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# [转载] An Overview of Elliptic Curve Primality Proving

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An Overview of Elliptic Curve Primality Proving

https://theory.stanford.edu/~dfr ... rimalityproving.pdf

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！

楼主| 发表于 2023-6-12 08:46:06 | 显示全部楼层

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

楼主| 发表于 2023-6-12 10:47:43 | 显示全部楼层
 https://www.detailedpedia.com/wiki-Pocklington_primality_test Pocklington primality test

楼主| 发表于 2023-6-12 11:08:01 | 显示全部楼层

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

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

楼主| 发表于 2023-6-12 16:05:47 | 显示全部楼层
 Needs["PrimalityProving`"] 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

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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/

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