分享一个594位的大整数完全分解10^593+1

mathematica

第一个素数
2909076542620598524499532435958736860811671130747534094532375046661903\
161


第二个素数
3125015432807993452395038634013309617867717582914358894173268713097150\
5373764272326219859833643623810375723087939125084732442155817887830503\
6643302130660220509569558512336082568703738448093632414784406090765363\
6389193668837605678869741546508709934354266735495475343271268446929051\
7857796496330665342593974635670938957580267302778238155907245547983612\
7271156058041608178980954177779877360633471270141664420670089493620653\
0047039287732255861170965984971136826555598096883703505206688714709410\
112221639166983114001153395131



第三个是11
三个数的乘积

1. 2909076542620598524499532435958736860811671130747534094532375046661903\
   
2. 161*312501543280799345239503863401330961786771758291435889417326871309\
   
3. 7150537376427232621985983364362381037572308793912508473244215581788783\
   
4. 0503664330213066022050956955851233608256870373844809363241478440609076\
   
5. 5363638919366883760567886974154650870993435426673549547534327126844692\
   
6. 9051785779649633066534259397463567093895758026730277823815590724554798\
   
7. 3612727115605804160817898095417777987736063347127014166442067008949362\
   
8. 0653004703928773225586117096598497113682655559809688370350520668871470\
   
9. 9410112221639166983114001153395131*11

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运行结果

1. 1000000000000000000000000000000000000000000000000000000000000000000000\
   
2. 0000000000000000000000000000000000000000000000000000000000000000000000\
   
3. 0000000000000000000000000000000000000000000000000000000000000000000000\
   
4. 0000000000000000000000000000000000000000000000000000000000000000000000\
   
5. 0000000000000000000000000000000000000000000000000000000000000000000000\
   
6. 0000000000000000000000000000000000000000000000000000000000000000000000\
   
7. 0000000000000000000000000000000000000000000000000000000000000000000000\
   
8. 0000000000000000000000000000000000000000000000000000000000000000000000\
   
9. 0000000000000000000000000000000001

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无心人

其实难度跟分解140位难度差不多，特殊形式，数域筛的多项式，可以很简单

mathematica

无心人 发表于 2019-9-12 09:21
其实难度跟分解140位难度差不多，特殊形式，数域筛的多项式，可以很简单

椭圆曲线算法！

无心人

mathematica 发表于 2019-9-16 09:23
椭圆曲线算法！

哦~

mathematica

无心人 发表于 2019-9-17 17:31
哦~

各种分解算法，各有优缺点，比如二次筛法、数域筛法，对于十进制上千位的整数，就很难分解出因子，
但是椭圆曲线却能分解出他们的小因子（比如四五十位的小因子），
对于费马合数，有时候试除法反而更快，毕竟模实在是太大了！
对于是素数的梅森素数，反而素数判定是最快的分解办法！

mathematica

@.·.·.
你这个二货，当梅森数被判定为素数的时候，不就相当于完成了质因数分解了吗？