Because the way matters #python and prime numbers

gistfile1.py

N = 100000

# First approximation, brute force
def is_prime(number):
    if number == 2:
        return True
    for x in range(2, number/2+1):
        if number % x == 0:
            return False
    return True

for i in range(2, N+1):
    if is_prime(i):
        print i

# A bit of python sauce to avoid the slow velocity of Python
def is_prime(x):
    if x == 2:
        return True
    for d in xrange(2, x/2 + 1):
        if x % d == 0:
            return False
    print x

map(is_prime, [x for x in xrange(1, N+1)])

# Memoization
primes = []
def is_prime(number, primes):
    if number == 2:
        return True
    for prime in primes:
        if number % prime == 0:
            return False
    return True

for i in range(2, N+1):
    if is_prime(i, primes):
        primes.append(i)

# it's the math stupid !!!

def primes_sieve(limit):
    limitn = limit+1
    not_prime = set()
    primes = []

    for i in range(2, limitn):
        if i in not_prime:
            continue

        for f in range(i*2, limitn, i):
            not_prime.add(f)

        primes.append(i)

    return primes

primes_sieve(n)