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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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�