Known 16-digit prime factors of Googolplex + 10

  1. Alpertron
  2. Number Theory
  3. Known 16-digit prime factors of Googolplex + 10

This is a list of known 16-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. 100302 6954441971 (David Broadhurst, k=85)
  2. 100672 0295102281 (Patrick Demichel, k=135060)
  3. 102211 8181715971 (Patrick Demichel, k=562165)
  4. 103589 8302479437 (David Broadhurst, k=2)
  5. 105067 6720661059 (Patrick Demichel, k=615613)
  6. 107316 0000107317 (David Broadhurst, k=2)
  7. 107552 3893788647 (David Broadhurst, k=73)
  8. 107711 8820880499 (David Broadhurst, k=1)
  9. 108718 3282390063 (Patrick Demichel, k=3066557)
  10. 112043 2498958653 (David Broadhurst, k=2)
  11. 113311 9999886689 (David Broadhurst, k=16)
  12. 115335 6267058579 (David Broadhurst, k=1)
  13. 117164 8352287117 (David Broadhurst, k=2)
  14. 121978 5108226939 (David Broadhurst, k=31)
  15. 123492 0000123493 (David Broadhurst, k=2)
  16. 123534 8918217019 (David Broadhurst, k=1)
  17. 123904 7675106847 (David Broadhurst, k=1)
  18. 124301 6782041211 (Patrick Demichel, k=335585)
  19. 124664 4597155623 (Phil Carmody, k=1337)
  20. 126738 6073339357 (David Broadhurst, k=2)
  21. 128850 6094732099 (David Broadhurst, k=1)
  22. 129306 8705277493 (Patrick Demichel, k=1075854)
  23. 130264 7094651241 (Patrick Demichel, k=954980)
  24. 130835 5967371729 (David Broadhurst, k=8)
  25. 133569 5307313357 (David Broadhurst, k=2)
  26. 134891 3486122117 (Patrick Demichel, k=136666)
  27. 136445 0869724933 (Patrick Demichel, k=40706)
  28. 137200 9238798053 (David Broadhurst, k=2)
  29. 137383 5841721543 (David Broadhurst, k=1)
  30. 139175 0021955277 (David Broadhurst, k=2)
  31. 143248 0520273771 (Phil Carmody, k=835)
  32. 143962 5716980303 (David Broadhurst, k=67)
  33. 150120 7407273367 (Phil Carmody, k=2847)
  34. 155088 3347674849 (David Broadhurst, k=16)
  35. 157403 6143481161 (Patrick Demichel, k=307420)
  36. 165434 5811915207 (David Broadhurst, k=23)
  37. 165475 4514646573 (Patrick Demichel, k=24734)
  38. 171818 7198754717 (David Broadhurst, k=2)
  39. 174157 6278750859 (David Broadhurst, k=1)
  40. 174666 7474572809 (David Broadhurst, k=4)
  41. 176844 7645428619 (Paul Leyland, k=33901)
  42. 178928 1960077263 (David Broadhurst, k=7)
  43. 182913 0098184379 (Patrick Demichel, k=85461)
  44. 188101 8462027277 (Phil Carmody, k=962)
  45. 192413 8627456543 (David Broadhurst, k=7)
  46. 193403 8332062647 (David Broadhurst, k=1)
  47. 193934 3338296253 (David Broadhurst, k=14)
  48. 198186 1951924201 (Patrick Demichel, k=3055700)
  49. 203670 0107142859 (David Broadhurst, k=1)
  50. 204280 1428681063 (Phil Carmody, k=1799)
  51. 205720 4287437157 (Phil Carmody, k=442)
  52. 209634 3084084247 (David Broadhurst, k=47)
  53. 212975 8002832087 (Phil Carmody, k=2427)
  54. 213052 4850507773 (Phil Carmody, k=146)
  55. 215206 2083942167 (David Broadhurst, k=1)
  56. 216427 6969480543 (David Broadhurst, k=7)
  57. 220389 1704838699 (John Gamble, k=16513)
  58. 220945 8610615169 (David Broadhurst, k=64)
  59. 221154 9151064569 (John Gamble, k=17948)
  60. 222684 3038912321 (Phil Carmody, k=160)
  61. 228467 6055210979 (Paul Leyland, k=37141)
  62. 236576 8009273573 (David Broadhurst, k=34)
  63. 237852 5902525343 (Phil Carmody, k=151)
  64. 241572 3359991493 (Phil Carmody, k=5162)
  65. 243771 0938307361 (Patrick Demichel, k=5520)
  66. 245290 2601380727 (David Broadhurst, k=1)
  67. 246045 1627870237 (Phil Carmody, k=3822)
  68. 249600 0288036407 (David Broadhurst, k=73)
  69. 257224 5804128093 (David Broadhurst, k=86)
  70. 257842 1692686361 (Phil Carmody, k=2260)
  71. 260502 0910622531 (Patrick Demichel, k=747965)
  72. 263993 9630732317 (David Broadhurst, k=2)
  73. 270047 7882224299 (David Broadhurst, k=71)
  74. 270152 1570314143 (Paul Leyland, k=37769)
  75. 274433 7704177807 (Phil Carmody, k=323)
  76. +2753565111483733 (David Broadhurst using ECM) (k=30286248174)
  77. 276003 3263034847 (David Broadhurst, k=1)
  78. 277954 1917816687 (David Broadhurst, k=1)
  79. 280411 9298082703 (Patrick Demichel, k=89459)
  80. 283279 9999716721 (David Broadhurst, k=40)
  81. 288934 1920551637 (David Broadhurst, k=2)
  82. 290479 4504164477 (Patrick Demichel, k=47222)
  83. 290879 2794093847 (David Broadhurst, k=1)
  84. 291552 0172979041 (David Broadhurst, k=80)
  85. 297482 9618713717 (Phil Carmody, k=842)
  86. 297900 7715023321 (Patrick Demichel, k=301820)
  87. 298292 3342029247 (Patrick Demichel, k=189413)
  88. 302696 4439111447 (Phil Carmody, k=1037)
  89. 307668 6865124623 (Phil Carmody, k=2679)
  90. 310732 3068820939 (David Broadhurst, k=1)
  91. 312804 8548411139 (David Broadhurst, k=19)
  92. 321437 8373662303 (David Broadhurst, k=7)
  93. 322947 3318594623 (David Broadhurst, k=1)
  94. 327924 7441229521 (David Broadhurst, k=40)
  95. 328332 5512280263 (Patrick Demichel, k=254819)
  96. 334093 7027375663 (Phil Carmody, k=2431)
  97. 341017 6446423451 (David Broadhurst, k=25)
  98. 347770 5337905613 (David Broadhurst, k=22)
  99. 349855 7134438699 (Patrick Demichel, k=21913)
  100. 352704 3388643539 (David Broadhurst, k=1)
  101. 353452 1220421333 (Patrick Demichel, k=840682)
  102. 357311 4783845077 (David Broadhurst, k=2)
  103. 358948 8316291219 (David Broadhurst, k=23)
  104. 361647 3785019811 (Phil Carmody, k=1885)
  105. 366685 1530167211 (Patrick Demichel, k=1524635)
  106. 368628 5229795331 (David Broadhurst, k=5)
  107. 374041 0538942437 (Patrick Demichel, k=2742122)
  108. 376858 9235000407 (David Broadhurst, k=1)
  109. 397083 9137855437 (David Broadhurst, k=42)
  110. 399996 0000399997 (David Broadhurst, k=2)
  111. 401879 5643966237 (David Broadhurst, k=98)
  112. 403984 8456872903 (David Broadhurst, k=1)
  113. 410771 7028414063 (Phil Carmody, k=259)
  114. 417771 9853578277 (Patrick Demichel, k=157106)
  115. 424697 7092803369 (David Broadhurst, k=28)
  116. 435431 7013989259 (David Broadhurst, k=1)
  117. 439575 5428206139 (David Broadhurst, k=31)
  118. 446017 9138545373 (David Broadhurst, k=2)
  119. 446716 5232203397 (David Broadhurst, k=2)
  120. 450569 6052413293 (Patrick Demichel, k=29734)
  121. 450684 4443993761 (David Broadhurst, k=80)
  122. 451867 8007528213 (Phil Carmody, k=1402)
  123. 456805 9350403543 (Patrick Demichel, k=7819)
  124. 464708 2268910973 (David Broadhurst, k=2)
  125. 467467 9518572779 (David Broadhurst, k=13)
  126. 476993 8362880837 (Patrick Demichel, k=7562)
  127. 494415 7235277943 (Patrick Demichel, k=8587)
  128. 497149 1256108647 (Phil Carmody, k=323)
  129. 500497 0369228369 (Phil Carmody, k=1176)
  130. 501129 7986078847 (David Broadhurst, k=7)
  131. 507054 3590196157 (Patrick Demichel, k=1412266)
  132. 522554 8559586967 (Phil Carmody, k=117)
  133. 527230 7758746887 (David Broadhurst, k=13)
  134. 531801 7190615449 (Phil Carmody, k=876)
  135. 535043 8817276779 (Phil Carmody, k=3811)
  136. 536610 0795320761 (Patrick Demichel, k=149860)
  137. 541041 6502446451 (Patrick Demichel, k=284825)
  138. 554602 9348420201 (Phil Carmody, k=1900)
  139. 557657 6359164383 (Patrick Demichel, k=145561)
  140. 562310 6883251983 (David Broadhurst, k=67)
  141. 562345 7588814253 (David Broadhurst, k=2)
  142. 563222 0000563223 (David Broadhurst, k=1)
  143. 567505 2295109539 (Phil Carmody, k=171)
  144. 570596 4788818493 (David Broadhurst, k=46)
  145. 573252 3228350557 (David Broadhurst, k=2)
  146. 583252 8320743477 (David Broadhurst, k=46)
  147. 594116 2925256773 (Phil Carmody, k=386)
  148. 614262 0000614263 (Phil Carmody, k=227)
  149. 614843 5347029543 (Patrick Demichel, k=130781)
  150. 621878 7885890647 (David Broadhurst, k=1)
  151. 634373 9208555167 (Phil Carmody, k=283)
  152. 659327 2782359413 (David Broadhurst, k=2)
  153. 663472 9563268531 (David Broadhurst, k=5)
  154. 672254 1951674543 (Patrick Demichel, k=68831)
  155. 690598 8683196241 (David Broadhurst, k=40)
  156. 697062 3403366459 (David Broadhurst, k=1)
  157. 706138 6276702091 (David Broadhurst, k=95)
  158. 716155 6728051133 (David Broadhurst, k=22)
  159. 735870 7804142179 (David Broadhurst, k=1)
  160. 743428 6050641077 (David Broadhurst, k=2)
  161. 774350 3914592077 (Phil Carmody, k=522)
  162. 776219 3076178649 (David Broadhurst, k=4)
  163. 780608 1679614971 (Phil Carmody, k=485)
  164. 808079 0820900139 (David Broadhurst, k=1)
  165. 809884 7020623967 (David Broadhurst, k=1)
  166. 813884 8794023971 (David Broadhurst, k=15)
  167. 825791 0960083819 (David Broadhurst, k=23)
  168. 845780 5489481851 (Patrick Demichel, k=147725)
  169. 856094 8826290891 (Patrick Demichel, k=1109315)
  170. 881889 8208336019 (David Broadhurst, k=31)
  171. 895923 6261367087 (David Broadhurst, k=27)
  172. 898905 2539826503 (David Broadhurst, k=39)
  173. 903087 2573622659 (David Broadhurst, k=59)
  174. 903463 5213588811 (David Broadhurst, k=35)
  175. 910731 2788258939 (David Broadhurst, k=1)
  176. 921525 1209966367 (Patrick Demichel, k=21317)
  177. 925410 9914903899 (Norm Dresner, k=10411)
  178. 935284 1769617743 (Paul Leyland, k=32449)
  179. 958726 8380415997 (David Broadhurst, k=2)
  180. 962261 4910986859 (Patrick Demichel, k=266843)
  181. 965341 8032254327 (Phil Carmody, k=4937)
  182. 975475 6030010179 (David Broadhurst, k=1)
  183. 978396 2734725367 (David Broadhurst, k=1)
  184. 984634 7753151361 (Phil Carmody, k=320)
  185. 987632 4585966499 (David Broadhurst, k=1)
  186. 998911 2328612357 (Phil Carmody, k=226)

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.