Sieve of Eratosthenes

sieve-of-eratosthenes.py

#!/usr/bin/python3
from math import sqrt


def sieve(limit, limit_list=[]):
    '''
    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).
    >>> sieve(30)
        [2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]
    '''
    max_num = int(sqrt(limit))
    limit_list = [n for n in range(2, limit)]
    first_el = limit_list[0]
    limit_list = [first_el] + [n for n in limit_list if n % first_el > 0]
    return (first_el != max_num and limit_list) or sieve(limit, limit_list)

print(sieve(int(input('the limit: '))))