import os
import numpy as np


# Find the largest prime factor of 600851475143


def isDivisible(n, ms):
    res = False
    for m in ms:
        if n % m == 0:
            res = True
            break
    return res


def getNextPrime(ps):
    if len(ps) == 0:
        return [2]
    else:
        p = ps[-1] + 1
        while isDivisible(p, [q for q in ps if q <= np.sqrt(p)]):
            p = p + 1
        ps.append(p)
        return ps

def findFactors(n):
    ps = [2]
    res = []
    rest = n
    stop = np.sqrt(n)

    while rest != 1:
        if rest % ps[-1] == 0:
            res.append(ps[-1])
            rest = rest / ps[-1]
        else:
            ps = getNextPrime(ps)
            if stop < ps[-1]:
                break
    return res



def main():
    print("Hello, this is Patrick")

    number = 600851475143
    fs = findFactors(number)

    print(max(fs))


if __name__ == "__main__":
    main()