function: factor_integer()

# function: factor_integer()

def factor_integer(n):
    """
    prints the integer and the list of its factors

    E.g.
    >>> factor_integer(198273646782734)
    198,273,646,782,734 [2, 17, 2243, 2599900957]

    Employs a data file of primes to 100 million (5,761,459 primes),
       thereby ensuring quick factorization of any integer up to
       10 quadrillion (1e17).

    This data file may be downloaded from
       http://www.rcblue.com/Misc2/primes_to_100_million.dat

    gmpy2 is available at http://code.google.com/p/gmpy/
    """
    import pickle
    import os.path
    import gmpy2
    from gmpy2 import is_prime

    def int_commas(n):
        """
        inserts commas into integers and returns the string

        E.g. -12345678 -> -12,345,789
        """
        return format(n, ',d')

    def test_of_list_of_prime_factors_of_int(n, list_):
        """
        Remains silent unless error detected.
        """
        error_flag = 0
        for e in list_:
            if not is_prime(e):
                error_flag = 1
                print(e, "is not prime!")
        if error_flag == 1:
            print("Not all elements of list of factors are prime! (n = ", n,")", sep='')
        product = 1
        for e in list_:
            product *= e
        if n != product:
            print("Product of factors doesn't equal n! (n = ", n,")", sep='')

    def load_pickled_data(path):

        if os.path.getsize(path) == 0:
            #The file exists, but is empty: leave it alone
            pass

        elif os.path.exists(path):
            #The file exists and is not empty: use it
            with open(path, "rb") as f:
                data = pickle.load(f)

        D = data
        primes = D
        return primes

    def int_factors(n, primes):
        factors = []
        #limit = int(n**.5) + 1

        if is_prime(n):
            return [int(n)]

        if n == 1:
            return []

        for x in primes:
            while n % x == 0:
                factors.append(int(x))
                n = n // x
                if is_prime(n):
                    factors.append(int(n))
                    return factors
        while True:

            x += 2

            while n % x == 0:
                factors.append(int(x))
                n = n // x
                if is_prime(n):
                    factors.append(n)
                    return factors

    path = 'C:\P32Working\Data\primes_to_100_million.dat'
    primes = load_pickled_data(path)
    factors = int_factors(n, primes)
    test_of_list_of_prime_factors_of_int(n, factors)
    print(int_commas(n), factors)

print(factor_integer(94583726378))

"""
OUTPUT:
94,583,726,378 [2, 19, 2489045431]
"""