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Consider the following language

$$\mathsf{PRIMES} = \Biggl\{ \underbrace{111 \dots 11}_{p \: \text{ times} } : \: p \: \text{ is prime } \Biggl\}$$

Then, which of the following is TRUE?

  1. $\mathsf{PRIMES}$ is regular
  2. $\mathsf{PRIMES}$ is undecidable
  3. $\mathsf{PRIMES}$ is decidable in polynomial time
  4. $\mathsf{PRIMES}$ is context free but not regular
  5. $\mathsf{PRIMES}$ is NP-complete and P $\neq$ NP
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The language is $\{1^p \ | \ p \ is \ prime\}$, which is wel-known to be CSL.

Option C

Answer:

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