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Problem27.m

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+function [] = Problem27()
+%ProjectEuler/Octave/Problem27.m
+%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.
+%{
+	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/>.
+%}
+
+
+%Setup variables
+topA = 0;
+topB = 0;
+topN = 0;
+primeNums = primes(12000);
+
+%Start timer
+startTime = clock();
+
+
+%Start with the lowest possible A and check all possibilities after that
+for a = -999 : 999
+	%Start with the lowest possible B and check all possibilities after that
+	for b = -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(isFound(primeNums, quadratic))
+			++n;
+			quadratic = (n * n) + (a * n) + b;
+		end
+		--n;
+
+		%Set all the largest number if this creaed more primes than any other
+		if(n > topN)
+			topN = n;
+			topB = b;
+			topA = a;
+		end
+	end
+end
+
+
+%End the timer
+endTime = clock();
+
+%Print the results
+printf("The greatest number of primes found is %d", topN)
+printf("\nIt was found with A = %d, B = %d", topA, topB)
+printf("\nThe product of A and B is %d\n", topA * topB)
+printf("It took %f seconds to run this algorithm\n", etime(endTime, startTime))
+
+end
+
+function [found] = isFound(array, key)
+	found = false;	%Start with a false. It only turns true if you find key in array
+	for location = 1 : size(array)(2)
+		if(key < array(location))
+			return;
+		elseif(key == array(location))
+			found = true;
+			return;
+		end
+	end
+end
+
+%{
+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 1298.651146 seconds to run this algorithm
+%}