Simple prime number generator in Python

Solution 1:

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 math

def 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.

Solution 2:

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 said you want something very simple. ;)

Solution 3:

re is powerful:

import re


def isprime(n):
    return re.compile(r'^1?$|^(11+)\1+$').match('1' * n) is None

print [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]

Solution 4:

print [x for x in range(2,100) if not [t for t in range(2,x) if not x%t]]

Solution 5:

def primes(n): # simple sieve of multiples 
   odds = range(3, n+1, 2)
   sieve = set(sum([list(range(q*q, n+1, q+q)) for q in odds], []))
   return [2] + [p for p in odds if p not in sieve]

>>> primes(50)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]

To test if a number is prime:

>>> 541 in primes(541)
True
>>> 543 in primes(543)
False