Sage also has an is_prime function, which provably show that p is not prime: "is_prime(p)". This takes less than 1ms to run. Proving primality of a 1024 bit prime in Sage takes a few seconds, and for a 2048 bit prime about a minute. Sage uses PARI for this, with sophisticated elliptic curve based algorithms called ECPP("=elliptic curve primality proving"), which are non-deterministic (unlike AKS) but fast in practice and provably correct. https://goo.gl/34uxJl