Pumping Lemma with Prime Number $\text {Could someone please help me with this proof: }$
$L:=\left\{a^{n} d^{m} b^{k} | n, m, k \in \mathbb{N} \wedge m \text { is a prime number}\right\}$

$\text {Maybe we can say, that } w=a^{n}d^{m_s}b^{k} \text { and } d^{m_s} \text{ is a prime number with } |w| \ge n. \text{And we choose xyz arbitrarily with } w= xyz \text { } \wedge |y| \ge1 \wedge |xy| \le n\text {. And now I don't know how to go on. Maybe someone can help me, please.}$
Helpful property of prime numbers: The gaps between consecutive prime numbers become arbitrarily large. That means for every r, there is a prime p such that none of the numbers p+1 to p+r are primes. That means $a^nd^mb^k$ is not in the language for p+1 ≤ m ≤ p+r. 

That would generally work for "m is a member of an infinite set with arbitrarily large gaps between members of the set", like "m is a square, a cube, a factorial" and many others.