Project Euler Problem Number 3

Project Euler problem 3 reads as follows:

The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143 ?

There are no special Python features here that really require explaining. The logic is also straightforward: find the smallest prime that divides evenly into "number"; reset "number" to number/prime; if prime is greater than the square root of number, you have your answer. Solution works in both Python and IronPython.

def GetNextPrime(allPrimes):
    """Given a sequential list of prime numbers, return 
    the next prime number
    """
    value = allPrimes[-1]
    if value == 2:
        return 3
    
    while True:
        value += 2
        for prime in allPrimes:
            if value % prime == 0:
                break;
        else:
            return value

def Euler003(number = 600851475143):
    # import the square root function, seed the primes list
    # and determine what
    # the largest possible factor
    from math import sqrt
    primes = [2,3]
    limit = sqrt(number)
    
    # if the last prime number exceeds our limit, we're out
    while primes[-1] <= limit:
        for prime in primes:
            if number == prime:
                # if the prime and the number are the same, 
                # we've found our answer. break out of
                # the loop
                return number
            elif number % prime == 0:
                # number isn't prime! largest prime factor
                # will be in number/prime.
                number /= prime
                limit = sqrt(number)
                break
        else:
            # still didn't find number % prime == 0? Maybe
            # we need bigger prime numbers
            while primes[-1] <= limit:
                # get next prime number
                primes.append(GetNextPrime(primes))
                # if number is divisible by next prime number
                if number % primes[-1] == 0:
                    if number == primes[-1]:
                        break
                    number /= primes[-1]
                    limit = sqrt(number)
                    break
    return number

print Euler003()