How can I prove this language is not CFL?
The easiest way goes as follows: if $L$ were context-free than so $L \cap a^*$ would be. Now $L' = L \cap a^* = \{ a^m : m \text{ is prime}\}$ is a unary language, so $L'$ is context-free iff it is regular iff it is eventually periodic. If it were eventually periodic then it would be either finite or have finite asymptotic density, but we know that primes are infinite and have zero asymptotic density.

You can also prove that $L'$ is not context-free using the pumping lemma. The pumping lemma shows that for some $p$, every prime $q &gt; p$ satisfies the following: there is $1 \leq t \leq p$ such that $q + (\ell-1)t$ is prime for all $\ell$. Choosing $\ell = q+1$, we get that $q(t+1)$ has to be prime, which it isn't.