Question

I have a code to calculate highest prime factor of 600851475143.

def PRIME(a):                #Check if no is prime
    f = 0
    i = 2
    while(i < a/2):          #No factor of a no can be greater than a/2
        if (a % i == 0):
            f = 1
            break
        i = i + 1

    if(f == 1):
        return 0
    else:
        return 1


def PFIND(a):
    for i in range(1, 100000):   #Iteratively check if the no is prime
        if PRIME(a/2 - i):       #No factor of a no can be greater than a/2.
            if (a % (a/2 - i) == 0):
                return (a/2 - i)
print PFIND(600851475143)

But the code runs on and on and on and does’nt give any output.

Answer 1

Python’s support for large integers is fine. I think your problem is that you’re doing very slow algorithms for both brute-force finding the factor and testing whether your factor is prime. If you just invert the order of those two tests (ie, test whether it’s a factor, then test whether it’s prime), it’ll go a lot faster.

But perhaps the problem was about using more sophisticated algorithms. Maybe you should use the Rabin-Miller test instead of brute-force.