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数学研发论坛»论坛 › 【数学研究】 › 难题征解 › 谁能分解10^200+3分解质因数
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[提问] 谁能分解10^200+3分解质因数

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mathematica
 楼主| 发表于 2019-1-25 10:05:42 | 显示全部楼层
.·.·. 发表于 2019-1-25 09:47
2^2^14+1
应该是查的
毕竟是费马数的因子

2^2^14+2
也能分解。
2 · 3^2 · 1033 · 3049 · 112059721 · 1591582393<10> · 2932031007403<13> · 5831992772873<13> · 15686603697451<14> · 24474915268259<14> · 2028925864752043<16> · 38257184231365987<17> · 1588264559403825049<19> · 56713727820156410577229101238628035243<38> · 8272317928...13<56> · 1181109434...17<1568> · 2623595095...53<3145>
有一个是1568的整数，一个3145的整数
两个读是合数，你说怎么搞出来的呢？

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mathematica
似乎是因为公因子2能被提出来  发表于 2019-1-25 10:07
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dlpg070
发表于 2019-1-25 17:03:41 | 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 的查询结果与10^200+3的 结果有本质差别

对 10^200+3 给出的是3个素因子连乘， 符合楼主要求
对2^2^14+1 给出的是2个因子连乘， 不一定是素因子
2^(2^14)+1<4933> = 1169280858...13<54> · 1017489926...09<4880>
进一步查询得知 第一个因子 1169280858...13<54>是素数，
第二个因子  1017489926...09<4880> 是合数，且不知其素因子
不符合楼主要求
factordb.com 很好，但本质是数据库查询系统，对于大数难题，常常查不到理想答案

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mathematica
 楼主| 发表于 2020-8-6 17:37:44 | 显示全部楼层
本帖最后由 mathematica 于 2020-8-6 17:38 编辑
.·.·. 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


[Thu Aug 06 17:13:40 2020]
ECM found a factor in curve #12, stage #2
Sigma=2363227094296319, B1=8000000, B2=800000000.
10^200+3 has a factor: 16892897616604738393032473779 (ECM curve 12, B1=8000000, B2=800000000)

我也用软件找到了这个因子，并且给出了sigma

[ <2, 2>, <3, 2>, <7, 1>, <3329, 1>, <4549, 1>, <15773, 1>, <690919, 1>, <406193003, 1> ]
因为这个光滑数，所以得到了这个因子，这个光滑数出卖了这个素数因子
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mathematica
 楼主| 发表于 2020-8-7 10:48:55 | 显示全部楼层
mathematica 发表于 2020-8-6 17:37
[Thu Aug 06 17:13:40 2020]
ECM found a factor in curve #12, stage #2
Sigma=2363227094296319, B ...

[Fri Aug 07 10:44:54 2020]
ECM found a factor in curve #2, stage #2
Sigma=4920276195392524, B1=8000000, B2=800000000.
10^200+3 has a factor: 16892897616604738393032473779 (ECM curve 2, B1=8000000, B2=800000000)
估计两三分钟不到，找到了这个因子
  1. FindGroupOrder := function (p, sigma)
  2.    K := GF(p);
  3.    v := K ! (4*sigma);
  4.    u := K ! (sigma^2-5);
  5.    x := u^3;
  6.    b := 4*x*v;
  7.    a := (v-u)^3*(3*u+v);
  8.    A := a/b-2;
  9.    x := x/v^3;
  10.    b := x^3 + A*x^2 + x;
  11.    E := EllipticCurve([0,b*A,0,b^2,0]);
  12.    return FactoredOrder(E);
  13. end function;
  14. p:=16892897616604738393032473779;
  15. sigma:=4920276195392524;
  16. FindGroupOrder(p,sigma);
复制代码


[ <2, 3>, <3, 2>, <5, 2>, <29, 1>, <186397, 1>, <196817, 1>, <449971, 1>, <19604131, 1> ]

http://magma.maths.usyd.edu.au/calc/

又是光滑数出卖了这个素数！
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mathematica
 楼主| 发表于 2020-8-7 11:00:27 | 显示全部楼层
mathematica 发表于 2020-8-7 10:48
[Fri Aug 07 10:44:54 2020]
ECM found a factor in curve #2, stage #2
Sigma=4920276195392524, B1=8 ...

[Fri Aug 07 10:54:45 2020]
ECM found a factor in curve #7, stage #2
Sigma=2101670469519597, B1=8000000, B2=800000000.
10^200+3 has a factor: 16892897616604738393032473779 (ECM curve 7, B1=8000000, B2=800000000)

[ <2, 8>, <3, 1>, <17, 1>, <929, 1>, <2137, 1>, <243673, 1>, <295871, 1>, <9039907, 1> ]
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mathematica
 楼主| 发表于 2020-8-7 11:43:13 | 显示全部楼层
mathematica 发表于 2020-8-7 11:00
[Fri Aug 07 10:54:45 2020]
ECM found a factor in curve #7, stage #2
Sigma=2101670469519597, B1=8 ...

[Fri Aug 07 11:41:18 2020]
ECM found a factor in curve #10, stage #2
Sigma=893918023258991, B1=8000000, B2=800000000.
10^200+3 has a factor: 16892897616604738393032473779 (ECM curve 10, B1=8000000, B2=800000000)

[ <2, 8>, <3, 2>, <31063, 1>, <211493, 1>, <1421309, 1>, <785224379, 1> ]
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mathematica
 楼主| 发表于 2020-8-11 09:05:34 | 显示全部楼层
mathematica 发表于 2020-8-7 11:43
[Fri Aug 07 11:41:18 2020]
ECM found a factor in curve #10, stage #2
Sigma=893918023258991, B1=8 ...

08/11/20 09:01:17 v1.34.5 @ USER-20180508HK, prp29 = 16892897616604738393032473779 (curve 17 stg2 B1=10000008 sigma=3770300193 thread=0)
08/11/20 09:01:17 v1.34.5 @ USER-20180508HK, Finished 17 curves using Lenstra ECM method on C201 input, B1=10000008, B2=gmp-ecm default
感觉不错！这软件，大概花了十分钟左右，得到一个29位的素数因子，剩下的C172表示172位的合数
QQ截图20200811090308.png
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.·.·.
发表于 2020-8-18 15:31:40 | 显示全部楼层
mathematica 发表于 2020-8-11 09:05
08/11/20 09:01:17 v1.34.5 @ USER-20180508HK, prp29 = 16892897616604738393032473779 (curve 17 stg2  ...
  1. factorint(10^200+3)
  2. IFAC: cracking composite
  3.         100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
  4. IFAC: checking for pure square
  5. IFAC: trying Pollard-Brent rho method
  6. Rho: searching small factor of 665-bit integer
  7. Rho: using X^2-1 for up to 49152 rounds of 32 iterations
  8. Rho: time =    932 ms,        24576 rounds
  9. Rho: fast forward phase (8192 rounds of 64)...
  10. Rho: time =    413 ms,        32772 rounds, back to normal mode
  11. Rho: time =    244 ms,        40960 rounds
  12. Rho: time =    266 ms,        Pollard-Brent giving up.
  13. IFAC: trying Shanks' SQUFOF, will fail silently if input
  14.       is too large for it.
  15. IFAC: trying Lenstra-Montgomery ECM
  16. ECM: working on 64 curves at a time; initializing for up to 220 rounds...
  17. ECM: time =      0 ms
  18. ECM: B1 = 1800,        B2 = 198000,        gss =  128*420
  19. ECM: time =    861 ms, B1 phase done, p = 1801, setting up for B2
  20. ECM: time =     14 ms, entering B2 phase, p = 2017
  21. ECM: time =    545 ms
  22. ECM: B1 = 2200,        B2 = 242000,        gss =  128*420
  23. ECM: time =    985 ms, B1 phase done, p = 2203, setting up for B2
  24. ECM: time =     15 ms, entering B2 phase, p = 2413
  25. ECM: time =    632 ms
  26. ECM: B1 = 2700,        B2 = 297000,        gss =  256*420
  27. ECM: time =   1249 ms, B1 phase done, p = 2707, setting up for B2
  28. ECM: time =     17 ms, entering B2 phase, p = 2917
  29. ECM: time =    772 ms
  30. ECM: B1 = 3250,        B2 = 357500,        gss =  256*420
  31. ECM: time =   1422 ms, B1 phase done, p = 3251, setting up for B2
  32. ECM: time =     14 ms, entering B2 phase, p = 3461
  33. ECM: time =    904 ms
  34. ECM: B1 = 4000,        B2 = 440000,        gss =  256*420
  35. ECM: time =   1664 ms, B1 phase done, p = 4001, setting up for B2
  36. ECM: time =     14 ms, entering B2 phase, p = 4211
  37. ECM: time =   1076 ms
  38. ECM: B1 = 4850,        B2 = 533500,        gss =  256*420
  39. ECM: time =   2053 ms, B1 phase done, p = 4861, setting up for B2
  40. ECM: time =     18 ms, entering B2 phase, p = 5077
  41. ECM: time =   1303 ms
  42. ECM: B1 = 5800,        B2 = 638000,        gss =  256*420
  43. ECM: time =   2475 ms, B1 phase done, p = 5801, setting up for B2
  44. ECM: time =     15 ms, entering B2 phase, p = 6011
  45. ECM: time =   1443 ms
  46. ECM: B1 = 7100,        B2 = 781000,        gss =  256*420
  47. ECM: time =   2767 ms, B1 phase done, p = 7103, setting up for B2
  48. ECM: time =     18 ms, entering B2 phase, p = 7313
  49. ECM: time =   1792 ms
  50. ECM: B1 = 8700,        B2 = 957000,        gss =  256*420
  51. ECM: time =   3907 ms, B1 phase done, p = 8707, setting up for B2
  52. ECM: time =     18 ms, entering B2 phase, p = 8921
  53. ECM: time =   2241 ms
  54. ECM: B1 = 10600,        B2 = 1166000,        gss =  512*420
  55. ECM: time =   4368 ms, B1 phase done, p = 10601, setting up for B2
  56. ECM: time =     20 ms, entering B2 phase, p = 10813
  57. ECM: time =   2827 ms
  58. ECM: B1 = 12900,        B2 = 1419000,        gss =  512*420
  59. ECM: time =   6017 ms, B1 phase done, p = 12907, setting up for B2
  60. ECM: time =     18 ms, entering B2 phase, p = 13117
  61. ECM: time =   3223 ms
  62. ECM: B1 = 15700,        B2 = 1727000,        gss =  512*420
  63. ECM: time =   6468 ms, B1 phase done, p = 15727, setting up for B2
  64. ECM: time =     18 ms, entering B2 phase, p = 15937
  65. ECM: time =   3965 ms
  66. ECM: B1 = 19000,        B2 = 2090000,        gss =  512*420
  67. ECM: time =   7982 ms, B1 phase done, p = 19001, setting up for B2
  68. ECM: time =     17 ms, entering B2 phase, p = 19217
  69. ECM: time =   4907 ms
  70. ECM: B1 = 23200,        B2 = 2552000,        gss =  512*420
  71. ECM: time =   9698 ms, B1 phase done, p = 23201, setting up for B2
  72. ECM: time =     14 ms, entering B2 phase, p = 23411
  73. ECM: time =   5675 ms
  74. ECM: B1 = 28000,        B2 = 3080000,        gss =  512*420
  75. ECM: time =  11633 ms, B1 phase done, p = 28001, setting up for B2
  76. ECM: time =     23 ms, entering B2 phase, p = 28223
  77. ECM: time =   6416 ms
  78. ECM: B1 = 34500,        B2 = 3795000,        gss =  512*420
  79. ECM: time =  14322 ms, B1 phase done, p = 34501, setting up for B2
  80. ECM: time =     16 ms, entering B2 phase, p = 34717
  81. ECM: time =   7514 ms
  82. ECM: B1 = 43000,        B2 = 4730000,        gss = 1024*420
  83. ECM: time =  17566 ms, B1 phase done, p = 43003, setting up for B2
  84. ECM: time =     17 ms, entering B2 phase, p = 43219
  85. ECM: time =   9777 ms
  86. ECM: B1 = 53800,        B2 = 5918000,        gss = 1024*420
  87. ECM: time =  20504 ms, B1 phase done, p = 53813, setting up for B2
  88. ECM: time =     16 ms, entering B2 phase, p = 54023
  89. ECM: time =  10757 ms
  90. ECM: B1 = 67750,        B2 = 7452500,        gss = 1024*420
  91. ECM: time =  25413 ms, B1 phase done, p = 67751, setting up for B2
  92. ECM: time =     15 ms, entering B2 phase, p = 67961
  93. ECM: time =  13933 ms
  94. ECM: B1 = 85300,        B2 = 9383000,        gss = 1024*420
  95. ECM: time =  33857 ms, B1 phase done, p = 85303, setting up for B2
  96. ECM: time =     19 ms, entering B2 phase, p = 85517
  97. ECM: time =  17912 ms
  98. ECM: B1 = 107400,        B2 = 11814000,        gss = 1024*420
  99. ECM: time =  43500 ms, B1 phase done, p = 107441, setting up for B2
  100. ECM: time =     16 ms, entering B2 phase, p = 107657
  101. ECM: time =  21778 ms
  102. ECM: B1 = 135400,        B2 = 14894000,        gss = 1024*420
  103. ECM: time =  51415 ms, B1 phase done, p = 135403, setting up for B2
  104. ECM: time =     26 ms, entering B2 phase, p = 135617
  105. ECM: time =  25173 ms
  106. ECM: B1 = 170800,        B2 = 18788000,        gss = 1024*420
  107. ECM: time =  64824 ms, B1 phase done, p = 170801, setting up for B2
  108. ECM: time =     15 ms, entering B2 phase, p = 171013
  109. ECM: time =  33090 ms
  110. ECM: B1 = 215400,        B2 = 23694000,        gss = 1024*420
  111. ECM: time =  81681 ms, B1 phase done, p = 215417, setting up for B2
  112. ECM: time =     16 ms, entering B2 phase, p = 215651
  113. ECM: time =  42665 ms
  114. ECM: B1 = 271400,        B2 = 29854000,        gss = 1024*420
  115. ECM: time = 105048 ms, B1 phase done, p = 271409, setting up for B2
  116. ECM: time =     18 ms, entering B2 phase, p = 271637
  117. ECM: time =  53946 ms
  118. ECM: B1 = 341500,        B2 = 37565000,        gss = 1024*420
  119. ECM: time = 130142 ms, B1 phase done, p = 341501, setting up for B2
  120. ECM: time =     18 ms, entering B2 phase, p = 341713
  121. ECM: time =  69894 ms
  122. ECM: B1 = 429700,        B2 = 47267000,        gss = 1024*420
  123. ECM: time = 169417 ms, B1 phase done, p = 429701, setting up for B2
  124. ECM: time =     16 ms, entering B2 phase, p = 429923
  125. ECM: time =  26946 ms
  126.         found factor = 16892897616604738393032473779
  127. IFAC: cofactor = 5919647550678682918318585392550030687321219331802429980672060525048639901448866420111089641083403610030206379807979210510870824800479444820240779860283084327969945191577457
  128. IFAC: factor 5919647550678682918318585392550030687321219331802429980672060525048639901448866420111089641083403610030206379807979210510870824800479444820240779860283084327969945191577457
  129.         is composite
  130. IFAC: factor 16892897616604738393032473779
  131.         is prime
  132. IFAC: prime 16892897616604738393032473779
  133.         appears with exponent = 1
  134. IFAC: main loop: 1 factor left
  135. IFAC: cracking composite
  136.         5919647550678682918318585392550030687321219331802429980672060525048639901448866420111089641083403610030206379807979210510870824800479444820240779860283084327969945191577457
  137. IFAC: checking for pure square
  138. IFAC: trying Pollard-Brent rho method
  139. Rho: searching small factor of 571-bit integer
  140. Rho: using X^2+5 for up to 49152 rounds of 32 iterations
  141. Rho: time =    822 ms,        24576 rounds
  142. Rho: fast forward phase (8192 rounds of 64)...
  143. Rho: time =    394 ms,        32772 rounds, back to normal mode
  144. Rho: time =    235 ms,        40960 rounds
  145. Rho: time =    229 ms,        Pollard-Brent giving up.
  146. IFAC: trying Shanks' SQUFOF, will fail silently if input
  147.       is too large for it.
  148. IFAC: trying Lenstra-Montgomery ECM
  149. ECM: working on 64 curves at a time; initializing for up to 173 rounds...
  150. ECM: time =      0 ms
  151. ECM: B1 = 1800,        B2 = 198000,        gss =  128*420
  152. ECM: time =    692 ms, B1 phase done, p = 1801, setting up for B2
  153. ECM: time =     15 ms, entering B2 phase, p = 2017
  154. ECM: time =    471 ms
  155. ECM: B1 = 2200,        B2 = 242000,        gss =  128*420
  156. ECM: time =    840 ms, B1 phase done, p = 2203, setting up for B2
  157. ECM: time =     14 ms, entering B2 phase, p = 2413
  158. ECM: time =    507 ms
  159. ECM: B1 = 2700,        B2 = 297000,        gss =  256*420
  160. ECM: time =   1003 ms, B1 phase done, p = 2707, setting up for B2
  161. ECM: time =     14 ms, entering B2 phase, p = 2917
  162. ECM: time =    604 ms
  163. ECM: B1 = 3250,        B2 = 357500,        gss =  256*420
  164. ECM: time =   1107 ms, B1 phase done, p = 3251, setting up for B2
  165. ECM: time =     13 ms, entering B2 phase, p = 3461
  166. ECM: time =    741 ms
  167. ECM: B1 = 4000,        B2 = 440000,        gss =  256*420
  168. ECM: time =   1453 ms, B1 phase done, p = 4001, setting up for B2
  169. ECM: time =     15 ms, entering B2 phase, p = 4211
  170. ECM: time =    879 ms
  171. ECM: B1 = 4850,        B2 = 533500,        gss =  256*420
  172. ECM: time =   1612 ms, B1 phase done, p = 4861, setting up for B2
  173. ECM: time =     11 ms, entering B2 phase, p = 5077
  174. ECM: time =   1031 ms
  175. ECM: B1 = 5800,        B2 = 638000,        gss =  256*420
  176. ECM: time =   2051 ms, B1 phase done, p = 5801, setting up for B2
  177. ECM: time =     13 ms, entering B2 phase, p = 6011
  178. ECM: time =   1172 ms
  179. ECM: B1 = 7100,        B2 = 781000,        gss =  256*420
  180. ECM: time =   2447 ms, B1 phase done, p = 7103, setting up for B2
  181. ECM: time =     15 ms, entering B2 phase, p = 7313
  182. ECM: time =   1676 ms
  183. ECM: B1 = 8700,        B2 = 957000,        gss =  256*420
  184. ECM: time =   2978 ms, B1 phase done, p = 8707, setting up for B2
  185. ECM: time =     15 ms, entering B2 phase, p = 8921
  186. ECM: time =   1830 ms
  187. ECM: B1 = 10600,        B2 = 1166000,        gss =  512*420
  188. ECM: time =   3611 ms, B1 phase done, p = 10601, setting up for B2
  189. ECM: time =     15 ms, entering B2 phase, p = 10813
  190. ECM: time =   2122 ms
  191. ECM: B1 = 12900,        B2 = 1419000,        gss =  512*420
  192. ECM: time =   4171 ms, B1 phase done, p = 12907, setting up for B2
  193. ECM: time =     12 ms, entering B2 phase, p = 13117
  194. ECM: time =   2564 ms
  195. ECM: B1 = 15700,        B2 = 1727000,        gss =  512*420
  196. ECM: time =   5355 ms, B1 phase done, p = 15727, setting up for B2
  197. ECM: time =     11 ms, entering B2 phase, p = 15937
  198. ECM: time =   3090 ms
  199. ECM: B1 = 19000,        B2 = 2090000,        gss =  512*420
  200. ECM: time =   6011 ms, B1 phase done, p = 19001, setting up for B2
  201. ECM: time =     13 ms, entering B2 phase, p = 19217
  202. ECM: time =   3367 ms
  203. ECM: B1 = 23200,        B2 = 2552000,        gss =  512*420
  204. ECM: time =   7231 ms, B1 phase done, p = 23201, setting up for B2
  205. ECM: time =     14 ms, entering B2 phase, p = 23411
  206. ECM: time =   4046 ms
  207. ECM: B1 = 28000,        B2 = 3080000,        gss =  512*420
  208. ECM: time =   9137 ms, B1 phase done, p = 28001, setting up for B2
  209. ECM: time =     11 ms, entering B2 phase, p = 28223
  210. ECM: time =   4853 ms
  211. ECM: B1 = 34500,        B2 = 3795000,        gss =  512*420
  212. ECM: time =  10440 ms, B1 phase done, p = 34501, setting up for B2
  213. ECM: time =     19 ms, entering B2 phase, p = 34717
  214. ECM: time =   5798 ms
  215. ECM: B1 = 43000,        B2 = 4730000,        gss = 1024*420
  216. ECM: time =  12679 ms, B1 phase done, p = 43003, setting up for B2
  217. ECM: time =     12 ms, entering B2 phase, p = 43219
  218. ECM: time =   6920 ms
  219. ECM: B1 = 53800,        B2 = 5918000,        gss = 1024*420
  220. ECM: time =  15952 ms, B1 phase done, p = 53813, setting up for B2
  221. ECM: time =     16 ms, entering B2 phase, p = 54023
  222. ECM: time =   8713 ms
  223. ECM: B1 = 67750,        B2 = 7452500,        gss = 1024*420
  224. ECM: time =  20493 ms, B1 phase done, p = 67751, setting up for B2
  225. ECM: time =     15 ms, entering B2 phase, p = 67961
  226. ECM: time =  11596 ms
  227. ECM: B1 = 85300,        B2 = 9383000,        gss = 1024*420
  228. ECM: time =  26326 ms, B1 phase done, p = 85303, setting up for B2
  229. ECM: time =     14 ms, entering B2 phase, p = 85517
  230. ECM: time =  14705 ms
  231. ECM: B1 = 107400,        B2 = 11814000,        gss = 1024*420
  232. ECM: time =  33397 ms, B1 phase done, p = 107441, setting up for B2
  233. ECM: time =     17 ms, entering B2 phase, p = 107657
  234. ECM: time =  15557 ms
  235. ECM: B1 = 135400,        B2 = 14894000,        gss = 1024*420
  236. ECM: time =  40620 ms, B1 phase done, p = 135403, setting up for B2
  237. ECM: time =     13 ms, entering B2 phase, p = 135617
  238. ECM: time =  21753 ms
  239. ECM: B1 = 170800,        B2 = 18788000,        gss = 1024*420
  240. ECM: time =  54020 ms, B1 phase done, p = 170801, setting up for B2
  241. ECM: time =     14 ms, entering B2 phase, p = 171013
  242. ECM: time =  26966 ms
  243. ECM: B1 = 215400,        B2 = 23694000,        gss = 1024*420
  244. ECM: time =  65318 ms, B1 phase done, p = 215417, setting up for B2
  245. ECM: time =     12 ms, entering B2 phase, p = 215651
  246. ECM: time =  32216 ms
  247. ECM: B1 = 271400,        B2 = 29854000,        gss = 1024*420
  248. ECM: time =  84390 ms, B1 phase done, p = 271409, setting up for B2
  249. ECM: time =     15 ms, entering B2 phase, p = 271637
  250. ECM: time =  41819 ms
  251. ECM: B1 = 341500,        B2 = 37565000,        gss = 1024*420
  252. ECM: time = 104850 ms, B1 phase done, p = 341501, setting up for B2
  253. ECM: time =     17 ms, entering B2 phase, p = 341713
  254. ECM: time =  50177 ms
  255. ECM: B1 = 429700,        B2 = 47267000,        gss = 1024*420
  256. ECM: time = 126526 ms, B1 phase done, p = 429701, setting up for B2
  257. ECM: time =     12 ms, entering B2 phase, p = 429923
  258. ECM: time =  63064 ms
  259. ECM: B1 = 540400,        B2 = 59444000,        gss = 1024*420
  260. ^C  ***   at top-level: factorint(10^200+3)
  261.   ***                 ^-------------------
  262.   *** factorint: user interrupt after 36min, 57,769 ms
  263.   ***   Break loop: <Return> to continue; 'break' to go back to GP prompt
复制代码

pari/GP也找到了相同的结果
找到这个因子并不麻烦
（只是我不知道该怎么要求Pari/GP找到这个因子之后停止，于是浪费了太多时间）
Pari/GP分解因数的效率其实挺高的
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mathematica
 楼主| 发表于 2020-8-21 13:52:29 | 显示全部楼层
.·.·. 发表于 2020-8-18 15:31
pari/GP也找到了相同的结果
找到这个因子并不麻烦
（只是我不知道该怎么要求Pari/GP找到这个因子之后 ...

你的pari/gp为什么会输出那么多东西呀，我的不会输出那么多东西
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.·.·.
发表于 2020-8-22 18:44:56 | 显示全部楼层
mathematica 发表于 2020-8-21 13:52
你的pari/gp为什么会输出那么多东西呀，我的不会输出那么多东西

\g 4
factorint(...)

大概效果是这样的
  1. neutron@Neutron:/me$ gp
  2. Reading GPRC: /etc/gprc ...Done.

  4.                                                      GP/PARI CALCULATOR Version 2.11.4 (released)
  5.                                              amd64 running linux (x86-64/GMP-6.2.0 kernel) 64-bit version
  6.                                             compiled: Apr 25 2020, gcc version 9.3.0 (Arch Linux 9.3.0-1)
  7.                                                               threading engine: pthread
  8.                                                     (readline v8.0 enabled, extended help enabled)

  10.                                                         Copyright (C) 2000-2018 The PARI Group

  12. PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER.

  14. Type ? for help, \q to quit.
  15. Type ?17 for how to get moral (and possibly technical) support.

  17. parisizemax = 34359738368, primelimit = 67108864, nbthreads = 12
  18. 18:44:22> \g 4
  19.    debug = 4
  20. 18:44:24> factorint(2^67-1)
  21. IFAC: cracking composite
  22.         147573952589676412927
  23. IFAC: checking for pure square
  24. IFAC: trying Pollard-Brent rho method
  25. Rho: searching small factor of 67-bit integer
  26. Rho: using X^2+5 for up to 57 rounds of 32 iterations
  27. Rho: time =      1 ms,        Pollard-Brent giving up.
  28. IFAC: trying Shanks' SQUFOF, will fail silently if input
  29.       is too large for it.
  30. IFAC: trying Lenstra-Montgomery ECM
  31. ECM: number too small to justify this stage
  32. IFAC: trying MPQS
  33. MPQS: number to factor N = 147573952589676412927
  34. MPQS: factoring number of 21 decimal digits
  35. MPQS: sieving interval = [-4500, 4500]
  36. MPQS: size of factor base = 121
  37. MPQS: striving for 163 relations
  38. MPQS: coefficients A will be built from 3 primes each
  39. MPQS: primes for A to be chosen near FB[19] = 179
  40. MPQS: smallest prime used for sieving FB[5] = 5
  41. MPQS: largest prime in FB = 1697
  42. MPQS: bound for `large primes' = 1697
  43. MPQS: first sorting at 40%, then every 10.0% / 5.0%

  45. MPQS: passing the 40.0% sort point, time = 1 ms
  46. MPQS: done sorting, time = 0 ms
  47. MPQS: found 41.1% of the required relations

  49. MPQS: passing the 51.1% sort point, time = 0 ms
  50. MPQS: done sorting, time = 0 ms
  51. MPQS: found 51.5% of the required relations

  53. MPQS: passing the 61.5% sort point, time = 0 ms
  54. MPQS: done sorting, time = 0 ms
  55. MPQS: found 60.7% of the required relations

  57. MPQS: passing the 70.7% sort point, time = 0 ms
  58. MPQS: done sorting, time = 0 ms
  59. MPQS: found 72.3% of the required relations

  61. MPQS: passing the 82.3% sort point, time = 0 ms
  62. MPQS: done sorting, time = 0 ms
  63. MPQS: found 82.2% of the required relations

  65. MPQS: passing the 87.2% sort point, time = 0 ms
  66. MPQS: done sorting, time = 0 ms
  67. MPQS: found 89.5% of the required relations

  69. MPQS: passing the 94.5% sort point, time = 0 ms
  70. MPQS: done sorting, time = 0 ms
  71. MPQS: found 100.0% of the required relations

  73. MPQS: starting Gauss over F_2 on 163 relations
  74. MPQS: Gauss done: kernel has rank 48, taking gcds...

  76. MPQS: time in Gauss and gcds = 0 ms
  77. MPQS: found factors = 761838257287
  78.         and 193707721
  79. IFAC: factor 761838257287
  80.         is prime
  81. IFAC: factor 193707721
  82.         is prime
  83. IFAC: prime 193707721
  84.         appears with exponent = 1
  85. IFAC: main loop: 1 factor left
  86. IFAC: prime 761838257287
  87.         appears with exponent = 1
  88. IFAC: main loop: this was the last factor
  89. IFAC: found 2 large prime (power) factors.
  90. time = 3 ms.
  91. %1 =
  92. [   193707721 1]

  94. [761838257287 1]

  96. 18:44:26>
复制代码
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