# Language of strings of lengths that are prime is regular? Is C^* regular? [duplicate]

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.