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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.

TheSalamander
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  • What have you tried? Have you tried any of the techniques found in our reference questions, http://cs.stackexchange.com/q/1331/755 and http://cs.stackexchange.com/q/1031/755? We discourage questions that just copy the statement of an exercise and ask us to solve it for you, but if you've made an attempt to self-study this area and apply standard techniques, then editing the question to include that information will help you obtain better answers. – D.W. Oct 13 '15 at 07:43
  • Also, searching on regular unary on this site immediately finds relevant questions: http://cs.stackexchange.com/q/10555/755, http://cs.stackexchange.com/q/21765/755, http://cs.stackexchange.com/q/16293/755, http://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. – D.W. Oct 13 '15 at 07:49

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