Known 20-digit prime factors of Googolplex - 10

  1. Alpertron
  2. Number Theory
  3. Known 20-digit prime factors of Googolplex − 10

This is a list of known 20-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. 1003456796 1003456797 (Phil Carmody, k=478)
  2. 1013715690 2877595951 (Phil Carmody, k=25)
  3. 1028823694 7204731369 (Phil Carmody, k=28)
  4. 1032971453 9250793237 (Phil Carmody, k=2)
  5. 1033122956 8149331561 (Phil Carmody, k=20)
  6. 1039175903 5940375711 (Phil Carmody, k=5)
  7. 1048998890 2265167969 (Phil Carmody, k=16)
  8. 1052336706 9485235151 (Phil Carmody, k=25)
  9. 1077307762 5433557347 (Dario Alpern, k=1853)
  10. 1112446015 7074038787 (Phil Carmody, k=1)
  11. 1122568746 9439400431 (Phil Carmody, k=5)
  12. 1137562915 1787166333 (Phil Carmody, k=122)
  13. 1142779475 3816733757 (Phil Carmody, k=46)
  14. 1173765304 9583818963 (Phil Carmody, k=487)
  15. 1177016695 5225238237 (Phil Carmody, k=2)
  16. 1181869589 4449196323 (Phil Carmody, k=1)
  17. 1210207771 0504406791 (Phil Carmody, k=5)
  18. 1227858514 1629698277 (Phil Carmody, k=42)
  19. 1244782224 7200933319 (Phil Carmody, k=31)
  20. 1276579545 6476507077 (Phil Carmody, k=2)
  21. 1292485968 9500346919 (Phil Carmody, k=1)
  22. 1301673030 0489672157 (Phil Carmody, k=102)
  23. 1310558366 5834704089 (Phil Carmody, k=4)
  24. 1318084467 9733926053 (Phil Carmody, k=26)
  25. 1323780264 4326745519 (Phil Carmody, k=1)
  26. 1330766340 2703259987 (Phil Carmody, k=1)
  27. 1332166615 9721089519 (Phil Carmody, k=103)
  28. 1348111750 2363175267 (Phil Carmody, k=987)
  29. 1348233213 6610920529 (Phil Carmody, k=8)
  30. 1359770258 2285599307 (Phil Carmody, k=1)
  31. 1366035872 4936655573 (Phil Carmody, k=2)
  32. 1394092801 1589007147 (Phil Carmody, k=1)
  33. 1398670880 4617589283 (Phil Carmody, k=157)
  34. 1421610795 7659234559 (Phil Carmody, k=1)
  35. 1422077823 7247545237 (Phil Carmody, k=182)
  36. 1423203038 1503626231 (Phil Carmody, k=385)
  37. 1426719066 1426719067 (Phil Carmody, k=1)
  38. 1461082201 6903568839 (Phil Carmody, k=1)
  39. 1463232981 6215990227 (Phil Carmody, k=487)
  40. 1466243682 5106494773 (Phil Carmody, k=2)
  41. 1478777369 3756005093 (Phil Carmody, k=2)
  42. 1496820620 6549676037 (Phil Carmody, k=2)
  43. 1517135674 1980281679 (Phil Carmody, k=1)
  44. 1520971285 3204139603 (Phil Carmody, k=821)
  45. 1526496465 3107649877 (Phil Carmody, k=242)
  46. 1527243804 0016132867 (Phil Carmody, k=1)
  47. 1528862407 3056602071 (Phil Carmody, k=15)
  48. 1550482683 7726089373 (Phil Carmody, k=2)
  49. 1561794216 1073898083 (Phil Carmody, k=1)
  50. 1567801353 2082448369 (Phil Carmody, k=8)
  51. 1578026137 5835451881 (Phil Carmody, k=980)
  52. 1583374386 1583374387 (Dario Alpern, k=1121)
  53. 1593915081 0024710197 (Phil Carmody, k=2)
  54. 1602589517 6850114271 (Dario Alpern, k=2795)
  55. 1612372492 1604096037 (Phil Carmody, k=2)
  56. 1656509952 9576494249 (Phil Carmody, k=4)
  57. 1662855811 7443708679 (Phil Carmody, k=19)
  58. 1663932636 2437754449 (Phil Carmody, k=8)
  59. 1687451878 4662309717 (Dario Alpern, k=1082)
  60. 1729218719 8758586159 (Phil Carmody, k=1)
  61. 1733110868 9378000243 (Phil Carmody, k=11)
  62. 1741942707 4113155653 (Phil Carmody, k=2)
  63. 1744297319 0987130923 (Phil Carmody, k=1)
  64. 1759685385 8378846563 (Phil Carmody, k=7)
  65. 1771869099 8320866559 (Phil Carmody, k=1)
  66. 1780055434 5561751369 (Phil Carmody, k=428)
  67. 1804803272 6133112471 (Phil Carmody, k=15)
  68. 1814877360 6440689279 (Phil Carmody, k=1)
  69. 1852446881 1636923917 (Phil Carmody, k=166)
  70. 1867368824 3894373559 (Phil Carmody, k=1)
  71. 1873921877 7686482519 (Phil Carmody, k=31)
  72. 1958699858 7358611547 (Phil Carmody, k=1)
  73. 1999584042 9637675511 (Phil Carmody, k=5)
  74. 2005793597 6368967843 (Phil Carmody, k=1)
  75. 2030945572 4071786759 (Phil Carmody, k=1)
  76. 2049975786 2043265147 (Phil Carmody, k=27)
  77. 2083469696 1885897271 (Phil Carmody, k=15)
  78. 2089238592 2232651523 (Phil Carmody, k=17)
  79. 2105028062 3725846963 (Phil Carmody, k=7)
  80. 2123793071 6072555123 (Phil Carmody, k=1)
  81. 2140642310 8854525787 (Phil Carmody, k=47)
  82. 2143627044 4614693449 (Phil Carmody, k=4)
  83. 2174013117 1983760933 (Phil Carmody, k=2)
  84. 2188702980 8593673329 (Phil Carmody, k=136)
  85. 2198582049 8509280249 (Phil Carmody, k=4)
  86. 2203119284 6953078043 (Phil Carmody, k=1)
  87. 2259022590 2259022591 (Phil Carmody, k=5)
  88. 2266266461 7299498111 (Phil Carmody, k=5)
  89. 2290800171 6708400489 (Phil Carmody, k=28)
  90. 2308680377 9302158919 (Phil Carmody, k=1)
  91. 2326685061 3950732843 (Phil Carmody, k=181)
  92. 2331281364 9183870151 (Phil Carmody, k=25)
  93. 2521503536 8660117399 (Phil Carmody, k=1)
  94. 2547671045 4740697883 (Phil Carmody, k=397)
  95. 2572443002 2572443003 (Phil Carmody, k=1)
  96. 2581308021 5500922719 (Phil Carmody, k=83)
  97. 2615231477 1289307569 (Phil Carmody, k=8)
  98. 2639758968 2639758969 (Phil Carmody, k=196)
  99. 2644585543 2676840399 (Phil Carmody, k=21)
  100. 2662135659 9839972653 (Phil Carmody, k=2)
  101. 2715830226 3430560161 (Phil Carmody, k=80)
  102. 2730603922 8141504799 (Phil Carmody, k=1)
  103. 2739185309 2572901243 (Phil Carmody, k=129)
  104. 2747115966 8752871761 (Phil Carmody, k=520)
  105. 2752416653 1806456209 (Phil Carmody, k=536)
  106. 2765219892 0309616027 (Phil Carmody, k=1)
  107. 2774835180 1317805747 (Phil Carmody, k=1)
  108. 2779478357 9014233911 (Phil Carmody, k=5)
  109. 2785546714 5907037363 (Dario Alpern, k=1861)
  110. 2848323375 5456115803 (Phil Carmody, k=391)
  111. 2860426587 6251515627 (Phil Carmody, k=1)
  112. 2902856942 1668826169 (Phil Carmody, k=316)
  113. 2905827932 8642869373 (Phil Carmody, k=2)
  114. 2922177648 5045302027 (Phil Carmody, k=1)
  115. 2934167744 5903877209 (Phil Carmody, k=308)
  116. 2935571907 9726320173 (Phil Carmody, k=2)
  117. 2940988092 3046848439 (Phil Carmody, k=181)
  118. 2978130444 0630574921 (Phil Carmody, k=20)
  119. 2987720068 0480260067 (Phil Carmody, k=477)
  120. 2992855560 3673811107 (Phil Carmody, k=1)
  121. 3073280476 9344873053 (Phil Carmody, k=26)
  122. 3110684149 5913442881 (Phil Carmody, k=160)
  123. 3192177195 0259375867 (Phil Carmody, k=1)
  124. 3368760347 7892561357 (Phil Carmody, k=2)
  125. 3386121173 5700887957 (Phil Carmody, k=2)
  126. 3415171975 0024016963 (Phil Carmody, k=1)
  127. 3417601829 7933275369 (Phil Carmody, k=4)
  128. 3425277790 7971617997 (Phil Carmody, k=2)
  129. 3442158961 0785728773 (Phil Carmody, k=2)
  130. 3459220960 7272486357 (Phil Carmody, k=2)
  131. 3459894927 6655364437 (Phil Carmody, k=2)
  132. 3482811242 3482811243 (Phil Carmody, k=1)
  133. 3513750112 8174733003 (Phil Carmody, k=299)
  134. 3526770031 8912254359 (Phil Carmody, k=1)
  135. 3529584922 8169247437 (Phil Carmody, k=2)
  136. 3567348853 8207724453 (Phil Carmody, k=2)
  137. 3721666107 8177111653 (Phil Carmody, k=982)
  138. 3731995605 8039222107 (Phil Carmody, k=287)
  139. 3750556109 2249261507 (Dario Alpern, k=1801)
  140. 3762376237 6237623763 (Phil Carmody, k=19)
  141. 3765328562 3765328563 (Phil Carmody, k=1)
  142. 3811510265 8429283587 (Phil Carmody, k=1)
  143. 3874587926 5099029083 (Phil Carmody, k=1)
  144. 3951084356 3927703523 (Phil Carmody, k=37)
  145. 3985138360 3174199803 (Phil Carmody, k=9)
  146. 3992347574 2408189159 (Phil Carmody, k=1)
  147. 4031285948 8021152883 (Phil Carmody, k=9)
  148. 4063050204 3484425271 (Phil Carmody, k=115)
  149. 4079310774 6856797919 (Phil Carmody, k=1)
  150. 4109057840 3002976917 (Phil Carmody, k=2)
  151. 4138097934 0336855907 (Phil Carmody, k=1)
  152. 4143299193 2658150679 (Phil Carmody, k=203)
  153. 4236930329 5763069671 (Phil Carmody, k=15)
  154. 4269563510 0097316523 (Phil Carmody, k=431)
  155. 4306121986 1457790199 (Dario Alpern, k=2129)
  156. 4311453721 3226733013 (Phil Carmody, k=2)
  157. 4381865968 5473295643 (Phil Carmody, k=547)
  158. 4505032001 1698133427 (Phil Carmody, k=7)
  159. 4527526954 4950718947 (Phil Carmody, k=1)
  160. 4639213131 5183185093 (Phil Carmody, k=2)
  161. 4664232050 4071179241 (Dario Alpern, k=2020)
  162. 4716986497 0906475227 (Phil Carmody, k=221)
  163. 4737609515 5686431089 (Phil Carmody, k=8)
  164. 4742798082 4742798083 (Phil Carmody, k=347)
  165. 4757330264 9960580551 (Phil Carmody, k=25)
  166. 4783070424 3313028561 (Dario Alpern, k=2680)
  167. 4870724662 6101799759 (Phil Carmody, k=1)
  168. 4950210046 6892381107 (Phil Carmody, k=1)
  169. 4979181685 8952821271 (Phil Carmody, k=95)
  170. 4987447513 0569253289 (Phil Carmody, k=4)
  171. 5030904715 9970999849 (Dario Alpern, k=1204)
  172. 5060996096 2392878443 (Phil Carmody, k=9)
  173. 5092820741 8865720239 (Phil Carmody, k=53)
  174. 5187029858 0267515597 (Phil Carmody, k=2)
  175. 5226004510 6941494561 (Phil Carmody, k=80)
  176. 5263386108 7199063027 (Phil Carmody, k=193)
  177. 5289438094 2579949879 (Phil Carmody, k=413)
  178. 5311407658 4381089267 (Phil Carmody, k=11)
  179. 5340113145 3856260637 (Phil Carmody, k=142)
  180. 5341330479 5231729797 (Phil Carmody, k=42)
  181. 5344649094 2341973227 (Phil Carmody, k=1)
  182. 5381302892 8916577643 (Phil Carmody, k=7)
  183. 5549670360 2635611493 (Phil Carmody, k=2)
  184. 5647738830 5883012529 (Phil Carmody, k=8)
  185. 5662355290 0794145999 (Phil Carmody, k=1)
  186. 5676807865 6114537321 (Phil Carmody, k=140)
  187. 5806475691 3710518841 (Phil Carmody, k=20)
  188. 5826243385 2764542523 (Phil Carmody, k=1)
  189. 5997223465 9560795751 (Phil Carmody, k=125)
  190. 6104538704 0562127963 (Phil Carmody, k=607)
  191. 6127174595 2470015601 (Phil Carmody, k=200)
  192. 6133345917 1160347813 (Phil Carmody, k=2)
  193. 6134086480 4965124479 (Phil Carmody, k=1)
  194. 6154207314 2589850879 (Dario Alpern, k=1993)
  195. 6175061119 7239573027 (Phil Carmody, k=417)
  196. 6254239078 2794451409 (Phil Carmody, k=456)
  197. 6285253801 9761503443 (Phil Carmody, k=169)
  198. 6316942645 8258703111 (Phil Carmody, k=45)
  199. 6381070168 6737252277 (Dario Alpern, k=2066)
  200. 6449798916 6449798917 (Phil Carmody, k=2)
  201. 6522039351 5951282797 (Phil Carmody, k=2)
  202. 6664336599 2797670689 (Phil Carmody, k=16)
  203. 6666666666 6666666667 (Phil Carmody, k=1)
  204. 6678536958 1123051693 (Phil Carmody, k=362)
  205. 6694591799 9565878929 (Phil Carmody, k=8)
  206. 6700951614 0428643757 (Phil Carmody, k=26)
  207. 6725873961 7699015123 (Phil Carmody, k=17)
  208. 6777664146 6777664147 (Phil Carmody, k=27)
  209. 6787493665 3190906119 (Phil Carmody, k=1)
  210. 6877500711 9355823947 (Phil Carmody, k=1)
  211. 6908049556 0175376289 (Phil Carmody, k=16)
  212. 6917613764 1462870041 (Phil Carmody, k=20)
  213. 6932636957 6896001329 (Phil Carmody, k=696)
  214. 6949602990 6949602991 (Phil Carmody, k=5)
  215. 6956930944 2636564991 (Phil Carmody, k=715)
  216. 6958819697 2774777639 (Phil Carmody, k=1)
  217. 6978031728 6136877773 (Phil Carmody, k=2)
  218. 7089999009 2910000991 (Phil Carmody, k=5)
  219. 7283552414 4852846763 (Phil Carmody, k=7)
  220. 7297835774 2607863283 (Phil Carmody, k=1)
  221. 7328329813 9500938479 (Phil Carmody, k=1)
  222. 7347381938 2521789481 (Phil Carmody, k=60)
  223. 7374080612 3073089947 (Phil Carmody, k=1)
  224. 7397004250 8042433237 (Phil Carmody, k=2)
  225. 7408059252 7408059253 (Phil Carmody, k=2)
  226. 7521130747 8275855947 (Phil Carmody, k=1)
  227. 7591331960 9432644879 (Dario Alpern, k=1421)
  228. 7772088415 5994088557 (Phil Carmody, k=2)
  229. 7799637252 7799637253 (Phil Carmody, k=22)
  230. 7800800948 2780137443 (Phil Carmody, k=71)
  231. 7887276210 8673627557 (Phil Carmody, k=938)
  232. 7967442236 6606303083 (Phil Carmody, k=7)
  233. 8035676013 8630990653 (Phil Carmody, k=22)
  234. 8169483401 8664532907 (Phil Carmody, k=1)
  235. 8183049269 5257518293 (Phil Carmody, k=2)
  236. 8263771631 4006345889 (Phil Carmody, k=16)
  237. 8451563838 0530771759 (Phil Carmody, k=19)
  238. 8523155797 4199800197 (Phil Carmody, k=2)
  239. 8599858663 8506656003 (Phil Carmody, k=7)
  240. 8820438254 6048161027 (Phil Carmody, k=1)
  241. 8846214379 1598247843 (Phil Carmody, k=367)
  242. +88919086325289033199 () (k=91879769863)
  243. 9031976108 1051179723 (Phil Carmody, k=1)
  244. 9036903690 3690369037 (Phil Carmody, k=2)
  245. 9043074895 0400330671 (Phil Carmody, k=15)
  246. 9055053908 9901437893 (Phil Carmody, k=2)
  247. 9163617117 7317040627 (Phil Carmody, k=361)
  248. 9193452589 9072230067 (Phil Carmody, k=7)
  249. 9200207378 6991791677 (Phil Carmody, k=2)
  250. 9248933510 5368793483 (Phil Carmody, k=629)
  251. 9264952084 0203142597 (Phil Carmody, k=122)
  252. 9359520636 2395669643 (Phil Carmody, k=1)
  253. 9425370434 7301676563 (Phil Carmody, k=7)
  254. 9515244701 3434763437 (Phil Carmody, k=122)
  255. 9662416480 1368695431 (Phil Carmody, k=565)
  256. 9729444186 9729444187 (Phil Carmody, k=7)
  257. 9736275908 2647155813 (Phil Carmody, k=26)
  258. 9756097560 9756097561 (Phil Carmody, k=20)
  259. 9830726612 3169305347 (Phil Carmody, k=1)
  260. 9856444382 7869971711 (Phil Carmody, k=45)
  261. 9929067242 8795401929 (Phil Carmody, k=4)