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?
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?
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.
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.