Here's my attempt: #!/usr/bin/env python import math for x in range(3,1000,2): isPrime = True for y in range(3,(math.sqrt(x) + 1)): if x % y == 0: isPrime = False break if isPrime: print "%d is prime." % x Notes: This doesn't bother with even numbers at all, and uses the square root function of "math." Any improvements anyone?