证明强可能的素数素性 [英] Proving the primality of strong probable primes

问题描述

使用米勒罗宾测试的概率版本，我已生成介质 - 大（200-300位）可能素数的列表。但可能还不够好！我需要的知道的这些数字都是素数。有一个库 - preferably包装或可包装在Python - ？实现的更有效的素性证明算法之一

Using the probabilistic version of the Miller-Rabin test, I have generated a list of medium-large (200-300 digit) probable primes. But probable ain't good enough! I need to know these numbers are prime. Is there a library -- preferably wrapped or wrappable in Python -- that implements one of the more efficient primality proving algorithms?

另外，有没有人知道我在哪里能找到的明确的详细和完整的ECPP的说明（或类似的快速算法）这不承担大量的先验知识吗？

Alternatively, does anyone know where I can find a clear, detailed, and complete description of ECPP (or a similarly fast algorithm) that does not assume a great deal of prior knowledge?

更新：我发现一个 Java实现的另一个测试，APRT-CLE，这决定性地证明了素数。它在10分钟的Atom处理器验证了一个291位数的总理候选人。不过希望的东西快，但是这似乎是一个良好的开端。

Update: I've found a Java implementation of another test, APRT-CLE, that conclusively proves primality. It verified a 291-digit prime candidate in under 10 minutes on an atom processor. Still hoping for something faster, but this seems like a promising start.

推荐答案

作为一个算法，给出了一个可靠的多项式素性测试，考虑的 AKS 的。有一个旧的SO文章引用算法的实现和presentations。

As an algorithm that gives a reliable polynomial primality test, consider AKS. There is an older SO article referencing implementations and presentations of the algorithm.

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