Solution to problem 46

src/Python/Problem046.py

@@ -0,0 +1,48 @@
+#!/usr/bin/env python3
+"""
+Created on 12 Sep 2021
+
+@author: David Doblas Jiménez
+@email: daviddoji@pm.me
+
+Solution for problem 46 of Project Euler
+https://projecteuler.net/problem=46
+"""
+
+from utils import timeit, is_prime
+
+def is_goldbach(number):
+    for i in range(number - 1, 1, -1):
+        if is_prime(i) and ((number - i) / 2)**0.5 % 1 == 0:
+            return True
+    return False
+
+@timeit("Problem 46")
+def compute():
+    """
+    It was proposed by Christian Goldbach that every odd composite number 
+    can be written as the sum of a prime and twice a square.
+
+    9 = 7 + 2×1^2
+    15 = 7 + 2×2^2
+    21 = 3 + 2×3^2
+    25 = 7 + 2×3^2
+    27 = 19 + 2×2^2
+    33 = 31 + 2×1^2
+
+    It turns out that the conjecture was false.
+
+    What is the smallest odd composite that cannot be written as the sum 
+    of a prime and twice a square?
+    """
+    ans = 9
+    while True:
+        ans += 2
+        if not is_prime(ans) and not is_goldbach(ans):
+            return ans
+            
+
+
+if __name__ == "__main__":
+
+    print(f"Result for Problem 46: {compute()}")