Even numbers has the form $a+b$ where $\frac{a^2+b^2}{2}$ is prime

Question

Conjecture:
All even numbers $n>2$ can be written $n=a+b$ where $a,b\in\mathbb N^+$ and $\frac{a^2+b^2}{2}\in\mathbb P$.

Is tested for $n<10,000,000$.

This conjecture is related to and maybe dependent on Any odd number is of form $a+b$ where $a^2+b^2$ is prime.