#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
"""