overflow - Python "OverflowError"

Question

I am just starting to learn to code in Python. I am trying to write some code to answer this Project Euler Question:

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?

My program works with the test case of 13195, but when I try to enter 600851475143, I get the error: "OverflowError: range() results has too many items" Does anyone know how I can fix this?

Here is my code:

class Euler3:
    "A class to find the largest prime factor of a given number"
     n = 600851475143
     primeFactors = []
     for i in range(2,n):
         if (n%i ==0):
            primeFactors.append(i)
            n = n/i
            i = i -1 #reset i
     print primeFactors

Any help or suggestions would be much appreciated!

Answer 1

The range function creates a list and tries to store it in memory. Creating a list many numbers long is what's causing the OverflowError. You can use xrange instead to get a generator which produces the numbers on demand.

That said, I think you'll find that your algorithm is way too slow for calculating large primes. There are a lot of prime number algorithms, but I might suggest checking out the Sieve of Eratosthenes as a starting point.

EDIT: Properly xrange actually doesn't return a generator, but an xrange object which behaves a lot like a generator. I'm not sure if you care, but it was bugging me that i wasn't precise!