Problem 46

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.

9 = 7 + 21^{2}

15 = 7 + 22^{2}

21 = 3 + 23^{2}

25 = 7 + 23^{2}

27 = 19 + 22^{2}

33 = 31 + 21^{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?

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