Over the alphabet $\Sigma=\{a,b\}$, we define $$L=\{a^pb^m: p\text{ is prime }, m>0\}+\{a^r:r\geq 0\}.$$
I must show that this laguage is not regular using the pumping lemma. I guess I should apply it to a word of the form $a^pb^m$, and my intuition is that I should come to the contradiction of $p$ not being prime. But I'm not very familiar with the pumping lemma, this is my first try, so I'll appreciate any hint in order to choose a word $x=a^pb^m$ with $p+m\geq n$ ($n$ from the lemma) which yields a contradiction.