This method or algorithm takes too long to find very large prime numbers , but it is less complicated than methods used for very large primes , like Fermat 's primality test or the Miller-Rabin primality test . Many mathematicians have worked on primality tests for large numbers , often restricted to specific number forms . This includes PÃ pin 's test for Fermat numbers ( 1877 ) , Proth 's theorem ( around 1878 ) , the Lucasâ `` Lehmer primality test ( originated 1856 ) , and the generalized Lucas primality test .