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Problem27.py

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+#ProjectEuler/Python/Problem27.py
+#Matthew Ellison
+# Created: 09-15-19
+#Modified: 09-15-19
+#Find the product of the coefficients, |a| < 1000 and |b| <= 1000, for the quadratic expression that produces the maximum number of primes for consecutive values of n, starting with n=0.
+#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
+"""
+	Copyright (C) 2019  Matthew Ellison
+
+	This program is free software: you can redistribute it and/or modify
+	it under the terms of the GNU Lesser General Public License as published by
+	the Free Software Foundation, either version 3 of the License, or
+	(at your option) any later version.
+
+	This program is distributed in the hope that it will be useful,
+	but WITHOUT ANY WARRANTY; without even the implied warranty of
+	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+	GNU Lesser General Public License for more details.
+
+	You should have received a copy of the GNU Lesser General Public License
+	along with this program.  If not, see <https://www.gnu.org/licenses/>.
+"""
+
+
+from Stopwatch import Stopwatch
+import Algorithms
+
+
+def Problem27():
+	#Setup the variables
+	topA = 0	#The A for the most n's generated
+	topB = 0	#The B for the most n's generated
+	topN = 0	#The most n's generated
+	primes = Algorithms.getPrimes(12000)	#A list of all primes that could possibly be generated with this formula
+
+	#Start with the lowest possible A and check all possibilities after that
+	for a in range(-999, 999):
+		#Start with the lowest possible B and check all possibilities after that
+		for b in range(-1000, 1000):
+			#Start with n=0 and check the formula to see how many primes you can get get with concecutive n's
+			n = 0
+			quadratic = (n * n) + (a * n) + b
+			while(quadratic in primes):
+				n += 1
+				quadratic = (n * n) + (a * n) + b
+			n -= 1  #Negate an n because the last formula failed
+
+			#Set all the largest numbers if this created more primes than any other
+			if(n > topN):
+				topN = n
+				topB = b
+				topA = a
+	print("The greatest number of primes found is " + str(topN))
+	print("It was found with A = " + str(topA) + ", B = " + str(topB))
+	print("The product of A and B is " + str(topA * topB))
+
+
+#This calls the appropriate functions if the script is called stand alone
+if __name__ == "__main__":
+	timer = Stopwatch()
+	timer.start()
+	Problem27()
+	timer.stop()
+	print("It took " + timer.getString() + " to run this algorithm")
+
+""" Results:
+The greatest number of primes found is 70
+It was found with A = -61, B = 971
+The product of A and B is -59231
+It took 35.775 seconds to run this algorithm
+"""