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78 lines
2.6 KiB
Lua
78 lines
2.6 KiB
Lua
--ProjectEuler/lua/Problem27.lua
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--Matthew Ellison
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-- Created: 09-15-19
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--Modified: 09-15-19
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--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.
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--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
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--[[
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Copyright (C) 2019 Matthew Ellison
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with this program. If not, see <https://www.gnu.org/licenses/>.
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]]
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require "Stopwatch"
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require "Algorithms"
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--Setup the variables
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local timer = Stopwatch:create();
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local topA = 0; --The A for the most n's generated
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local topB = 0; --The B for the most n's generated
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local topN = 0; --The most n's generated
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local primes = getPrimes(12000) --A list of all primes that could possibly be generated with this formula
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--Start the timer
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timer:start();
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--Start with the lowest possible A and check all possibilities after that
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for a = -999, 999 do
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--Start with the lowest possible B and check all possibilities after that
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for b = -1000, 1000 do
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--Start with n=0 and check the formula to see how many primes you can get get with concecutive n's
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local n = 0;
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local quadratic = (n * n) + (a * n) + b;
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while(isFound(primes, quadratic)) do
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n = n + 1;
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quadratic = (n * n) + (a * n) + b;
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end
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n = n - 1; --Negate an n because the last formula failed
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--Set all the largest numbers if this created more primes than any other
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if(n > topN) then
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topN = n;
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topB = b;
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topA = a;
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end
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end
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end
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--Stop the timer
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timer:stop();
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--Print the results
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io.write("The greatest number of primes found is " .. topN .. '\n');
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io.write("It was found with A = " .. topA .. ", B = " .. topB .. '\n');
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io.write("The product of A and B is " .. topA * topB .. '\n');
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io.write("It took " .. timer:getString() .. " to run this algorithm\n");
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--[[ Results:
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The greatest number of primes found is 70
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It was found with A = -61, B = 971
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The product of A and B is -59231
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It took 119.350 seconds to run this algorithm
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]]
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