Source code for primes

def count_primes(max):
    """
    This function is supposed to search for prime numbers up to a given maximum value. 
    
    The program uses a modified Sieve of Eratosthenes algorithm. 
    For each number, the program tests if smaller numbers divide 
    the integer being checked. 
    If no divisor is found, the number is a prime.

    Unfortunately, the program does not work.
    
    .. note ::
        This function is incomplete!
    
    Args:
        max (int): the maximum number to be tested
        
    Returns:
        int: number of prime numbers between 2 and max
    """

    i = 0
    nPrimes = 0
    isDivisible = False

    # Integer j gets values from 2 to max.
    # This is the number we check for primality.
    for j in range(2,max):

    
        #
        # Integer i is the number we test for being
        # a factor of j.
        #
        # We let i get values from 2 to sqrt(j), since
        # if j is not prime, one of its factors must
        # be at most sqrt(j) so there's no need to check 
        # larger numbers.
        #
        # If i divides j, j is not prime and we can stop
        # the search.
        #
        while i < sqrt(j) and not isDivisible:
        
            # check if i divides j
            # if it does, j is not a prime number
            if j%1 == 0:
                isDivisible = True
        
            if isDivisible:
                pass
            else:
                print( j+" is a prime number" )
                nPrimes += 1
            
    return nPrimes
       

# do this if the program is executed, not if it is loaded as a module
if __name__ == "__main__":

    # search for primes
    max = 10
    nPrimes = count_primes(max)

    # in the end, tell how many primes were found 
    print( "there are "+str(nPrimes)+" primes between 2 and "+(max) )