In number theory, a provable prime is an integer that has been calculated to be prime using a primality-proving algorithm.
Boot-strapping techniques using Pocklington primality test are the most common ways to generate provable primes for cryptography.
[1][2] Contrast with probable prime, which is likely (but not certain) to be prime, based on the output of a probabilistic primality test.
In principle, every prime number can be proved to be prime in polynomial time by using the AKS primality test.
[3] Provable primes have also been generated on embedded devices.