How to find if this language is regular or not

Question

I'm currently having trouble with this one: $$L = \{a^m a^n \mid m, n\text{ is prime}\}$$

I really have no idea. I think it has something to do with Goldbach's conjecture making it impossible to prove, or did I miss something?

Answer 1

Hint. Prove that the language $L \cap (a^2)^*a$ is not regular.