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[提问] 谁能分解10^200+3分解质因数

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发表于 2019-1-24 15:28:24 | 显示全部楼层 |阅读模式

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给出每一个质因数
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2019-1-24 15:51:59 | 显示全部楼层
10^200也就700bit的级别,应该不是很费时啊。但你分解这个干啥?

点评

不是当年768bit的RSA大家一起搞了两年吗?为啥说700bit不费事?  发表于 2019-1-25 00:34
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2019-1-24 16:03:17 | 显示全部楼层

评分

参与人数 1威望 +3 收起 理由
mathe + 3 赞,给出了1000000000...03<201> = 168.

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毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2019-1-24 16:09:35 | 显示全部楼层
风云🗡给出的网站的分解结果
16892897616604738393032473779*
142382085188774470405910710620318311201708781764203691159141491*
41575789136886395098758671741723670103749259409601292912421292205993178486578323921284022171938244838107449227

点评

显然是查询出来的,计算哪有这么快的  发表于 2019-1-25 09:28
我怀疑这个计算结果是从数据库里面查询出来的,而不是计算出来的  发表于 2019-1-25 09:07
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2019-1-24 16:55:53 | 显示全部楼层
mathe 发表于 2019-1-24 16:09
风云🗡给出的网站的分解结果
16892897616604738393032473779*
142382085188774470405910710620318 ...

我还以为知道那个网站的人不多呢

点评

知道答案你还问  发表于 2019-1-24 17:31
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2019-1-25 01:09:36 | 显示全部楼层
第一个因子很容易找
00:25:54> factorint(10^200+3,1+4+8)
IFAC: cracking composite
        100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
IFAC: checking for pure square
IFAC: trying Lenstra-Montgomery ECM
ECM: working on 64 curves at a time; initializing for up to 220 rounds...
ECM: time =      0 ms
ECM: B1 = 1800, B2 = 198000,    gss =  128*420
ECM: time =   1751 ms, B1 phase done, p = 1801, setting up for B2
ECM: time =     31 ms, entering B2 phase, p = 2017
ECM: time =   1156 ms
ECM: B1 = 2200, B2 = 242000,    gss =  128*420
ECM: time =   2078 ms, B1 phase done, p = 2203, setting up for B2
ECM: time =     31 ms, entering B2 phase, p = 2413
ECM: time =   1376 ms
ECM: B1 = 2700, B2 = 297000,    gss =  256*420
ECM: time =   2516 ms, B1 phase done, p = 2707, setting up for B2
ECM: time =     31 ms, entering B2 phase, p = 2917
ECM: time =   1657 ms
ECM: B1 = 3250, B2 = 357500,    gss =  256*420
ECM: time =   2970 ms, B1 phase done, p = 3251, setting up for B2
ECM: time =     31 ms, entering B2 phase, p = 3461
ECM: time =   1923 ms
ECM: B1 = 4000, B2 = 440000,    gss =  256*420
ECM: time =   3642 ms, B1 phase done, p = 4001, setting up for B2
ECM: time =     31 ms, entering B2 phase, p = 4211
ECM: time =   2344 ms
ECM: B1 = 4850, B2 = 533500,    gss =  256*420
ECM: time =   4328 ms, B1 phase done, p = 4861, setting up for B2
ECM: time =     47 ms, entering B2 phase, p = 5077
ECM: time =   2751 ms
ECM: B1 = 5800, B2 = 638000,    gss =  256*420
ECM: time =   5094 ms, B1 phase done, p = 5801, setting up for B2
ECM: time =     47 ms, entering B2 phase, p = 6011
ECM: time =   3250 ms
ECM: B1 = 7100, B2 = 781000,    gss =  256*420
ECM: time =   6407 ms, B1 phase done, p = 7103, setting up for B2
ECM: time =     31 ms, entering B2 phase, p = 7313
ECM: time =   3892 ms
ECM: B1 = 8700, B2 = 957000,    gss =  256*420
ECM: time =   7656 ms, B1 phase done, p = 8707, setting up for B2
ECM: time =     31 ms, entering B2 phase, p = 8921
ECM: time =   4735 ms
ECM: B1 = 10600,        B2 = 1166000,   gss =  512*420
ECM: time =   9297 ms, B1 phase done, p = 10601, setting up for B2
ECM: time =     47 ms, entering B2 phase, p = 10813
ECM: time =   5563 ms
ECM: B1 = 12900,        B2 = 1419000,   gss =  512*420
ECM: time =  10970 ms, B1 phase done, p = 12907, setting up for B2
ECM: time =     31 ms, entering B2 phase, p = 13117
ECM: time =   6767 ms
ECM: B1 = 15700,        B2 = 1727000,   gss =  512*420
ECM: time =  13391 ms, B1 phase done, p = 15727, setting up for B2
ECM: time =     47 ms, entering B2 phase, p = 15937
ECM: time =   7985 ms
ECM: B1 = 19000,        B2 = 2090000,   gss =  512*420
ECM: time =  15923 ms, B1 phase done, p = 19001, setting up for B2
ECM: time =     31 ms, entering B2 phase, p = 19217
ECM: time =   9501 ms
ECM: B1 = 23200,        B2 = 2552000,   gss =  512*420
ECM: time =  19516 ms, B1 phase done, p = 23201, setting up for B2
ECM: time =     31 ms, entering B2 phase, p = 23411
ECM: time =  11454 ms
ECM: B1 = 28000,        B2 = 3080000,   gss =  512*420
ECM: time =  23625 ms, B1 phase done, p = 28001, setting up for B2
ECM: time =     47 ms, entering B2 phase, p = 28223
ECM: time =  13563 ms
ECM: B1 = 34500,        B2 = 3795000,   gss =  512*420
ECM: time =  28845 ms, B1 phase done, p = 34501, setting up for B2
ECM: time =     31 ms, entering B2 phase, p = 34717
ECM: time =  16469 ms
ECM: B1 = 43000,        B2 = 4730000,   gss = 1024*420
ECM: time =  35876 ms, B1 phase done, p = 43003, setting up for B2
ECM: time =     31 ms, entering B2 phase, p = 43219
ECM: time =  20000 ms
ECM: B1 = 53800,        B2 = 5918000,   gss = 1024*420
ECM: time =  43657 ms, B1 phase done, p = 53813, setting up for B2
ECM: time =     47 ms, entering B2 phase, p = 54023
ECM: time =  24735 ms
ECM: B1 = 67750,        B2 = 7452500,   gss = 1024*420
ECM: time =  55484 ms, B1 phase done, p = 67751, setting up for B2
ECM: time =     31 ms, entering B2 phase, p = 67961
ECM: time =  30250 ms
ECM: B1 = 85300,        B2 = 9383000,   gss = 1024*420
ECM: time =  69782 ms, B1 phase done, p = 85303, setting up for B2
ECM: time =     47 ms, entering B2 phase, p = 85517
ECM: time =  37688 ms
ECM: B1 = 107400,       B2 = 11814000,  gss = 1024*420
ECM: time =  87704 ms, B1 phase done, p = 107441, setting up for B2
ECM: time =     47 ms, entering B2 phase, p = 107657
ECM: time =  46938 ms
ECM: B1 = 135400,       B2 = 14894000,  gss = 1024*420
ECM: time = 108578 ms, B1 phase done, p = 135403, setting up for B2
ECM: time =     47 ms, entering B2 phase, p = 135617
ECM: time =  57501 ms
ECM: B1 = 170800,       B2 = 18788000,  gss = 1024*420
ECM: time = 136954 ms, B1 phase done, p = 170801, setting up for B2
ECM: time =     47 ms, entering B2 phase, p = 171013
ECM: time =  71798 ms
ECM: B1 = 215400,       B2 = 23694000,  gss = 1024*420
ECM: time = 174281 ms, B1 phase done, p = 215417, setting up for B2
ECM: time =     47 ms, entering B2 phase, p = 215651
ECM: time =  89656 ms
ECM: B1 = 271400,       B2 = 29854000,  gss = 1024*420
ECM: time = 215923 ms, B1 phase done, p = 271409, setting up for B2
ECM: time =     47 ms, entering B2 phase, p = 271637
ECM: time = 110704 ms
ECM: B1 = 341500,       B2 = 37565000,  gss = 1024*420
ECM: time = 272297 ms, B1 phase done, p = 341501, setting up for B2
ECM: time =     48 ms, entering B2 phase, p = 341713
ECM: time = 137250 ms
ECM: B1 = 429700,       B2 = 47267000,  gss = 1024*420
ECM: time = 341970 ms, B1 phase done, p = 429701, setting up for B2
ECM: time =     47 ms, entering B2 phase, p = 429923
ECM: time =  55438 ms
        found factor = 16892897616604738393032473779
IFAC: cofactor = 5919647550678682918318585392550030687321219331802429980672060525048639901448866420111089641083403610030206379807979210510870824800479444820240779860283084327969945191577457
IFAC: factor 5919647550678682918318585392550030687321219331802429980672060525048639901448866420111089641083403610030206379807979210510870824800479444820240779860283084327969945191577457
        is composite
IFAC: factor 16892897616604738393032473779
        is prime
IFAC: prime 16892897616604738393032473779
        appears with exponent = 1
IFAC: main loop: 1 factor left
IFAC: cracking composite
        5919647550678682918318585392550030687321219331802429980672060525048639901448866420111089641083403610030206379807979210510870824800479444820240779860283084327969945191577457
IFAC: checking for pure square
IFAC: trying Lenstra-Montgomery ECM
然后……

点评

16892897616604738393032473779这个29位数的因子居然能找到  发表于 2019-2-24 14:47
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2019-1-25 04:34:43 | 显示全部楼层
.·.·. 发表于 2019-1-25 01:09
第一个因子很容易找
00:25:54> factorint(10^200+3,1+4+8)
IFAC: cracking composite

你这啥软件?我只看到了ecm

点评

pari/gp,改了config文件  发表于 2019-1-25 05:12
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2019-1-25 08:45:19 | 显示全部楼层
.·.·. 发表于 2019-1-25 01:09
第一个因子很容易找
00:25:54> factorint(10^200+3,1+4+8)
IFAC: cracking composite

你是在Linux上,还是Windows上,如何改config?
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2019-1-25 09:09:15 | 显示全部楼层
mathe 发表于 2019-1-24 16:09
风云🗡给出的网站的分解结果
16892897616604738393032473779*
142382085188774470405910710620318 ...

2^2^14+1
这个也给出了结果,不过我认为是查询出来的
116928085873074369829035993834596371340386703423373313
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2019-1-25 09:47:32 | 显示全部楼层
mathematica 发表于 2019-1-25 09:09
2^2^14+1
这个也给出了结果,不过我认为是查询出来的
1169280858730743698290359938345963713403867034 ...

2^2^14+1
应该是查的
毕竟是费马数的因子
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
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