670502781396266997 (k=32567107090198378)
  108. 272255927 6487493489 (David Broadhurst, k=8)
  109. 273328636 9580259331 (Phil Carmody, k=305)
  110. 273927596 8210920889 (Phil Carmody, k=1748)
  111. 274224796 4234620837 (Phil Carmody, k=102)
  112. 276436627 0488421453 (David Broadhurst, k=14)
  113. 277638614 7608900971 (Phil Carmody, k=2015)
  114. 277929647 7125103211 (Phil Carmody, k=2435)
  115. 279961498 0612921087 (David Broadhurst, k=7)
  116. 281363931 5430241013 (David Broadhurst, k=26)
  117. 282995455 8413736967 (Patrick Demichel, k=684631)
  118. 283839059 5520019139 (David Broadhurst, k=1)
  119. 285909248 9351145059 (Paul Leyland, k=33619)
  120. 292917659 4468539047 (Norm Dresner, k=13917)
  121. 295843257 9711847729 (David Broadhurst, k=56)
  122. 302209772 0935602607 (David Broadhurst, k=11)
  123. 302528288 5709344927 (Patrick Demichel, k=25121)
  124. 316687225 0204017983 (David Broadhurst, k=1)
  125. 320510022 2559555143 (Patrick Demichel, k=1944541)
  126. 320928908 6637286207 (David Broadhurst, k=1)
  127. 321234652 0051435979 (Patrick Demichel, k=88489)
  128. 322597593 7880493529 (Phil Carmody, k=556)
  129. 324242919 6803624917 (Phil Carmody, k=18582)
  130. 324567146 5243235689 (Patrick Demichel, k=25348)
  131. 327806689 6771002811 (Patrick Demichel, k=1238645)
  132. 329001879 4108853743 (David Broadhurst, k=39)
  133. 333494859 7171148299 (Patrick Demichel, k=112883)
  134. 337980621 3504643807 (Patrick Demichel, k=552721)
  135. 340249806 9121122247 (David Broadhurst, k=11)
  136. 341038658 0224447693 (David Broadhurst, k=2)
  137. 342281942 6818776529 (Phil Carmody, k=248)
  138. 342668978 4071862487 (Patrick Demichel, k=53787)
  139. 347068878 0258991729 (David Broadhurst, k=8)
  140. 347850912 4888941001 (Patrick Demichel, k=604500)
  141. 349215708 8195469739 (David Broadhurst, k=1)
  142. 352902552 5869872619 (Patrick Demichel, k=100973)
  143. 355426113 0312880571 (Phil Carmody, k=3385)
  144. 356709007 8140439601 (Patrick Demichel, k=598200)
  145. 358133931 0523752823 (Phil Carmody, k=2479)
  146. 362936274 6191798179 (David Broadhurst, k=1)
  147. 365315993 1542679143 (Phil Carmody, k=221)
  148. 367069461 1719343009 (Patrick Demichel, k=101488)
  149. 371888012 0451297253 (Patrick Demichel, k=290462)
  150. 373223351 0023680619 (Patrick Demichel, k=27361)
  151. 375923845 4128983013 (David Broadhurst, k=2)
  152. 377761168 7889591931 (Norm Dresner, k=13055)
  153. 381251347 4362696093 (Phil Carmody, k=194)
  154. 382894533 4606931179 (David Broadhurst, k=1)
  155. 388397577 0039597613 (Phil Carmody, k=2174)
  156. 391174311 0961375579 (Phil Carmody, k=161)
  157. 391863336 8768028263 (David Broadhurst, k=1)
  158. 392077687 0971637213 (Patrick Demichel, k=87322)
  159. 392876467 5577047967 (John Gamble, k=17837)
  160. 393393181 9606606819 (David Broadhurst, k=91)
  161. 397270188 6680592367 (Patrick Demichel, k=196301)
  162. 398637284 3327740087 (Phil Carmody, k=1937)
  163. 399541262 5450933567 (David Broadhurst, k=1)
  164. 400843935 3822395383 (Phil Carmody, k=1089)
  165. 404526380 7902156687 (Phil Carmody, k=3493)
  166. 408879334 6257787333 (Patrick Demichel, k=2443502)
  167. 410085288 9717015983 (David Broadhurst, k=1)
  168. 411921052 2705394117 (Phil Carmody, k=182)
  169. 414362938 7249597731 (David Broadhurst, k=5)
  170. 415657836 0415657837 (David Broadhurst, k=2)
  171. 415783505 7374910011 (David Broadhurst, k=5)
  172. 417030996 2497865317 (Patrick Demichel, k=517582)
  173. 418374330 0418374331 (David Broadhurst, k=5)
  174. 419381203 3533983569 (David Broadhurst, k=8)
  175. 420682473 0208877899 (Patrick Demichel, k=8093)
  176. 423232537 4831361259 (David Broadhurst, k=1)
  177. 424960027 8666541921 (Phil Carmody, k=3440)
  178. 425400221 7893607367 (Phil Carmody, k=3551)
  179. 426810663 3697048099 (David Broadhurst, k=1)
  180. 434085790 1483563921 (Patrick Demichel, k=624440)
  181. 437182575 3436754773 (Phil Carmody, k=114)
  182. 438476860 6228189807 (Patrick Demichel, k=25691)
  183. 447379905 9540402331 (David Broadhurst, k=5)
  184. 448017276 5677443979 (Patrick Demichel, k=169741)
  185. 459674599 1946388237 (David Broadhurst, k=2)
  186. 465710702 5695027691 (Phil Carmody, k=155)
  187. 466155734 4822591379 (David Broadhurst, k=1)
  188. 471078284 5621382641 (David Broadhurst, k=40)
  189. 471168131 3520387889 (David Broadhurst, k=8)
  190. 477431233 7755595651 (Phil Carmody, k=575)
  191. 479476940 3635487167 (David Broadhurst, k=17)
  192. 480744118 1511465481 (David Broadhurst, k=60)
  193. 484336888 1960033011 (Patrick Demichel, k=20035)
  194. 486468868 0235437813 (David Broadhurst, k=2)
  195. 493324175 4800017201 (Phil Carmody, k=200)
  196. 493561605 1949948647 (John Gamble, k=17317)
  197. +4964361517926013823 (David Broadhurst using ECM) (k=491423630758861)
  198. 498940206 8849892013 (David Broadhurst, k=2)
  199. 501586963 3439607779 (Patrick Demichel, k=3078329)
  200. 502601020 0659387361 (Patrick Demichel, k=46320)
  201. 503184184 2464336401 (Phil Carmody, k=3400)
  202. 506193109 0188913813 (David Broadhurst, k=2)
  203. 507390139 9874213677 (Patrick Demichel, k=2223382)
  204. 510698991 4289208727 (David Broadhurst, k=1)
  205. 513848089 6265073011 (David Broadhurst, k=5)
  206. 514466460 5555441143 (David Broadhurst, k=19)
  207. 520035910 1999954369 (Phil Carmody, k=224)
  208. 530627798 8993936489 (Patrick Demichel, k=47108)
  209. 531715611 8739258917 (David Broadhurst, k=38)
  210. 533872355 0729985739 (Phil Carmody, k=931)
  211. 535870413 1921678183 (Patrick Demichel, k=7069)
  212. 552319579 6259912299 (David Broadhurst, k=1)
  213. 554311636 0710991927 (David Broadhurst, k=31)
  214. 557644225 4996829499 (David Broadhurst, k=1)
  215. 562140873 7064404813 (David Broadhurst, k=54)
  216. 568272932 3918705077 (Patrick Demichel, k=283802)
  217. 573240071 2467224687 (Phil Carmody, k=193)
  218. 573615650 9695868863 (Phil Carmody, k=1667)
  219. 576090339 6364042699 (David Broadhurst, k=1)
  220. 580694555 8204456933 (David Broadhurst, k=14)
  221. 581830045 2859057769 (David Broadhurst, k=4)
  222. 584003561 1277384477 (David Broadhurst, k=2)
  223. 588351320 9512384081 (Patrick Demichel, k=6680)
  224. 594056726 0351187481 (Patrick Demichel, k=1718060)
  225. 594785012 8902109957 (David Broadhurst, k=22)
  226. 597057487 1336893093 (David Broadhurst, k=22)
  227. 600631742 0997184237 (Patrick Demichel, k=6506)
  228. 611045575 2294213893 (Norm Dresner, k=13546)
  229. 616692160 3056788179 (David Broadhurst, k=1)
  230. 617742488 0617742489 (David Broadhurst, k=4)
  231. 620136976 1884824691 (David Broadhurst, k=5)
  232. 621458140 0406915317 (Norm Dresner, k=12806)
  233. 625199586 5205228601 (Phil Carmody, k=700)
  234. 640897285 7719979383 (Phil Carmody, k=107)
  235. 641315404 5312654487 (David Broadhurst, k=7)
  236. 642857953 3453593983 (David Broadhurst, k=1)
  237. 646124144 0833852927 (Phil Carmody, k=4741)
  238. 649211119 7363205613 (David Broadhurst, k=2)
  239. 667988169 1908552733 (David Broadhurst, k=2)
  240. 675966111 2809362451 (Patrick Demichel, k=210525)
  241. 684017876 4149685007 (Patrick Demichel, k=2566447)
  242. 685620660 5078877251 (Phil Carmody, k=2375)
  243. 688290983 5218529531 (David Broadhurst, k=55)
  244. 691611064 7462470477 (David Broadhurst, k=2)
  245. 695821078 5157837459 (David Broadhurst, k=1)
  246. 696857856 5567928277 (Patrick Demichel, k=6042)
  247. 697809921 2578998041 (David Broadhurst, k=20)
  248. 699213293 0427364219 (David Broadhurst, k=1)
  249. 705967353 8235376567 (David Broadhurst, k=1)
  250. 709057932 0709057933 (David Broadhurst, k=2)
  251. 711417755 1658305943 (Phil Carmody, k=159)
  252. 714877819 7286467767 (David Broadhurst, k=1)
  253. 727154211 9859524383 (John Gamble, k=16301)
  254. 728577645 3995904379 (David Broadhurst, k=1)
  255. 731527271 6759247637 (Patrick Demichel, k=5542)
  256. 752361294 2712960367 (Phil Carmody, k=637)
  257. 752858369 1426971053 (Patrick Demichel, k=197894)
  258. 756937152 6941630743 (David Broadhurst, k=7)
  259. 759158627 5031962921 (David Broadhurst, k=20)
  260. 763164244 4452210253 (Phil Carmody, k=2386)
  261. 771733767 3542137609 (Phil Carmody, k=188)
  262. 773186724 6972535819 (David Broadhurst, k=1)
  263. 781893508 6368245929 (Phil Carmody, k=188)
  264. 784530753 8731773223 (David Broadhurst, k=7)
  265. 785055325 8012778099 (Patrick Demichel, k=21271)
  266. 795348130 3241128579 (Phil Carmody, k=1141)
  267. 799082525 0901867133 (David Broadhurst, k=2)
  268. 799195523 6922784447 (David Broadhurst, k=31)
  269. 816042600 1006045579 (Phil Carmody, k=931)
  270. 816776193 2910161077 (David Broadhurst, k=2)
  271. 826535538 0826535539 (David Broadhurst, k=1)
  272. 835074490 2535159213 (David Broadhurst, k=2)
  273. 840817557 4136626601 (Phil Carmody, k=1300)
  274. 846228861 3560515207 (David Broadhurst, k=1)
  275. 847043164 5403627663 (David Broadhurst, k=7)
  276. 855571732 4221908367 (Norm Dresner, k=13721)
  277. 862373699 2278794077 (Patrick Demichel, k=83126)
  278. 863506194 5021922037 (David Broadhurst, k=2)
  279. 878322221 7230384023 (Patrick Demichel, k=151007)
  280. 884001081 3925347013 (David Broadhurst, k=2)
  281. 890712132 1331265649 (David Broadhurst, k=56)
  282. 901348996 1846781247 (David Broadhurst, k=11)
  283. 902248734 5194139503 (Paul Leyland, k=31507)
  284. 903173254 2733190383 (Patrick Demichel, k=5589)
  285. 906754527 3778992331 (David Broadhurst, k=5)
  286. 909439358 4636752503 (David Broadhurst, k=9)
  287. 915523184 8216985491 (Phil Carmody, k=3505)
  288. 917430466 3117597477 (David Broadhurst, k=22)
  289. 918223739 0125665823 (Norm Dresner, k=13749)
  290. 927630475 6317141973 (Patrick Demichel, k=58682)
  291. 932912255 9347945099 (Patrick Demichel, k=497803)
  292. 940589214 8805802211 (David Broadhurst, k=5)
  293. 945440465 0951977489 (Paul Leyland, k=37816)
  294. 947260446 0947260447 (Phil Carmody, k=211)
  295. 947415938 0128438249 (Patrick Demichel, k=6876)
  296. 957929954 0441234407 (David Broadhurst, k=1)
  297. 967450358 0550164819 (Phil Carmody, k=329)
  298. 976323715 5373274849 (Patrick Demichel, k=2287664)
  299. 976769298 8313123601 (Phil Carmody, k=200)
  300. 989547501 4010111173 (Phil Carmody, k=362)
  301. 996265769 6964313837 (David Broadhurst, k=2)

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.