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大きな数の素因数分解がしたいっ!!! #日曜数学会 in 札幌

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2016年2月21日に開催の 第1回日曜数学会 in 札幌 で発表したスライドです。
「二次ふるい法」を用いて、大きな数の素因数分解をするための方法について紹介しました。

第1回日曜数学会 in 札幌:
https://www.facebook.com/events/1728707524032747/

ソースコード(Ruby):
mpqs.rb
https://gist.github.com/junpeitsuji/5b515578941a23686953
以下のソースも組み合わせて使います(gauss_mod.rb)
https://gist.github.com/junpeitsuji/b371dce4b402e550085c

Published in: Education
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  • DOWNLOAD THIS BOOKS INTO AVAILABLE FORMAT (Unlimited) ......................................................................................................................... ......................................................................................................................... Download Full PDF EBOOK here { https://tinyurl.com/y6a5rkg5 } ......................................................................................................................... Download Full EPUB Ebook here { https://tinyurl.com/y6a5rkg5 } ......................................................................................................................... ACCESS WEBSITE for All Ebooks ......................................................................................................................... Download Full PDF EBOOK here { https://tinyurl.com/y6a5rkg5 } ......................................................................................................................... Download EPUB Ebook here { https://tinyurl.com/y6a5rkg5 } ......................................................................................................................... Download doc Ebook here { https://tinyurl.com/y6a5rkg5 } ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... .............. Browse by Genre Available eBooks ......................................................................................................................... Art, Biography, Business, Chick Lit, Children's, Christian, Classics, Comics, Contemporary, Cookbooks, Crime, Ebooks, Fantasy, Fiction, Graphic Novels, Historical Fiction, History, Horror, Humor And Comedy, Manga, Memoir, Music, Mystery, Non Fiction, Paranormal, Philosophy, Poetry, Psychology, Religion, Romance, Science, Science Fiction, Self Help, Suspense, Spirituality, Sports, Thriller, Travel, Young Adult,
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大きな数の素因数分解がしたいっ!!! #日曜数学会 in 札幌

  1. 1. @tsujimotter
  2. 2. 391961320150251294647
  3. 3. Simple is best!!!
  4. 4. 391961320150251294647 / 2 = 391961320150251294647 / 3 = 391961320150251294647 / 5 = 391961320150251294647 / 7 = 391961320150251294647 / 11 = …
  5. 5. 391961320150251294647 / 2 = 391961320150251294647 / 3 = 391961320150251294647 / 5 = 391961320150251294647 / 7 = 391961320150251294647 / 11 = …
  6. 6. Quadratic Sieve
  7. 7. X2 – Y2 n (X – Y), (X – Y) n n X2 – Y2 = (X – Y)(X + Y)
  8. 8. X2 – Y2 = n ∴ X2 – n = Y2
  9. 9. X X2 – Y2 = n ∴ X2 – n = Y2 X2 – n = ( )
  10. 10. n = 112373 X2 – n = ( ) 3362 – 112373 = 5231 3372 – 112373 = 22 x 131 x 231 3382 – 112373 = 18711
  11. 11. n = 112373 X2 – n = ( ) 3362 – 112373 = 5231 3372 – 112373 = 22 x 131 x 231 3382 – 112373 = 18711
  12. 12. # 2 3372 – 112373 = 22 x 131 x 231   # 4 3392 – 112373 = 22 x 72 x 131 # 18 3532 – 112373 = 22 x 71 x 191 x 231 # 84 4172 – 112373 = 22 x 71 x 133 #112 4452 – 112373 = 22 x 72 x 191 x 231
  13. 13. # 2 3372 – 112373 = 22 x 131 x 231   # 4 3392 – 112373 = 22 x 72 x 131 # 18 3532 – 112373 = 22 x 71 x 191 x 231 # 84 4172 – 112373 = 22 x 71 x 133 #112 4452 – 112373 = 22 x 72 x 191 x 231 = 28 x 76 x 134 x 192 x 232 =(24 x 73 x 132 x 191 x 23)2 = 4053052642
  14. 14. x1 2 – n = p1p2 x2 2 – n = p2p3 x3 2 – n = p1 p3 (x1 2–n) (x2 2–n) (x3 2–n) = (p1 2p2 2p3 2) (x1x2x3)2 + n ( ) = (p1p2p3)2 Y2 X2
  15. 15. x1 2 – n = p1p2 x2 2 – n = p2p3 x3 2 – n = p1 p3 (x1 2–n) (x2 2–n) (x3 2–n) = (p1 2p2 2p3 2) (x1x2x3)2 + n ( ) = (p1p2p3)2 Y2 X2
  16. 16. x1 2 – n = p1p2 x2 2 – n = p2p3 x3 2 – n = p1 p3 (x1 2–n) (x2 2–n) (x3 2–n) = (p1 2p2 2p3 2) (x1x2x3)2 + n ( ) = (p1p2p3)2 Y2 X2
  17. 17. x1 2 – n = p1p2 x2 2 – n = p2p3 x3 2 – n = p1 p3 (x1 2–n) (x2 2–n) (x3 2–n) = (p1 2p2 2p3 2) (x1x2x3)2 + n ( ) = (p1p2p3)2 X2 Y2
  18. 18. x1 2 – n = p1p2 x2 2 – n = p2p3 x3 2 – n = p1 p3 (x1 2–n) (x2 2–n) (x3 2–n) = (p1 2p2 2p3 2) (x1x2x3)2 + n ( ) = (p1p2p3)2 X2 Y2 X2 – Y2 = n ( )
  19. 19. 222060068552 – 4053052642 = 112373 ( ) (22206006855 – 405305264) x (22206006855 + 405305264) 21800701591 x 22611312119 = = n
  20. 20. 222060068552 – 4053052642 = 112373 ( ) (22206006855 – 405305264) x (22206006855 + 405305264) 21800701591 x 22611312119 = = n
  21. 21. 222060068552 – 4053052642 = 112373 ( ) (22206006855 – 405305264) x (22206006855 + 405305264) 21800701591 x 22611312119 = = 112373
  22. 22. 21800701591 112373 21800701591 = 194003 x 112373 + 2472 112373 = 45 x 2472 + 1133 2472 = 2 x 1133 + 206 1133 = 5 x 206 + 103
  23. 23. 21800701591 112373 21800701591 = 194003 x 112373 + 2472 112373 = 45 x 2472 + 1133 2472 = 2 x 1133 + 206 1133 = 5 x 206 + 103
  24. 24. 21800701591 112373 21800701591 = 194003 x 112373 + 2472 112373 = 45 x 2472 + 1133 2472 = 2 x 1133 + 206 1133 = 5 x 206 + 103
  25. 25. 21800701591 112373 21800701591 = 194003 x 112373 + 2472 112373 = 45 x 2472 + 1133 2472 = 2 x 1133 + 206 1133 = 5 x 206 + 103
  26. 26. 112373 103
  27. 27. p-1
  28. 28. 391961320150251294647
  29. 29. 391961320150251294647 = 182521213001 x 2147483647
  30. 30. Script is here! GitHub Gist https://gist.github.com/junpeitsuji/ 5b515578941a23686953
  31. 31. x2 - n = kp ✓ n p ◆ = 1 p X X2 – n = ( )
  32. 32. n = 15347 X2 – n = ( ) 1242 – 15347 = 291 1252 – 15347 = 21 x 1391 1262 – 15347 = 232
  33. 33. 1262 – 232 = 15347 (126 - 23)(126 + 23) = 15347 103 x 149 = 15347

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