Mersenne prime

This article defines a property that can be evaluated for a prime number. In other words, every prime number either satisfies this property or does not satisfy this property.
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Definition

A Mersenne prime is a Mersenne number that is also a prime number. In other words, it is a number of the form $M_{n}=2^{n}-1$ that is prime, where $n$ is a natural number.

It turns out that if $M_{n}$ is prime, then $n$ itself is also prime, though the converse is not true (the smallest counterexample is $n=11$, because $M_{11}=2047=23\cdot 89$).