Known 14-digit prime factors of Googolplex + 10

  1. Alpertron
  2. Number Theory
  3. Known 14-digit prime factors of Googolplex + 10

This is a list of known 14-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. 1008 3087720779 (David Broadhurst, k=79)
  2. 1010 4024425413 (David Broadhurst, k=2)
  3. 1016 6721266197 (David Broadhurst, k=2)
  4. 1085 3082333529 (Patrick Demichel, k=7268)
  5. 1087 9988089703 (David Broadhurst, k=1)
  6. 1092 6252536383 (David Broadhurst, k=9)
  7. 1112 2405477489 (Phil Carmody, k=3176)
  8. 1123 9119488983 (David Broadhurst, k=7)
  9. 1127 5330722619 (David Broadhurst, k=53)
  10. 1142 5773343339 (David Broadhurst, k=51)
  11. 1150 8715053397 (David Broadhurst, k=2)
  12. 1168 9776162899 (Patrick Demichel, k=26539)
  13. 1174 5292359967 (David Broadhurst, k=1)
  14. 1177 4755178209 (David Broadhurst, k=16)
  15. 1196 8932442813 (David Broadhurst, k=2)
  16. 1208 6964595813 (David Broadhurst, k=2)
  17. 1227 8243483287 (Phil Carmody, k=1721)
  18. 1233 0924308011 (Phil Carmody, k=245)
  19. 1287 6363635077 (David Broadhurst, k=2)
  20. 1330 5938526277 (Phil Carmody, k=106)
  21. 1361 2800426847 (David Broadhurst, k=1)
  22. 1404 0977880997 (David Broadhurst, k=2)
  23. 1426 5358959619 (Phil Carmody, k=1131)
  24. 1471 5477308797 (David Broadhurst, k=46)
  25. 1599 8314081927 (David Broadhurst, k=61)
  26. 1606 4262173731 (David Broadhurst, k=5)
  27. 1617 4253286091 (David Broadhurst, k=5)
  28. 1630 4056359823 (David Broadhurst, k=49)
  29. 1645 1199835093 (David Broadhurst, k=54)
  30. 1683 8302581343 (David Broadhurst, k=9)
  31. +16841396094139 (Dario Alpern using trial division) (k=3322431)
  32. 1724 1247719133 (David Broadhurst, k=2)
  33. 1782 2804725727 (Patrick Demichel, k=721903)
  34. 1813 5692903087 (Phil Carmody, k=3743)
  35. 1815 2592117133 (David Broadhurst, k=2)
  36. 1832 2118058289 (David Broadhurst, k=8)
  37. 1874 0591276767 (David Broadhurst, k=1)
  38. +19349762545459 (Dario Alpern using trial division) (k=5190891)
  39. 1977 0364305847 (David Broadhurst, k=7)
  40. 1990 4015715533 (David Broadhurst, k=26)
  41. 2006 0675908087 (Patrick Demichel, k=8341)
  42. 2074 3205180717 (Phil Carmody, k=2818)
  43. 2080 0235145727 (Paul Leyland, k=35897)
  44. 2088 3092290237 (David Broadhurst, k=2)
  45. +21133205065837 (Dario Alpern using trial division) (k=105667082)
  46. 2140 5727309693 (David Broadhurst, k=2)
  47. 2161 9074007099 (David Broadhurst, k=1)
  48. 2205 1211574569 (Patrick Demichel, k=359404)
  49. 2240 4213501253 (David Broadhurst, k=2)
  50. 2253 7158996889 (Phil Carmody, k=1636)
  51. 2311 0760178019 (David Broadhurst, k=1)
  52. 2313 3294930637 (David Broadhurst, k=2)
  53. +24147831404611 (Dario Alpern using trial division) (k=62686145)
  54. 2480 1283246717 (David Broadhurst, k=2)
  55. 2480 3048833699 (David Broadhurst, k=53)
  56. 2495 8605764293 (Phil Carmody, k=142)
  57. 2583 5378565583 (David Broadhurst, k=59)
  58. +27309041033689 (Dario Alpern using trial division) (k=55429796)
  59. 2824 5919737979 (David Broadhurst, k=1)
  60. 2827 3461662557 (David Broadhurst, k=2)
  61. 2844 2426572891 (David Broadhurst, k=5)
  62. 2969 6458630477 (Phil Carmody, k=3886)
  63. 3022 0675002607 (David Broadhurst, k=1)
  64. 3044 8413281089 (Patrick Demichel, k=412576)
  65. 3045 7184311291 (Phil Carmody, k=265)
  66. 3055 4561197103 (David Broadhurst, k=1)
  67. 3153 1283429647 (David Broadhurst, k=91)
  68. 3243 2920166201 (David Broadhurst, k=100)
  69. 3300 2349216013 (Phil Carmody, k=4574)
  70. 3367 3333329967 (David Broadhurst, k=1)
  71. 3458 7722943503 (David Broadhurst, k=1)
  72. 3492 1221669739 (David Broadhurst, k=1)
  73. 3507 1702912291 (Patrick Demichel, k=188165)
  74. 3537 7374097477 (David Broadhurst, k=2)
  75. 3540 0951333247 (David Broadhurst, k=1)
  76. 3546 6059872651 (David Broadhurst, k=25)
  77. 3555 5124060721 (David Broadhurst, k=40)
  78. 3595 4419019333 (Phil Carmody, k=526)
  79. 3614 8112732059 (Phil Carmody, k=1853)
  80. 3668 0792082877 (David Broadhurst, k=2)
  81. 3692 5666027339 (Phil Carmody, k=1843)
  82. 3797 4024117811 (Paul Leyland, k=31595)
  83. 3865 6340020811 (David Broadhurst, k=5)
  84. 3904 5758278957 (David Broadhurst, k=26)
  85. 3960 3564360397 (David Broadhurst, k=2)
  86. 4004 7140780677 (David Broadhurst, k=2)
  87. 4009 8278801813 (Phil Carmody, k=406)
  88. 4041 6097701649 (David Broadhurst, k=8)
  89. 4118 2420705009 (David Broadhurst, k=8)
  90. +42773180062447 (Dario Alpern using trial division) (k=230909317)
  91. 4323 8148014197 (David Broadhurst, k=2)
  92. 4326 6964059367 (David Broadhurst, k=1)
  93. 4372 8954485173 (David Broadhurst, k=2)
  94. 4519 0235689939 (David Broadhurst, k=1)
  95. 4713 4513273607 (David Broadhurst, k=73)
  96. 4886 2601621131 (David Broadhurst, k=5)
  97. 4993 3744148623 (David Broadhurst, k=17)
  98. 5107 7750443219 (Phil Carmody, k=771)
  99. 5287 3957116103 (Paul Leyland, k=38237)
  100. +54739703326331 (Dario Alpern using trial division) (k=702673915)
  101. 5567 7797909053 (David Broadhurst, k=2)
  102. 5623 2727630939 (David Broadhurst, k=1)
  103. +56423906565049 (Dario Alpern using trial division) (k=10411356)
  104. 5804 7126922927 (Norm Dresner, k=11337)
  105. 5913 9975393841 (David Broadhurst, k=40)
  106. 6136 0954784317 (David Broadhurst, k=22)
  107. 6147 7127365127 (David Broadhurst, k=53)
  108. +61939627928693 (Dario Alpern using trial division) (k=5339926)
  109. 6237 6432958093 (David Broadhurst, k=2)
  110. 6265 1786273407 (Phil Carmody, k=2447)
  111. 6371 5318478411 (David Broadhurst, k=5)
  112. 6444 6252477499 (David Broadhurst, k=1)
  113. 6656 3945516333 (Phil Carmody, k=4126)
  114. 6724 8118818607 (David Broadhurst, k=1)
  115. 6787 6562667931 (David Broadhurst, k=5)
  116. +70139947146967 (David Broadhurst using ECM) (k=1100441607)
  117. +70653467727613 (Dario Alpern using trial division) (k=39251534)
  118. 7211 9394897023 (David Broadhurst, k=1)
  119. 7241 0408896849 (David Broadhurst, k=8)
  120. 7247 3237015939 (Phil Carmody, k=829)
  121. 7288 8004324477 (David Broadhurst, k=2)
  122. 7380 8834276971 (David Broadhurst, k=65)
  123. 7581 1124328371 (Phil Carmody, k=685)
  124. 7623 2583248567 (Phil Carmody, k=4163)
  125. 7772 7139681357 (David Broadhurst, k=2)
  126. 7874 7341400289 (David Broadhurst, k=16)
  127. 7956 7254545329 (Patrick Demichel, k=350536)
  128. 8013 7636033333 (Patrick Demichel, k=2078522)
  129. 8081 7029711053 (David Broadhurst, k=2)
  130. 8198 1186030739 (David Broadhurst, k=1)
  131. 8313 6876284179 (John Gamble, k=17531)
  132. 8384 5468565899 (David Broadhurst, k=13)
  133. 8447 2727264281 (Phil Carmody, k=460)
  134. 8711 6405716663 (David Broadhurst, k=7)
  135. 8755 5815774293 (David Broadhurst, k=2)
  136. 8816 4441235597 (Patrick Demichel, k=6866)
  137. 8870 3838374969 (Phil Carmody, k=124)
  138. 9075 5208936929 (Patrick Demichel, k=2537104)
  139. 9181 1782339663 (David Broadhurst, k=7)
  140. 9390 0855048727 (David Broadhurst, k=1)
  141. 9474 6068051207 (David Broadhurst, k=13)
  142. 9610 8418401847 (David Broadhurst, k=1)
  143. 9736 2066410929 (Patrick Demichel, k=5256)
  144. 9789 3010797209 (David Broadhurst, k=4)
  145. 9826 4582985493 (David Broadhurst, k=14)

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.