Mersenne number

Definition

For a natural number $n$ , the $n$ -th Mersenne number is $M_n = 2^n - 1$ .

Remarks

The first values are $M_1 = 1$ , $M_2 = 3$ , $M_3 = 7$ , $M_4 = 15$ and $M_5 = 31$ . In binary, $M_n$ is written with $n$ digits $1$ . Some texts call $M_n$ a Mersenne number only when $n$ is prime. A Mersenne number that is prime is a Mersenne prime.

Where this leads

4 pages build on this one.

Lucas–Lehmer test
Mersenne prime
If 2^p − 1 is prime then p is prime
Euclid–Euler theorem

Tag	`0GJBJ19NXR`
URI	`m2://0GJBJ19NXR`
Kind	definition
Writing	W1 stated
MSC	11A41
Defines	Mersenne number

Mersenne number

Definition

Remarks

Where this leads

Further reading

What this page needs for W2

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