My sieve of eratosthenes implementation in Python

Question

Could you please take a look at my implementation of the sieve of eratosthenes in Python and tell me how can I improve/optimize it?

I'm a beginner in programming, so I don't have any ideas how to optimize it, and I'd really appreciate it if you check it out and tell me what can be improved.

# -*- coding: utf-8 -*-
"""
Created on Fri Sep 27 19:57:14 2013

@author: stefan
"""
def sqrt_int(n):
    n = n**0.5
    if n == int(n):
        return True
    else:
        return False

def cbrt_int(n):
    n = n**(1.0/3)
    if n == int(n):
        return True
    else:
        return False

def sieve(limit):
    first_primes = [2,3,5,7]
    primes = [x for x in range (2,limit+1)]

    for y in first_primes:
        primes = filter(lambda x: x % y != 0, primes)

    primes = filter(lambda x: not sqrt_int(x), primes)
    primes = filter(lambda x: not cbrt_int(x), primes)

    if limit > 10: 
        primes = first_primes + primes
    else:
        primes = filter(lambda x: x <= limit, first_primes)
    return primes

Requests for improvement of existing code might get better answers on http://codereview.stackexchange.com — Robᵩ, Sep 27 '13 at 19:26

score 0 · Accepted Answer · answered Sep 27 '13 at 19:27

Here is a much simpler version of the Sieve of Eratosthenes:

def primes(n): # sieve of eratosthenes
    ps, sieve = [], [True] * (n + 1)
    for p in range(2, n + 1):
        if sieve[p]:
           ps.append(p)
           for i in range(p * p, n + 1, p):
               sieve[i] = False
    return ps

There are ways to make that run faster without too much complexity. If you are interested in programming with prime numbers, I modestly recommend this essay at my blog.

Thanks, I will check it out. I figured out mine doesn't even work correctly for huge numbers. — HelloEarth', Sep 27 '13 at 19:29

My sieve of eratosthenes implementation in Python

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