大きな数の素因数分解がしたいっ!!! #日曜数学会 in 札幌
TRANSCRIPT
@tsujimotter
391961320150251294647
Simpleisbest!!!
391961320150251294647/2=391961320150251294647/3=391961320150251294647/5=
391961320150251294647/7=391961320150251294647/11=…
391961320150251294647/2=391961320150251294647/3=391961320150251294647/5=
391961320150251294647/7=391961320150251294647/11=…
Quadratic Sieve
X2–Y2 n
(X–Y),(X–Y) n
n
X2–Y2=(X–Y)(X+Y)
X2–Y2=n∴X2–n=Y2
X
X2–Y2=n∴X2–n=Y2
X2–n=( )
n=112373
X2–n=( )
3362–112373=52313372–112373=22x131x2313382–112373=18711
n=112373
X2–n=( )
3362–112373=52313372–112373=22x131x2313382–112373=18711
#2 3372–112373=22x131x231 #4 3392–112373=22x72x131#18 3532–112373=22x71x191x231#84 4172–112373=22x71x133#112 4452–112373=22x72x191x231
#2 3372–112373=22x131x231 #4 3392–112373=22x72x131#18 3532–112373=22x71x191x231#84 4172–112373=22x71x133#112 4452–112373=22x72x191x231
=28x76x134x192x232
=(24x73x132x191x23)2
=4053052642
x12–n=p1p2�
x22–n=p2p3�
x32–n=p1p3�
�(x1
2–n)(x22–n)(x32–n)=(p12p22p32)��
(x1x2x3)2+n()=(p1p2p3)
2�� Y2X2
x12–n=p1p2�
x22–n=p2p3�
x32–n=p1p3�
�(x1
2–n)(x22–n)(x32–n)=(p12p22p32)��
(x1x2x3)2+n()=(p1p2p3)
2�� Y2X2
x12–n=p1p2�
x22–n=p2p3�
x32–n=p1p3�
�(x1
2–n)(x22–n)(x32–n)=(p12p22p32)��
(x1x2x3)2+n()=(p1p2p3)
2�� Y2X2
x12–n=p1p2�
x22–n=p2p3�
x32–n=p1p3�
�(x1
2–n)(x22–n)(x32–n)=(p12p22p32)��
(x1x2x3)2+n()=(p1p2p3)
2��
X2 Y2
x12–n=p1p2�
x22–n=p2p3�
x32–n=p1p3�
�(x1
2–n)(x22–n)(x32–n)=(p12p22p32)��
(x1x2x3)2+n()=(p1p2p3)
2��
X2 Y2
X2–Y2=n()
222060068552–4053052642=112373()
(22206006855–405305264)x(22206006855+405305264)
21800701591x22611312119
==
n
222060068552–4053052642=112373()
(22206006855–405305264)x(22206006855+405305264)
21800701591x22611312119
==
n
222060068552–4053052642=112373()
(22206006855–405305264)x(22206006855+405305264)
21800701591x22611312119
==
112373
21800701591 112373
21800701591=194003x112373+2472
112373=45x2472+1133
2472=2x1133+206
1133=5x206+103
21800701591 112373
21800701591=194003x112373+2472
112373=45x2472+1133
2472=2x1133+206
1133=5x206+103
21800701591 112373
21800701591=194003x112373+2472
112373=45x2472+1133
2472=2x1133+206
1133=5x206+103
21800701591 112373
21800701591=194003x112373+2472
112373=45x2472+1133
2472=2x1133+206
1133=5x206+103
112373103
p-1
391961320150251294647
391961320150251294647�
=182521213001x2147483647
Scriptishere!
GitHubGist
https://gist.github.com/junpeitsuji/5b515578941a23686953
x
2 - n = kp
✓n
p
◆= 1 p
X
X2–n=( )
n=15347
X2–n=( )
1242–15347=2911252–15347=21x13911262–15347=232
1262–232=15347��
(126-23)(126+23)=15347��
103x149=15347�