#!/usr/bin/env python
# -*- coding: utf-8 -*-

def count_primes(n):
    sieve = [True] * (n+1)
    sieve[0] = sieve[1] = False
    for i in range(2, int(n**0.5) + 1):
        if sieve[i]:
            for j in range(i*i, n+1, i):
                sieve[j] = False
    return sum(sieve)


print(count_primes(20))  # Outputs: 8