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72 lines
2.6 KiB
Python
72 lines
2.6 KiB
Python
#ProjectEuler/Python/Problem27.py
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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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#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
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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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from Stopwatch import Stopwatch
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import Algorithms
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def Problem27():
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#Setup the variables
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topA = 0 #The A for the most n's generated
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topB = 0 #The B for the most n's generated
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topN = 0 #The most n's generated
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primes = Algorithms.getPrimes(12000) #A list of all primes that could possibly be generated with this formula
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#Start with the lowest possible A and check all possibilities after that
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for a in range(-999, 999):
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#Start with the lowest possible B and check all possibilities after that
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for b in range(-1000, 1000):
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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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n = 0
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quadratic = (n * n) + (a * n) + b
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while(quadratic in primes):
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n += 1
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quadratic = (n * n) + (a * n) + b
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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):
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topN = n
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topB = b
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topA = a
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print("The greatest number of primes found is " + str(topN))
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print("It was found with A = " + str(topA) + ", B = " + str(topB))
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print("The product of A and B is " + str(topA * topB))
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#This calls the appropriate functions if the script is called stand alone
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if __name__ == "__main__":
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timer = Stopwatch()
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timer.start()
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Problem27()
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timer.stop()
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print("It took " + timer.getString() + " to run this algorithm")
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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 35.775 seconds to run this algorithm
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"""
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