Adopted new convention from template
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@ -1,4 +1,4 @@
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#!/usr/bin/env python3
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#!/usr/bin/env python
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"""
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Created on 12 Sep 2021
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@ -9,40 +9,42 @@ Solution for problem 46 of Project Euler
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https://projecteuler.net/problem=46
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"""
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from utils import timeit, is_prime
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from utils import is_prime, timeit
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def is_goldbach(number):
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for i in range(number - 1, 1, -1):
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if is_prime(i) and ((number - i) / 2)**0.5 % 1 == 0:
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if is_prime(i) and ((number - i) / 2) ** 0.5 % 1 == 0:
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return True
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return False
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@timeit("Problem 46")
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def compute():
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"""
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It was proposed by Christian Goldbach that every odd composite number
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It was proposed by Christian Goldbach that every odd composite number
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can be written as the sum of a prime and twice a square.
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9 = 7 + 2×1^2
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15 = 7 + 2×2^2
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21 = 3 + 2×3^2
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25 = 7 + 2×3^2
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27 = 19 + 2×2^2
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33 = 31 + 2×1^2
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9 = 7 + 2x1^2
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15 = 7 + 2x2^2
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21 = 3 + 2x3^2
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25 = 7 + 2x3^2
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27 = 19 + 2x2^2
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33 = 31 + 2x1^2
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It turns out that the conjecture was false.
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What is the smallest odd composite that cannot be written as the sum
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What is the smallest odd composite that cannot be written as the sum
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of a prime and twice a square?
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"""
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ans = 9
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while True:
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ans += 2
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if not is_prime(ans) and not is_goldbach(ans):
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return ans
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if __name__ == "__main__":
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print(f"Result for Problem 46: {compute()}")
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print(f"Result for Problem 46 is {compute()}")
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