Prime factor of 300 000 000 000?

Question

I need to find out the prime factors of over 300 billion. I have a function that is adding to the list of them...very slowly! It has been running for about an hour now and i

Answer 1

Your algorithm must be FUBAR. This only takes about 0.1s on my 1.6 GHz netbook in Python. Python isn't known for its blazing speed. It does, however, have arbitrary precision integers...

import math
import operator

def factor(n):
    """Given the number n, to factor yield a it's prime factors.
    factor(1) yields one result: 1. Negative n is not supported."""
    M = math.sqrt(n)  # no factors larger than M
    p = 2             # candidate factor to test
    while p <= M:     # keep looking until pointless
        d, m = divmod(n, p)
        if m == 0:
            yield p   # p is a prime factor
            n = d     # divide n accordingly
            M = math.sqrt(n)  # and adjust M
        else:
            p += 1    # p didn't pan out, try the next candidate
    yield n  # whatever's left in n is a prime factor

def test_factor(n):
    f = factor(n)
    n2 = reduce(operator.mul, f)
    assert n2 == n

def example():
    n = 600851475143
    f = list(factor(n))
    assert reduce(operator.mul, f) == n
    print n, "=", "*".join(str(p) for p in f)

example()

# output:
# 600851475143 = 71*839*1471*6857

(This code seems to work in defiance of the fact that I don't know enough about number theory to fill a thimble.)