Puzzle 3 without cheating

I am about 2800 times slower than the cheat I downloaded. But I get the right answer, and in a tolerable time (30 seconds). Pure brute forcing this seems like it would take much longer.

from sys import argv
from math import sqrt
from time import time

# PRIME GENERATOR

def nextprime():
    """ generate next prime """

    myprimes = [2]
    candidate = 3
    yield 2
    while True:
        factors = factorize(candidate,myprimes)
        if len(factors.keys()) == 1:
            myprimes.append(candidate)
            yield candidate
        candidate += 2

def primesupto(upto):
    """ collect primes from the generator"""

    result = []
    primes = nextprime()
    p = None
    while not p or p < upto:
        if p:
            result.append(p)
        p = primes.next()
    return result

def factorize(target,allprimes=None,verbose=False):
    """ get factors of an integer

    this works but is very slow if the primes aren't cached """

    factors = {}
    upto = int(sqrt(target))
    residual = target
    prime = nextprime()

    if allprimes:
        prime = allprimes.__iter__()

    while True:  # get factors and multiplicities up to sqrt(N)
        try:
            factor = prime.next()
        except StopIteration:
            break
        if factor > upto:
            break
        while not residual % factor:
            residual /= factor
            factors[factor] = factors.get(factor,0) + 1           

    if residual > 1: # if anything is left it is the sole prime factor > sqrt(N)
        factors[residual] = 1

    return factors
   
if __name__ == "__main__":
    target = int(argv[1]) # get target from command line
    upto = sqrt(target)
    starttime = time()
    allprimes = primesupto(upto)
    print max(factorize(int(argv[1]),allprimes).keys())
    endtime = time()
    print endtime - starttime

Update:

Best answer, wow!

from time import time
from sys import argv

n = int(argv[1])
d = 3

starttime = time()
while (d * d < n):
   if n % d == 0: n /= d
   else: d += 2
endtime = time()
print n
print endtime - startime

Runs in 0.7 msec. I feel like a complete idiot now. Oh well, it was interesting anyway.