Mersenne

Read the following statements carefully:

\([1]\). For all prime numbers \(p\), \(2^p-1\) is a prime number.

\([2]\). If \(p\) is a composite number, then it is impossible for \(2^p-1\) to be a prime number.

\([3]\). Statement number \([1]\) isn't true.

Which of these statements is/are correct?

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