It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.
$$\begin{align} 9 = 7 + 2 \times 1^2\\ 15 = 7 + 2 \times 2^2\\ 21 = 3 + 2 \times 3^2\\ 25 = 7 + 2 \times 3^2\\ 27 = 19 + 2 \times 2^2\\ 33 = 31 + 2 \times 1^2 \end{align}$$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?
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