 The algorithms with guaranteed-correct output include both deterministic (non-random) algorithms, such as the AKS primality test,
and randomized Las Vegas algorithms where the random choices made by the algorithm do not affect its final answer, such as some variations of elliptic curve primality proving.When the elliptic curve method concludes that a number is prime, it provides primality certificate that can be verified quickly.The elliptic curve primality test is the fastest in practice of the guaranteed-correct primality tests, but its runtime analysis is based on heuristic arguments rather than rigorous proofs.