### Original

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?

### 和訳

Christian Goldbachは全ての奇合成数は平方数の2倍と素数の和で表せると予想した.

• 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

### 当てにならないソースコード(C#)

 12345678910111213141516171819202122232425262728293031 using System; namespace ProjectEuler {     class Problem46 : Problem{         public Problem46() {             int answer = 0;             bool found = true;             Primes p = new Primes();             for (int i = 9; found; i += 2) {                 if (!IsOddComposite(i))                     continue;                 found = false;                 for (int j = 1; 2 * j * j < i && !found; j++) {                     if (p.IsPrime(i - 2 * j * j))                         found = true;                 }                 if (!found)                     answer = i;             }             Console.WriteLine(">" + answer);         }         bool IsOddComposite(int n) {             int root = (int)Math.Sqrt(n);             for (long i = 3; i<=root;i+=2 )                 if (n % i == 0)                     return true;             return false;         }     } }