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Problem 46

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Goldbach’s Other Conjecture

It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.
$$\begin{aligned}
9 = 7 + 2\times 1^2\\
15 = 7 + 2\times 2^2\\
21 = 3 + 2\times 3^2\\
25 = 7 + 2\times 3^2\\
27 = 19 + 2\times 2^2\\
33 = 31 + 2\times 1^2
\end{aligned}$$
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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哥德巴赫的另一个猜想

克里斯蒂安·哥德巴赫曾经猜想，每个奇合数都可以写成一个素数和一个平方的两倍之和。
$$\begin{aligned}
9 = 7 + 2\times 1^2\\
15 = 7 + 2\times 2^2\\
21 = 3 + 2\times 3^2\\
25 = 7 + 2\times 3^2\\
27 = 19 + 2\times 2^2\\
33 = 31 + 2\times 1^2
\end{aligned}$$

最终这个猜想被推翻了。

不能写成一个素数和一个平方的两倍之和的最小奇合数是多少？

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