Fastest primality test

Question

Could you suggest a fast, deterministic method that is usable in practice, for testing if a large number is prime or not?

Also, I would like to know how to use no

Answer 1

"Probably" actually means 1-ε, and ε gets as small as you need.

Most applications have some small yet nonzero probability of failing that is not connected to primality testing, for example

• in cryptographic applications, an attacker luckily guessing the secret with, for example, a probability of 2^(-100)

• a hardware failure (radiation-induced) randomly flipping some bit of your computer memory (maybe one that holds the output of your "deterministic" primality test

• bugs (indeed, more probable than the other type of failures)

So pressing the ε to that order of magnitude will suffice in practice.

For example, OpenSSL, GnuPG of use non-deterministic primality test only. ``Probably'' you don't really want no deterministic test. But check what is available to you: If you have any libraries at hand, and they perform enough - go on and use them.