# Is this Mersenne number a prime? 61

Computer Science Level 2

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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