A *Mersenne prime* is a prime number defined by \( M_{n} = 2^{n} - 1 \) and \( n \) is an integer. For some cases of \( n \), it's a prime but some cases, it does not.

Is \( M_{61} \) a prime?

As an explicit example, \( M_{2} = 2^{2} - 1 = 3 \), which is an obvious prime number. And \( M_{10} = 2^{10} - 1 = 1023 =3\times 11\times31\) which is a composite number.

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