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Problem27.lua

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+--ProjectEuler/lua/Problem27.lua
+--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.
+--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
+--[[
+	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/>.
+]]
+
+
+require "Stopwatch"
+require "Algorithms"
+
+
+--Setup the variables
+local timer = Stopwatch:create();
+local topA = 0; --The A for the most n's generated
+local topB = 0; --The B for the most n's generated
+local topN = 0; --The most n's generated
+local primes = getPrimes(12000) --A list of all primes that could possibly be generated with this formula
+
+
+--Start the timer
+timer:start();
+
+--Start with the lowest possible A and check all possibilities after that
+for a = -999, 999 do
+	--Start with the lowest possible B and check all possibilities after that
+	for b = -1000, 1000 do
+		--Start with n=0 and check the formula to see how many primes you can get get with concecutive n's
+		local n = 0;
+		local quadratic = (n * n) + (a * n) + b;
+		while(isFound(primes, quadratic)) do
+			n = n + 1;
+			quadratic = (n * n) + (a * n) + b;
+		end
+		n = 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) then
+			topN = n;
+			topB = b;
+			topA = a;
+		end
+	end
+end
+
+
+--Stop the timer
+timer:stop();
+
+--Print the results
+io.write("The greatest number of primes found is " .. topN .. '\n');
+io.write("It was found with A = " .. topA .. ", B = " .. topB .. '\n');
+io.write("The product of A and B is " .. topA * topB .. '\n');
+io.write("It took " .. timer:getString() .. " to run this algorithm\n");
+
+--[[ 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 119.350 seconds to run this algorithm
+]]