Goldbach's Lesser Conjecture

False Conjecture
Every positive odd integer $n$ can be expressed in the form:
 * $n = 2 a^2 + p$

where:
 * $a \in \Z_{\ge 0}$ is a non-negative integer
 * $p$ is a prime number or $1$.

Refutation
There are two known counterexamples:
 * $5777$ and $5993$

as follows: