This site uses the Baillie-PSW primality test. It has been proven to always work on numbers with up to 64 bits (18 digits), and **no one has ever found** a composite number that it thinks is prime. Therefore, if this website ever gives you a non-prime number, let everyone know! It would be a mathematical discovery.

That said, because we want you to feel truly safe and not rely on conjecture, we also apply the Miller-Rabin primality test with 7 rounds for numbers with more than 64 bits (mostly because we like the number 7). The default setting of 50 digits (166 bits) with 7 rounds provably has a chance of failure of one in 5 quadrillion (see this paper by Damgard, Landrock, and Pomerance for how we arrived at that estimate). Numbers with more digits have an even smaller chance of failure.

That said, because we want you to feel truly safe and not rely on conjecture, we also apply the Miller-Rabin primality test with 7 rounds for numbers with more than 64 bits (mostly because we like the number 7). The default setting of 50 digits (166 bits) with 7 rounds provably has a chance of failure of one in 5 quadrillion (see this paper by Damgard, Landrock, and Pomerance for how we arrived at that estimate). Numbers with more digits have an even smaller chance of failure.