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

import decorators
import time

# Create function that finds the next
# prime number when supplied with an
# intitial integer.

def primes_gen(start_n,max_n):
	"""
	Returns a generator object, containing the 
	primes inside a specified range.

		primes_gen(start_n,max_n)

			param 'start_n': Previous prime.
			param 'max_n': Maximum 

	"""

	start_n += 1
	for candidate in range(start_n,max_n):
		notPrime = False
		
		if candidate in [0,1,2,3]:
			yield candidate

		for dividend in range(2,candidate):
			
			if candidate%dividend == 0:
				notPrime = True
		
		if not notPrime:
			yield candidate

@decorators.function_timer
def main():

	result1 = orig = 600851475143
	returned_prime = prime_start = 2
	prime_factor_list = []

	while returned_prime < orig ** 0.5 and returned_prime<result1:
		

		returned_prime = primes_gen(prime_start,orig).__next__()

		result2 = result1/returned_prime
		if result1%returned_prime == 0:	
			#print(" {} / {} = {}".format(result1,returned_prime,result2))
			prime_factor_list.append(returned_prime)
			result1 = result2
		prime_start = returned_prime
	
	print("This highest prime factor of {} is {} ... ".format(orig,max(prime_factor_list)))

main()