I just answered the question on project euler about finding circular primes below 1 million using python. My solution is below. I was able to reduce the running time of the solution from 9 seconds to about 3 seconds. I would like to see what else can be done to the code to reduce its running time further. This is strictly for educational purposes and for fun.
import math import time def getPrimes(n): """returns set of all primes below n""" non_primes = [j for j in range(4, n, 2)] # 2 covers all even numbers for i in range(3, n, 2): non_primes.extend([j for j in range(i*2, n, i)]) return set([i for i in range(2, n)]) - set(non_primes) def getCircularPrimes(n): primes = getPrimes(n) is_circ =  for prime in primes: prime_str = str(prime) iter_count = len(prime_str) - 1 rotated_num =  while iter_count > 0: prime_str = prime_str[1:] + prime_str[:1] rotated_num.append(int(prime_str)) iter_count -= 1 if primes >= set(rotated_num): is_circ.append(prime) return len(is_circ)