Sieve of Eratosthenes The sieve of Eratosthenes is one of the most efficient ways to find all of the smaller primes (below 10 million or so). It is named after Eratosthenes of Cyrene, a Greek mathematician; although none of his works have survived, the sieve was described and attributed to Eratosthenes in the Introduction to Arithmetic by Nicomachus. (Wikipedia) My ruby example seems much simpler than many example implementations that I have seen online.