Known 23-digit prime factors of Googolplex - 10

  1. Alpertron
  2. Number Theory
  3. Known 23-digit prime factors of Googolplex − 10

This is a list of known 23-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. 100 4846458429 5737547439 (Phil Carmody, k=1)
  2. 103 1611962686 4201626521 (Phil Carmody, k=20)
  3. 103 3652225839 5267665347 (Phil Carmody, k=7)
  4. 103 9542830126 6310828307 (Phil Carmody, k=47)
  5. 106 3437257260 4598159841 (Phil Carmody, k=80)
  6. 106 9360328383 1752422443 (Phil Carmody, k=1)
  7. 108 5595891555 8220736837 (Phil Carmody, k=46)
  8. 109 5371956770 9763371517 (Phil Carmody, k=722)
  9. 109 7975442963 2343987067 (Phil Carmody, k=1)
  10. 110 1911776284 4104483769 (Phil Carmody, k=148)
  11. 110 8746689771 1718075321 (Phil Carmody, k=340)
  12. 111 0856179167 2070649991 (Phil Carmody, k=5)
  13. 112 7314361055 1578638521 (Phil Carmody, k=20)
  14. 114 1434927829 6460632831 (Phil Carmody, k=155)
  15. 115 4088453178 3498293841 (Phil Carmody, k=40)
  16. 116 8451042552 8451042437 (Phil Carmody, k=2)
  17. 116 9948102213 5092548077 (Phil Carmody, k=26)
  18. 117 2541184319 2834159561 (Phil Carmody, k=20)
  19. 117 3734228179 4875148707 (Phil Carmody, k=1)
  20. 118 9041306980 9140511083 (Phil Carmody, k=599)
  21. 120 2460587270 7038977213 (Phil Carmody, k=154)
  22. 120 3857158500 2015449321 (Phil Carmody, k=20)
  23. 120 8641553925 4350934729 (Dario Alpern, k=1228)
  24. 122 5138980866 4314194591 (Phil Carmody, k=5)
  25. 123 6559638073 3006969213 (Phil Carmody, k=2)
  26. 123 7936843105 3780328489 (Phil Carmody, k=4)
  27. 123 9731964333 1514021239 (Phil Carmody, k=1)
  28. 124 5006230296 1757978769 (Dario Alpern, k=2648)
  29. 125 1283914462 6615881311 (Phil Carmody, k=35)
  30. 126 8771063367 2278547003 (Phil Carmody, k=1)
  31. 127 4477072043 4477071917 (Dario Alpern, k=2738)
  32. 127 8497219173 9807324249 (Phil Carmody, k=36)
  33. 128 6853184666 3326844279 (Phil Carmody, k=53)
  34. 129 1371047664 6304676803 (Phil Carmody, k=487)
  35. 129 5682732102 8356077203 (Phil Carmody, k=1)
  36. 129 8893243927 9017502483 (Phil Carmody, k=277)
  37. 130 1071203914 1808367161 (Dario Alpern, k=1420)
  38. 130 5528327363 9850418719 (Phil Carmody, k=1)
  39. 130 7143579355 9842051391 (Phil Carmody, k=395)
  40. 131 3354591508 4264787723 (Phil Carmody, k=1)
  41. 132 3848638666 5076777729 (Phil Carmody, k=128)
  42. 133 6037646265 6037646133 (Phil Carmody, k=14)
  43. 134 2471400989 4064691511 (Phil Carmody, k=505)
  44. 134 3512902697 9637504689 (Phil Carmody, k=56)
  45. 136 1739079994 1484012843 (Phil Carmody, k=847)
  46. 136 8510228206 0670690689 (Phil Carmody, k=64)
  47. 137 0691495879 4151278039 (Dario Alpern, k=1931)
  48. 137 1073720394 4563035837 (Phil Carmody, k=2)
  49. 137 6741730888 6840740653 (Dario Alpern, k=1862)
  50. 141 8083435736 2875973717 (Phil Carmody, k=2)
  51. 144 8239873651 4879121031 (Phil Carmody, k=5)
  52. 145 6066277392 5891674839 (Phil Carmody, k=1)
  53. 147 0737257706 9294797013 (Phil Carmody, k=26)
  54. 148 2582224854 2582224707 (Phil Carmody, k=1)
  55. 148 4893564610 8150468639 (Phil Carmody, k=51)
  56. 148 6523353399 3848750049 (Phil Carmody, k=16)
  57. 148 7727066437 9163402319 (Phil Carmody, k=1)
  58. 150 6053529280 4607030631 (Phil Carmody, k=355)
  59. 151 4494327922 2216250209 (Phil Carmody, k=16)
  60. 151 8928106149 1321857867 (Phil Carmody, k=1)
  61. 151 9114135937 5749364969 (Phil Carmody, k=28)
  62. 156 5123914605 4826884747 (Phil Carmody, k=1)
  63. 157 1103728667 2223860123 (Phil Carmody, k=1)
  64. 157 2027727902 2437216591 (Phil Carmody, k=5)
  65. 163 2237027196 6626355027 (Phil Carmody, k=7)
  66. 164 2601626016 2601625853 (Phil Carmody, k=2)
  67. 164 9606707479 2494102453 (Phil Carmody, k=14)
  68. 165 1191773872 2786565747 (Phil Carmody, k=1)
  69. 165 8948821375 5667765627 (Phil Carmody, k=1)
  70. 166 0985660594 5070575603 (Phil Carmody, k=17)
  71. 166 1907539872 0682467681 (Phil Carmody, k=80)
  72. 166 6288878169 9031432689 (Phil Carmody, k=8)
  73. 167 6694148814 6749583003 (Phil Carmody, k=1)
  74. 168 2198028465 9628989637 (Phil Carmody, k=2)
  75. 168 7205997075 2794002757 (Phil Carmody, k=2)
  76. 169 5120211340 5671421399 (Phil Carmody, k=1)
  77. 169 7965199885 9549358133 (Phil Carmody, k=2)
  78. 170 2159738432 5932683759 (Phil Carmody, k=11)
  79. 170 3779453672 3388934397 (Phil Carmody, k=2)
  80. 171 0047554781 8624531769 (Phil Carmody, k=4)
  81. 172 6105890048 7294008689 (Phil Carmody, k=104)
  82. 172 7044318883 0733458723 (Phil Carmody, k=1)
  83. 173 0338815864 7607137837 (Phil Carmody, k=26)
  84. 173 4488314653 3408628427 (Dario Alpern, k=1973)
  85. 174 1510318717 9495200041 (Phil Carmody, k=20)
  86. 174 3554064967 3652906929 (Phil Carmody, k=8)
  87. 176 7001501883 1409069391 (Dario Alpern, k=1445)
  88. 183 6146578839 7929245533 (Dario Alpern, k=1514)
  89. 183 9188712701 0508256813 (Phil Carmody, k=2)
  90. 184 1246601744 7002037879 (Phil Carmody, k=1)
  91. 184 5662885281 3251058729 (Phil Carmody, k=28)
  92. 186 1281071703 3101781031 (Phil Carmody, k=455)
  93. 186 2001602426 2199622043 (Phil Carmody, k=17)
  94. 187 3020926368 3216711613 (Phil Carmody, k=566)
  95. 188 1859570791 2505112609 (Dario Alpern, k=1456)
  96. 191 5730884863 9881666119 (Phil Carmody, k=211)
  97. 191 7021316929 1625514803 (Phil Carmody, k=1)
  98. 196 7286750379 1612060437 (Phil Carmody, k=2)
  99. 198 7996478399 4803360071 (Phil Carmody, k=695)
  100. 201 9979800201 9979800203 (Phil Carmody, k=1)
  101. 204 1548480794 7567776917 (Phil Carmody, k=2)
  102. 205 3915538975 3717518969 (Phil Carmody, k=236)
  103. 205 4781380577 0820984333 (Phil Carmody, k=2)
  104. 207 9896026273 2662067991 (Phil Carmody, k=5)
  105. 208 6343889389 0341519933 (Phil Carmody, k=14)
  106. 208 8247633764 5176276387 (Phil Carmody, k=91)
  107. 212 5683679334 7326455253 (Dario Alpern, k=1786)
  108. 214 7107143068 2293911129 (Phil Carmody, k=4)
  109. 215 1947616113 0112531547 (Phil Carmody, k=1)
  110. 216 2545745609 0126699479 (Phil Carmody, k=1)
  111. 218 0784894215 2864101919 (Phil Carmody, k=1)
  112. 220 0134116810 4108307213 (Phil Carmody, k=2)
  113. 223 6278854475 1698227311 (Phil Carmody, k=35)
  114. 227 2818531156 5260910893 (Phil Carmody, k=2)
  115. 228 5017870617 2507543569 (Dario Alpern, k=1976)
  116. 231 2940646203 2940645973 (Phil Carmody, k=34)
  117. 234 5090934002 5090933769 (Phil Carmody, k=484)
  118. 235 8521657043 7531557799 (Phil Carmody, k=1)
  119. 237 3084288162 4680304681 (Phil Carmody, k=580)
  120. 238 2459654370 2459654133 (Phil Carmody, k=214)
  121. 241 4262119182 0198691083 (Phil Carmody, k=47)
  122. 242 2033952167 1726576653 (Phil Carmody, k=2)
  123. 242 3846406780 8994921391 (Phil Carmody, k=155)
  124. 242 7280641446 0192911867 (Phil Carmody, k=31)
  125. 243 3092598296 4553037471 (Phil Carmody, k=35)
  126. 247 0353780765 5304275569 (Phil Carmody, k=8)
  127. 250 1837910076 1837909827 (Phil Carmody, k=1)
  128. 250 4705595672 3415798961 (Phil Carmody, k=280)
  129. 252 5418425433 1305868831 (Phil Carmody, k=135)
  130. 255 6781393654 4203664413 (Phil Carmody, k=2)
  131. 256 3499116891 3428515111 (Phil Carmody, k=5)
  132. 258 1936450069 7457489067 (Phil Carmody, k=1)
  133. 263 7078012746 2812546649 (Phil Carmody, k=676)
  134. 265 7933221553 0004358093 (Phil Carmody, k=2)
  135. 270 6824701417 6923711049 (Phil Carmody, k=36)
  136. 271 4697819300 7429692613 (Phil Carmody, k=2)
  137. 272 0010350087 8103285323 (Phil Carmody, k=7)
  138. 272 5057971729 9282784591 (Phil Carmody, k=5)
  139. 273 0846109946 8253927707 (Dario Alpern, k=2567)
  140. 273 6008210812 3118864311 (Phil Carmody, k=635)
  141. 274 3961191194 0694836911 (Phil Carmody, k=5)
  142. 277 7581416114 5312521639 (Phil Carmody, k=1)
  143. 283 4780354328 6437304799 (Phil Carmody, k=71)
  144. 283 5758849125 3925990329 (Phil Carmody, k=116)
  145. 285 0194186575 8476415323 (Phil Carmody, k=1)
  146. 292 8790141846 1991965683 (Phil Carmody, k=499)
  147. 293 5988352723 6857175439 (Phil Carmody, k=13)
  148. 296 1630393452 1630393157 (Phil Carmody, k=2)
  149. 296 7430285984 8296492191 (Phil Carmody, k=5)
  150. 299 0527942390 2211110409 (Phil Carmody, k=876)
  151. 310 9118581064 2082973277 (Phil Carmody, k=26)
  152. 314 3679266613 3211114231 (Phil Carmody, k=5)
  153. 314 4218496670 8438143239 (Phil Carmody, k=1)
  154. 318 1170855472 2243778357 (Phil Carmody, k=2)
  155. 319 6684491356 6523194947 (Phil Carmody, k=941)
  156. 322 3022830228 3022829907 (Phil Carmody, k=1)
  157. 323 6258446076 7377917237 (Phil Carmody, k=2)
  158. 324 7363346289 4563672329 (Phil Carmody, k=4)
  159. 331 4136774499 4136774169 (Phil Carmody, k=76)
  160. 331 8484566663 8484566333 (Phil Carmody, k=26)
  161. 332 1028077863 8271793997 (Phil Carmody, k=266)
  162. 332 7873099300 1252847911 (Phil Carmody, k=235)
  163. 334 5750064256 8764080551 (Phil Carmody, k=175)
  164. 335 2834877804 2366725401 (Phil Carmody, k=700)
  165. 335 6031525863 6031525529 (Phil Carmody, k=148)
  166. 335 7238444280 6331795683 (Phil Carmody, k=1)
  167. 337 1082242932 0028867843 (Phil Carmody, k=1)
  168. 338 8504272083 3893879123 (Phil Carmody, k=7)
  169. 340 4864402283 2105294347 (Phil Carmody, k=331)
  170. 342 8474484744 8474484403 (Phil Carmody, k=89)
  171. 348 0515382054 0515381707 (Phil Carmody, k=1)
  172. 349 8849473656 6578557323 (Phil Carmody, k=119)
  173. 356 3579489922 7804395883 (Phil Carmody, k=9)
  174. 360 1068443582 6366884957 (Phil Carmody, k=806)
  175. 361 4368719329 9660812333 (Phil Carmody, k=2)
  176. 364 0878776572 2036026077 (Phil Carmody, k=26)
  177. 370 2046420902 6034386809 (Phil Carmody, k=4)
  178. 372 2779927215 4024291363 (Dario Alpern, k=1067)
  179. 377 1625043955 0106034293 (Phil Carmody, k=2)
  180. 380 9292278169 6362978003 (Phil Carmody, k=1)
  181. 384 5529664349 8037134591 (Phil Carmody, k=5)
  182. 384 6208462835 6703511957 (Phil Carmody, k=166)
  183. 384 7606998259 1905196479 (Phil Carmody, k=1)
  184. 385 7294647906 9150055599 (Phil Carmody, k=1)
  185. 386 2000709896 2000709511 (Phil Carmody, k=5)
  186. 386 4555606151 8443387089 (Phil Carmody, k=376)
  187. 389 4605045912 0414303893 (Phil Carmody, k=34)
  188. 393 9171341619 9171341227 (Phil Carmody, k=1)
  189. 394 7555320541 5875003853 (Phil Carmody, k=2)
  190. 395 2810835446 7189164159 (Phil Carmody, k=11)
  191. 395 3621277992 0511328627 (Phil Carmody, k=127)
  192. 397 8173038071 5994819853 (Phil Carmody, k=34)
  193. 402 1962677541 6524161471 (Phil Carmody, k=215)
  194. 405 3475139779 3371531187 (Phil Carmody, k=1)
  195. 408 6678803876 3962056787 (Phil Carmody, k=1)
  196. 410 4914920366 3269361067 (Phil Carmody, k=23)
  197. 411 8201725170 1780698443 (Phil Carmody, k=1)
  198. 414 3158849843 6821656547 (Phil Carmody, k=31)
  199. 414 6943988128 5743029237 (Dario Alpern, k=2462)
  200. 414 8412985565 0810421787 (Dario Alpern, k=1337)
  201. 415 7229565438 0331409757 (Phil Carmody, k=2)
  202. 416 8530505465 9841577839 (Phil Carmody, k=19)
  203. 419 3435768775 7020481799 (Phil Carmody, k=19)
  204. 421 7961250270 5089179813 (Phil Carmody, k=2)
  205. 426 9537093778 2342786997 (Phil Carmody, k=2)
  206. 431 3179334818 5409659919 (Dario Alpern, k=1883)
  207. 432 5091491218 0253398957 (Phil Carmody, k=2)
  208. 433 5783160597 0339637521 (Phil Carmody, k=40)
  209. 434 0194757859 5468889253 (Phil Carmody, k=2)
  210. 434 6251358203 5494386093 (Phil Carmody, k=2)
  211. 435 2873761061 5331423119 (Dario Alpern, k=1393)
  212. 435 5486043238 9538706079 (Phil Carmody, k=1)
  213. 451 4464344375 7557934951 (Phil Carmody, k=25)
  214. 457 8121704206 1168760969 (Phil Carmody, k=116)
  215. 458 1741198208 2130918169 (Phil Carmody, k=4)
  216. 458 6436610138 1647990067 (Phil Carmody, k=13)
  217. 461 4298410404 4171327199 (Phil Carmody, k=1)
  218. 462 3510682802 1290837479 (Phil Carmody, k=23)
  219. 465 2101217152 8717432391 (Phil Carmody, k=5)
  220. 477 8004604102 6646998769 (Phil Carmody, k=104)
  221. 481 5859203407 9116807237 (Phil Carmody, k=122)
  222. 489 2130584636 3912566639 (Phil Carmody, k=1)
  223. 489 2444659100 0563470493 (Phil Carmody, k=142)
  224. 489 9444402004 7761233199 (Dario Alpern, k=2881)
  225. 497 0130538649 4358378471 (Phil Carmody, k=65)
  226. 497 1374990942 4858771427 (Phil Carmody, k=1)
  227. 506 6029096985 0556268363 (Phil Carmody, k=29)
  228. 507 5084253468 9114188009 (Phil Carmody, k=4)
  229. 509 3895599657 8648074397 (Phil Carmody, k=2)
  230. 513 8759486837 2043495677 (Phil Carmody, k=266)
  231. 521 4467824564 0328922883 (Phil Carmody, k=7)
  232. 522 2301537289 6758101053 (Phil Carmody, k=22)
  233. 523 2848488936 3618620667 (Phil Carmody, k=1)
  234. 526 6569736651 7184882187 (Phil Carmody, k=31)
  235. 528 7159616150 6169516613 (Phil Carmody, k=234)
  236. 531 0496397790 4868318963 (Phil Carmody, k=1)
  237. 532 4792427559 6118952907 (Phil Carmody, k=1)
  238. 534 5185582290 5185581757 (Phil Carmody, k=2)
  239. 535 3478729639 1170716321 (Phil Carmody, k=240)
  240. 536 9370365927 9472293077 (Phil Carmody, k=26)
  241. 538 3622175074 0431992203 (Phil Carmody, k=1)
  242. 540 7386306408 5849094031 (Phil Carmody, k=5)
  243. 549 2063060092 7805420907 (Phil Carmody, k=1)
  244. 550 0929334177 9874073307 (Phil Carmody, k=1)
  245. 551 9512486033 9512485483 (Phil Carmody, k=1)
  246. 554 2972753917 3775213009 (Phil Carmody, k=8)
  247. 558 6858628047 9892638907 (Phil Carmody, k=1)
  248. 558 8937746755 4388195037 (Phil Carmody, k=2)
  249. 560 4939258116 4345198151 (Phil Carmody, k=175)
  250. 560 6348429338 9261326199 (Phil Carmody, k=1)
  251. 561 3088772412 7396918849 (Dario Alpern, k=1376)
  252. 565 7437565932 5159051439 (Phil Carmody, k=1)
  253. 581 2978439167 4176031797 (Phil Carmody, k=46)
  254. 581 5652555251 5256515067 (Phil Carmody, k=1)
  255. 583 0096094446 5227884573 (Phil Carmody, k=34)
  256. 585 8750224641 2158865683 (Phil Carmody, k=9)
  257. 593 0650506081 8329546763 (Dario Alpern, k=1531)
  258. 595 7023913635 4753367997 (Phil Carmody, k=82)
  259. 597 6335579933 4949008721 (Phil Carmody, k=40)
  260. 600 0255529147 3693187677 (Phil Carmody, k=526)
  261. 607 5494589190 1589839359 (Phil Carmody, k=31)
  262. 620 8782650554 3662836917 (Phil Carmody, k=2)
  263. 623 8721668769 8721668147 (Phil Carmody, k=731)
  264. 629 8652986864 1805253453 (Phil Carmody, k=2)
  265. 631 5991145689 6776142267 (Phil Carmody, k=1)
  266. 633 9663909321 5120469877 (Phil Carmody, k=662)
  267. 647 6298452220 8650894387 (Phil Carmody, k=1)
  268. 663 5062109398 4913687721 (Phil Carmody, k=20)
  269. 666 1468418338 2182403667 (Phil Carmody, k=61)
  270. 668 3837544094 6785751267 (Phil Carmody, k=1)
  271. 668 8354023677 3466007639 (Phil Carmody, k=1)
  272. 668 9087476746 1076572483 (Phil Carmody, k=347)
  273. 677 0076453013 4069674591 (Phil Carmody, k=5)
  274. 679 2124945224 0243756427 (Phil Carmody, k=1)
  275. 684 1089100593 4068128947 (Phil Carmody, k=1)
  276. 693 1476745120 6726351289 (Phil Carmody, k=4)
  277. 696 8565189194 6760163363 (Phil Carmody, k=59)
  278. 704 7719039088 3939240427 (Phil Carmody, k=1)
  279. 705 4011595525 2579777307 (Phil Carmody, k=1)
  280. 716 3292600856 9487671363 (Phil Carmody, k=9)
  281. 718 8808783278 3729819523 (Phil Carmody, k=7)
  282. 719 5603998702 8005167439 (Phil Carmody, k=1)
  283. 720 8853174501 2965006597 (Phil Carmody, k=2)
  284. 726 4459235594 8874097013 (Phil Carmody, k=2)
  285. 736 1472529272 0217853089 (Phil Carmody, k=16)
  286. 737 0813881917 9770444089 (Phil Carmody, k=148)
  287. 745 6705290073 8515170477 (Phil Carmody, k=2)
  288. 747 9764939725 8609043267 (Phil Carmody, k=1)
  289. 750 5513730228 5513729479 (Phil Carmody, k=1)
  290. 758 2130879917 7263058719 (Phil Carmody, k=703)
  291. 765 2140112667 0928441249 (Phil Carmody, k=16)
  292. 765 2893247363 3226485797 (Phil Carmody, k=482)
  293. 775 8149167326 0032650081 (Phil Carmody, k=560)
  294. 776 4414471633 5505365293 (Phil Carmody, k=534)
  295. 783 5298190072 5340215529 (Phil Carmody, k=188)
  296. 784 9971780861 9015653683 (Phil Carmody, k=7)
  297. 785 1913289439 7680805717 (Phil Carmody, k=2)
  298. 809 5388124178 2714856043 (Phil Carmody, k=1)
  299. 811 2668363552 2173313237 (Phil Carmody, k=26)
  300. 842 2963321994 3753613853 (Dario Alpern, k=1322)
  301. 851 8747850127 2256105649 (Phil Carmody, k=8)
  302. 858 0422430112 1602000093 (Phil Carmody, k=2)
  303. 865 1818090253 7358550449 (Phil Carmody, k=8)
  304. 866 5540486565 9293662769 (Phil Carmody, k=56)
  305. 872 2181624997 5460670879 (Phil Carmody, k=1)
  306. 894 1473811667 2892228281 (Phil Carmody, k=60)
  307. 894 7687595061 9954680467 (Phil Carmody, k=1)
  308. 906 0280955379 2043766963 (Phil Carmody, k=489)
  309. 908 9596794120 3411335053 (Phil Carmody, k=2)
  310. 909 6585688580 0731786117 (Phil Carmody, k=2)
  311. 922 9835409196 7917021951 (Phil Carmody, k=25)
  312. 938 3678668333 6170234679 (Phil Carmody, k=1)
  313. 941 5412438924 2477939039 (Dario Alpern, k=1341)
  314. 941 6233277972 4799709281 (Phil Carmody, k=560)
  315. 950 8568683643 0281393573 (Phil Carmody, k=62)
  316. 958 3783005136 4941081147 (Phil Carmody, k=1)
  317. 961 1814597984 6348383653 (Phil Carmody, k=2)
  318. 962 9050331834 1153249721 (Phil Carmody, k=20)
  319. 979 1643637681 6350348067 (Phil Carmody, k=1)
  320. 986 8208924708 5419302107 (Phil Carmody, k=1)
  321. 994 0453718814 8073034399 (Phil Carmody, k=301)
  322. 994 6183416063 8338173613 (Phil Carmody, k=2)
  323. 999 9998290104 9548852449 (Phil Carmody, k=16)