nyy 发表于 2023-6-7 14:12:08

An Overview of Elliptic Curve Primality Proving

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

https://theory.stanford.edu/~dfreeman/cs259c-f11/finalpapers/primalityproving.pdf

nyy 发表于 2023-6-12 08:44:23

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！

nyy 发表于 2023-6-12 08:46:06

https://inria.hal.science/inria-00138382v2/file/paper.pdf

nyy 发表于 2023-6-12 10:43:21

最近非常想搞明白用椭圆曲线如何证明素数

nyy 发表于 2023-6-12 10:47:43

https://www.detailedpedia.com/wiki-Pocklington_primality_test
Pocklington primality test

nyy 发表于 2023-6-12 11:08:01

https://www.detailedpedia.com/wiki-Elliptic_curve_primality_proving

nyy 发表于 2023-6-12 11:11:42

Elliptic curve primality (Redirected from Elliptic curve primality proving)

https://www.detailedpedia.com/wiki-Elliptic_curve_primality_proving

nyy 发表于 2023-6-12 15:55:28

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

nyy 发表于 2023-6-12 16:05:47

Needs["PrimalityProving`"]
ProvablePrimeQ, "Certificate" -> True]


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

nyy 发表于 2023-6-12 16:17:53

Primality certifications of near-repdigit-related prime numbers beginning with 1
https://stdkmd.net/nrr/cert/1/
页: [1] 2
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