#  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

#def treat_evens(n):
#	mod_is_zero = True
#	done = True
#	dividend = 2
#	while mod_is_zero or done:
#		done = dividend == n
#		num = n/dividend
#		mod_is_zero = 0 == n%dividend
#		dividend *= 2
#	print("{}".format(num))
#	return num

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

def return_next_prime(start_n,max_n):

	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():

	orig = 600851475143
	start = 3
	returned_prime = start
	while returned_prime < orig:
		returned_prime = return_next_prime(start,orig).__next__()
		print("A PRIME HAS BEEN FOUND!!!! ... {}".format(returned_prime))
		start = returned_prime

main()