Simple prime number generator in Python

There are some problems:

• Why do you print out count when it didn't divide by x? It doesn't mean it's prime, it means only that this particular x doesn't divide it
• continue moves to the next loop iteration - but you really want to stop it using break

Here's your code with a few fixes, it prints out only primes:

import mathdef main():    count = 3        while True:        isprime = True                for x in range(2, int(math.sqrt(count) + 1)):            if count % x == 0:                 isprime = False                break                if isprime:            print count                count += 1

For much more efficient prime generation, see the Sieve of Eratosthenes, as others have suggested. Here's a nice, optimized implementation with many comments:

# Sieve of Eratosthenes# Code by David Eppstein, UC Irvine, 28 Feb 2002# http://code.activestate.com/recipes/117119/def gen_primes():    """ Generate an infinite sequence of prime numbers.    """    # Maps composites to primes witnessing their compositeness.    # This is memory efficient, as the sieve is not "run forward"    # indefinitely, but only as long as required by the current    # number being tested.    #    D = {}        # The running integer that's checked for primeness    q = 2        while True:        if q not in D:            # q is a new prime.            # Yield it and mark its first multiple that isn't            # already marked in previous iterations            #             yield q            D[q * q] = [q]        else:            # q is composite. D[q] is the list of primes that            # divide it. Since we've reached q, we no longer            # need it in the map, but we'll mark the next             # multiples of its witnesses to prepare for larger            # numbers            #             for p in D[q]:                D.setdefault(p + q, []).append(p)            del D[q]                q += 1

Note that it returns a generator.

def is_prime(num):    """Returns True if the number is prime    else False."""    if num == 0 or num == 1:        return False    for x in range(2, num):        if num % x == 0:            return False    else:        return True>> filter(is_prime, range(1, 20))  [2, 3, 5, 7, 11, 13, 17, 19]

We will get all the prime numbers upto 20 in a list.I could have used Sieve of Eratosthenes but you saidyou want something very simple. ;)

re is powerful:

import redef isprime(n):    return re.compile(r'^1?$|^(11+)\1+$').match('1' * n) is Noneprint [x for x in range(100) if isprime(x)]###########Output#############[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]