With $\Sigma = \{a\}$ I want to see if a language $C = \{a^p \ | \ p \ \text{is prime}\}$ is regular and whether or not $C^*$ is regular.
How would I go about showing whether $C$ or $C^*$ are regular? I know I can construct a DFA/NFA to accept them but I am very confused about the fact that there are an infinite number of primes.
regular unaryon this site immediately finds relevant questions: cs.stackexchange.com/q/10555/755, cs.stackexchange.com/q/21765/755, cs.stackexchange.com/q/16293/755, cs.stackexchange.com/q/4984/755. We expect you to make a significant effort to search for answers before asking; the search bar in upper-right is helpful for this. $\endgroup$