#!/usr/bin/env python3
# -*- coding: utf-8 -*-
########################################################################
# Solves problem 46 from projectEuler.net.
# Finds the first composite number that can't be expressed as the
# sum between a prime and twice a square.
# Copyright (C) 2010 Santiago Alessandri
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU 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 General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see .
#
# You can contact me at san.lt.ss@gmail.com
# Visit my wiki at http://san-ss.wikidot.com
########################################################################
from CommonFunctions import find_primes_less_than
def has_property(n):
index = 0
while index < len(lst_two_squares) and lst_two_squares[index] < n:
if (n - lst_two_squares[index]) in primes:
return True
index += 1
return False
primes = set(find_primes_less_than(30000))
lst_two_squares = [2 * (i ** 2) for i in range(1,2000)]
if __name__ == '__main__':
result = 9
while has_property(result):
result += 2
while result in primes:
result += 2
print("The result is:", result)