5) Consider the following languages: PRIME = {ai where i is a prime number}, PRIME′ = {ai where i is not prime} i) Prove that PRIME′ is nonregular (hint: prove that PRIME is nonregular first - this is a challenge, since you'll have to choose your pumping factor K in a very clever way) ii) Show that PRIME′ does satisfy the pumping lemma (that is, it can't be proven nonregular using the pumping lemma) iii) How can this be? g