Finished 46 with quite a quick algorithm

46/main.py

@@ -0,0 +1,60 @@
+'''
+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 + 2×12
+15 = 7 + 2×22
+21 = 3 + 2×32
+25 = 7 + 2×32
+27 = 19 + 2×22
+33 = 31 + 2×12
+
+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?
+'''
+
+# So I guess I just go past all odd non-prime numbers and keep subtracting all double squares that fit and see if the rest is a prime
+
+import math
+import numpy as np
+
+def sieve(n):
+    assert n > 1
+
+    ns = [True] * n
+
+    for i in range(2, math.ceil(np.sqrt(n))):
+        if ns[i]:
+            j = pow(i, 2)
+
+            while j < n:
+                ns[j] = False
+                j = j + i
+
+    return [i for i,val in enumerate(ns) if val][2:]
+
+def main():
+    print("Hello this is Patrick")
+
+    end = 10000
+
+    primes = set(sieve(end))
+
+    for n in range(9, end, 2):
+        termination = True
+
+        if n not in primes:
+            x = 1
+            while n - 2 * x*x > 0:
+                if n - 2 * x*x in primes:
+                    termination = False
+                    break
+                
+                x += 1
+            
+            if termination:
+                print(n)
+                break
+
+if __name__ == "__main__":
+    main()