Goldbach's Lesser Conjecture/5777

Goldbach's Lesser Conjecture: $5777$ is a Stern Number
The number $5777$ cannot be represented in the form:
 * $5777 = 2 a^2 + p$

where:
 * $a \in \Z_{\ge 0}$ is a non-negative integer
 * $p$ is a prime number.

Proof
It will be shown that for all $a$ such that $2 a^2 \le 5777$, it is never the case that $5777 - 2 a^2$ is prime.

Thus:

That exhausts all $a$ such that $2 a^2 \le 5775$, as $2 \times 54^2 = 5832$.

Hence the result.