## Goldbach's other conjecture

### Problem 46

Published on Friday, 20th June 2003, 06:00 pm; Solved by 38054; Difficulty rating: 5%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?