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

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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.

## marked as duplicate by D.W.♦Oct 13 '15 at 7:49

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