Known 13-digit prime factors of Googolplex + 10

  1. Alpertron
  2. Number Theory
  3. Known 13-digit prime factors of Googolplex + 10

This is a list of known 13-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 5680009767 (David Broadhurst, k=1)
  2. 100 7272727173 (Phil Carmody, k=554)
  3. 100 7781552979 (Phil Carmody, k=1733)
  4. 101 4731220367 (David Broadhurst, k=37)
  5. 103 0245863293 (Phil Carmody, k=414)
  6. 105 1513405939 (David Broadhurst, k=1)
  7. 106 0734255967 (David Broadhurst, k=7)
  8. 107 2532986823 (David Broadhurst, k=11)
  9. 107 2722728089 (Patrick Demichel, k=253156)
  10. 112 6930693183 (David Broadhurst, k=7)
  11. 113 3269896223 (Patrick Demichel, k=68569)
  12. 114 0351600169 (David Broadhurst, k=76)
  13. 115 1544715333 (David Broadhurst, k=2)
  14. 115 2572719687 (David Broadhurst, k=1)
  15. 120 2444050237 (David Broadhurst, k=26)
  16. 124 9235322157 (David Broadhurst, k=2)
  17. 125 5261225769 (David Broadhurst, k=4)
  18. 128 7520475077 (David Broadhurst, k=2)
  19. 134 6138613997 (Phil Carmody, k=206)
  20. 137 7849069263 (David Broadhurst, k=1)
  21. 138 3031676863 (David Broadhurst, k=29)
  22. 140 3628163579 (David Broadhurst, k=1)
  23. 147 8499384847 (David Broadhurst, k=1)
  24. 151 5501354863 (David Broadhurst, k=1)
  25. 151 8966789517 (David Broadhurst, k=82)
  26. +1543972898449 (k=341738136)
  27. 155 7080475371 (David Broadhurst, k=35)
  28. 161 5968566983 (Patrick Demichel, k=298179)
  29. 163 6316949409 (John Gamble, k=15248)
  30. 164 2921657213 (David Broadhurst, k=2)
  31. 167 3333333167 (David Broadhurst, k=1)
  32. +1698933436807 (David Broadhurst using ECM) (k=79964861)
  33. 170 5784584853 (Patrick Demichel, k=47686)
  34. 172 3969599133 (David Broadhurst, k=2)
  35. 173 3245549757 (Phil Carmody, k=3598)
  36. 175 6223633407 (David Broadhurst, k=1)
  37. 180 9885240263 (David Broadhurst, k=1)
  38. 187 0534961131 (David Broadhurst, k=5)
  39. 188 2853260087 (David Broadhurst, k=1)
  40. 189 4220401237 (Phil Carmody, k=4166)
  41. 192 1546995721 (David Broadhurst, k=20)
  42. 206 5705020481 (Phil Carmody, k=3680)
  43. 206 8581485609 (David Broadhurst, k=4)
  44. +2094072609373 (Dario Alpern using trial division) (k=84282082)
  45. 212 4913260383 (John Gamble, k=15031)
  46. 214 1053513237 (Phil Carmody, k=102)
  47. 214 6060605847 (David Broadhurst, k=1)
  48. 230 1214357369 (Phil Carmody, k=3396)
  49. 235 0435234291 (David Broadhurst, k=65)
  50. 236 6001235687 (Phil Carmody, k=2201)
  51. 246 3902438779 (David Broadhurst, k=1)
  52. 246 8839200251 (Phil Carmody, k=125)
  53. 248 4356435893 (David Broadhurst, k=34)
  54. 250 3971804379 (David Broadhurst, k=53)
  55. 259 3827138013 (David Broadhurst, k=2)
  56. 264 6366716863 (Patrick Demichel, k=5169)
  57. 271 0835821453 (David Broadhurst, k=2)
  58. 275 3022911773 (Phil Carmody, k=742)
  59. 277 1980960849 (David Broadhurst, k=8)
  60. 282 4337757979 (David Broadhurst, k=1)
  61. 286 8895732979 (Patrick Demichel, k=46759)
  62. 287 0031599249 (Phil Carmody, k=184)
  63. 305 2357973677 (David Broadhurst, k=22)
  64. 307 4104014209 (David Broadhurst, k=64)
  65. 310 9736085437 (Patrick Demichel, k=630998)
  66. 333 8158228663 (Patrick Demichel, k=2686547)
  67. 355 5083151889 (David Broadhurst, k=8)
  68. 361 4037325933 (David Broadhurst, k=82)
  69. 374 1845018077 (David Broadhurst, k=2)
  70. 376 6161205819 (David Broadhurst, k=1)
  71. 379 2323543053 (David Broadhurst, k=2)
  72. 383 2473676931 (Phil Carmody, k=365)
  73. 387 4099161013 (David Broadhurst, k=2)
  74. 408 9578648527 (David Broadhurst, k=7)
  75. 421 1922718807 (David Broadhurst, k=1)
  76. 422 6099972183 (David Broadhurst, k=1)
  77. 438 0212687063 (David Broadhurst, k=1)
  78. 439 2816727729 (Phil Carmody, k=1768)
  79. 440 4313344619 (David Broadhurst, k=1)
  80. 456 4129240837 (David Broadhurst, k=2)
  81. 459 5481727651 (Phil Carmody, k=1425)
  82. 466 3400064721 (Patrick Demichel, k=47720)
  83. 479 8939952557 (David Broadhurst, k=2)
  84. 499 3439370259 (Phil Carmody, k=103)
  85. 501 8639185891 (Patrick Demichel, k=27605)
  86. 507 5654101489 (Phil Carmody, k=456)
  87. 507 7132298089 (David Broadhurst, k=68)
  88. 509 1484773533 (Phil Carmody, k=106)
  89. 512 1414140903 (David Broadhurst, k=1)
  90. +5231197153423 (Dario Alpern using trial division) (k=11463929)
  91. +5336435463727 (Dario Alpern using trial division) (k=14798521)
  92. 539 6173093081 (Norm Dresner, k=11060)
  93. 542 0000000543 (David Broadhurst, k=1)
  94. 548 2755025019 (David Broadhurst, k=79)
  95. 564 8675515957 (David Broadhurst, k=2)
  96. 585 5499673459 (Patrick Demichel, k=64693)
  97. 590 9805140383 (David Broadhurst, k=39)
  98. 624 0390013447 (Patrick Demichel, k=58151)
  99. +6392427361093 (k=1414879894)
  100. 656 1241357213 (Phil Carmody, k=1434)
  101. 657 0763668037 (David Broadhurst, k=2)
  102. 673 0782309607 (Patrick Demichel, k=2198951)
  103. 681 0913234903 (David Broadhurst, k=7)
  104. 693 3993339241 (Phil Carmody, k=180)
  105. 695 8656861517 (Phil Carmody, k=222)
  106. 698 3633197117 (David Broadhurst, k=2)
  107. 701 8051398613 (David Broadhurst, k=2)
  108. 713 1791768047 (Patrick Demichel, k=1797931)
  109. 738 0000000739 (David Broadhurst, k=1)
  110. 765 6006821209 (Patrick Demichel, k=24548)
  111. 778 1481414037 (David Broadhurst, k=2)
  112. 832 4612655481 (David Broadhurst, k=60)
  113. 846 0000000847 (David Broadhurst, k=47)
  114. 867 7821294721 (Patrick Demichel, k=5440)
  115. 889 5493348237 (David Broadhurst, k=2)
  116. 919 5643218259 (David Broadhurst, k=21)
  117. 928 1735317823 (David Broadhurst, k=1)
  118. 944 4821592727 (Norm Dresner, k=11427)
  119. 948 8903488087 (David Broadhurst, k=31)
  120. 965 1754481491 (Phil Carmody, k=205)
  121. 965 9405941561 (David Broadhurst, k=20)
  122. 966 6897759091 (Patrick Demichel, k=6955)
  123. 969 2663686487 (Phil Carmody, k=253)
  124. 991 2984418327 (David Broadhurst, k=1)

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.