Task 46

The Question

2. A composite number n is a positive integer n > 1which is not prime number. 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+2x2^2
21 = 3 + 2×3^2
25=7+2x3^2
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?

The solution to the problem is 5777