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[转载] An Overview of Elliptic Curve Primality Proving

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发表于 2023-6-7 14:12:08 | 显示全部楼层 |阅读模式

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An Overview of Elliptic Curve Primality Proving
用椭圆曲线来证明素数的,大概

https://theory.stanford.edu/~dfr ... rimalityproving.pdf
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 2023-6-12 08:44:23 | 显示全部楼层
Pocklington 似乎是这个定理在椭圆曲线里面的推广,简单的说就是阶足够大!
然后就是素数!
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
 楼主| 发表于 2023-6-12 08:46:06 | 显示全部楼层
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 2023-6-12 10:43:21 | 显示全部楼层
最近非常想搞明白用椭圆曲线如何证明素数
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
 楼主| 发表于 2023-6-12 10:47:43 | 显示全部楼层
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 2023-6-12 11:08:01 | 显示全部楼层
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 2023-6-12 11:11:42 | 显示全部楼层
Elliptic curve primality (Redirected from Elliptic curve primality proving)

https://www.detailedpedia.com/wi ... e_primality_proving
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 2023-6-12 15:55:28 | 显示全部楼层
算法数论上,有这个算法的介绍,但是我还是不怎么懂,只懂得了个大概
具体的细节,还是不怎么懂
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 2023-6-12 16:05:47 | 显示全部楼层
  1. Needs["PrimalityProving`"]
  2. ProvablePrimeQ[NextPrime[10^50], "Certificate" -> True]
复制代码


输出结果
{True, {{CertificatePrime ->
    100000000000000000000000000000000000000000000000151,
   CertificatePoint ->
    PointEC[5, 32152469496628130982654530506104266596224965157278,
     94248608534322820037105751391465677179962894248748,
     29499072356215213358070500927643784786641929499115,
     100000000000000000000000000000000000000000000000151],
   CertificateK -> 3,
   CertificateM ->
    100000000000000000000000012237459539715207026850107,
   CertificateNextPrime ->
    33333333333333333333333337412486513238402342283369,
   CertificateDiscriminant -> -11},
  33333333333333333333333337412486513238402342283369,
  13, {2, {3, 2, {2}}, {13599479,
    11, {2, {19, 2, {2, {3, 2, {2}}}}, {167,
      5, {2, {83, 2, {2, {41, 6, {2, {5, 2, {2}}}}}}}}, {2143,
      3, {2, {3, 2, {2}}, {7, 3, {2, {3, 2, {2}}}}, {17,
        3, {2}}}}}}, {224957901193,
    5, {2, {3, 2, {2}}, {317,
      2, {2, {79,
        3, {2, {3, 2, {2}}, {13, 2, {2, {3, 2, {2}}}}}}}}, {601,
      7, {2, {3, 2, {2}}, {5, 2, {2}}}}, {49199,
      13, {2, {17, 3, {2}}, {1447,
        3, {2, {3, 2, {2}}, {241,
          7, {2, {3, 2, {2}}, {5, 2, {2}}}}}}}}}}, {224625845527667,
    2, {2, {11, 2, {2, {5, 2, {2}}}}, {53,
      2, {2, {13, 2, {2, {3, 2, {2}}}}}}, {5827,
      2, {2, {3, 2, {2}}, {971,
        6, {2, {5, 2, {2}}, {97, 5, {2, {3, 2, {2}}}}}}}}, {33061013,
      2, {2, {1301,
        2, {2, {5, 2, {2}}, {13, 2, {2, {3, 2, {2}}}}}}, {6353,
        3, {2, {397,
          5, {2, {3, 2, {2}}, {11,
            2, {2, {5, 2, {2}}}}}}}}}}}}, {2021083499683643,
    2, {2, {16231,
      3, {2, {3, 2, {2}}, {5, 2, {2}}, {541,
        2, {2, {3, 2, {2}}, {5, 2, {2}}}}}}, {62259980891,
      2, {2, {5, 2, {2}}, {127,
        3, {2, {3, 2, {2}}, {7, 3, {2, {3, 2, {2}}}}}}, {49023607,
        3, {2, {3, 2, {2}}, {97, 5, {2, {3, 2, {2}}}}, {131,
          2, {2, {5, 2, {2}}, {13, 2, {2, {3, 2, {2}}}}}}, {643,
          11, {2, {3, 2, {2}}, {107,
            2, {2, {53,
              2, {2, {13, 2, {2, {3, 2, {2}}}}}}}}}}}}}}}}}}}
可是结果我看不懂

点评

nyy
结果太垃圾了,嵌套那么多层结果!  发表于 2023-6-12 16:08
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 2023-6-12 16:17:53 | 显示全部楼层
Primality certifications of near-repdigit-related prime numbers beginning with 1
https://stdkmd.net/nrr/cert/1/
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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