## Project Euler
## Problem 3
##
## The prime factors of 13195 are 5, 7, 13 and 29.
##
## What is the largest prime factor of the number 600851475143 ?

#the number we want to find
number = 600851475143

listprimes = []
result = [] #empty lists we will use later

#function to check if number is prime
def isprime(n):
    if n < 2:
        return False
    if n == 2:
        return True
    if not n & 1:
        return False
    for x in range(3, int(n**0.5)+1, 2):
        if n % x == 0:
            return False
    return True

print('Generating list...')

#generates a list of the first 10k prime numbers (arbitrary)
for i in range(1, 10001):
    test = isprime(i)
    if test == True:
        listprimes.append(i)
        print('Added '+str(i)+' to the list.')

print('Verifying divisors...')
i = 0 #starts up counter

try:
    while True:
        if number % listprimes[i] == 0:  ## this test checks if the number is divisible by the prime
            result.append(listprimes[i])              ## if it is, the number is added to a list
            print('Divisible by '+str(listprimes[i])) ## and it tells you so
        else:
            print('Not divisible by '+str(listprimes[i])) #if it isn't, it also tells you.
        i += 1 #moves the counter one position ahead
except IndexError:
    print('End of primes list')

print(result)