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problems/003_problem/003_problem.py

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+#!/usr/bin/env python
+
+#  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():
+
+	orig = 600851475143
+	result1 = orig
+	prime_start = 2
+	returned_prime = prime_start
+	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()