Question

I’m trying to solve the Project Euler problem 3 in Python:

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

What is the largest prime factor of the number 600851475143 ?

I know my program is inefficient and oversized, but I just wanted to know why doesn’t it work?
Here’s the code:

def check(z):

# checks if the given integer is prime

    for i in range(2, z):
        if z % i == 0:
            return False
            break
        i = i+1
    return True

def primegen(y):
# generates a list of prime integers in the given range

    tab = []
    while y >= 2:
        if check(y) == True:
            tab.append(y)
        i = i-1


def mainfuntion(x):
# main function; prints the largest prime factor of the given integer

    primegen(x)
    for i in range(len(tab)):
        if x % tab[i] == 0:
            print tab[i]
            break

mainfuntion(600851475143)

And here’s the error:

for i in range(2, z):
OverflowError: range() result has too many items

Answer 1

The reason is that a list in Python is limited to 536,870,912 elements (see How Big can a Python Array Get?) and when you create the range in your example, the number of elements exceeds that number, causing the error.

The fun of Project Euler is figuring out the stuff on your own (which I know you’re doing 🙂 ), so I will give one very small hint that will bypass that error. Think about what a factor of a number is – you know that it is impossible for 600851475142 to be a factor of 600851475143. Therefore you wouldn’t have to check all the way up to that number. Following that logic, is there a way you can significantly reduce the range that you check? If you do a bit of research into the properties of prime factors, you may find something interesting 🙂