Is it true that :
If $a^n+n^{a}$ is prime number and $a=3k-1$ then $n\equiv 0\pmod 3$
where $a>1,n>1 ; a,n,k \in \mathbb{Z^+}$
I have checked statement for many pairs $(a,n)$ and it seems to be true.
Small Maple code that prints $(a,n)$ pairs :
Any idea how to prove this statement ?