MersennePrimeExponent

The exponent $p$ of the $n$th Mersenne prime $2^p-1$.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageMersennePrimeExponent!↗

MersennePrimeExponent(n)the $n$th known Mersenne prime's exponent

Typed signatures

Type	Package	Applies
(integer) -> integer	number-theory	always

Domain: Number theory

Details

• From a fixed table of the first 20 known Mersenne prime exponents, proven complete this far since the 1950s — well short of GIMPS's ongoing search. Past the table the call stays unevaluated rather than searching.
• Feeds PerfectNumber: the $n$th even perfect number is $2^{p-1}(2^p-1)$.

Examples

Basic #

live ↗

In$\mathrm{MersennePrimeExponent}(1)$Out$2$

live ↗

In$\mathrm{MersennePrimeExponent}(5)$Out$13$

live ↗

In$\mathrm{MersennePrimeExponent}(10)$Out$89$

Scope #

Listable

live ↗

In$\mathrm{MersennePrimeExponent}(\bigl\lbrack1, 2, 3, 4, 5, 6\bigr\rbrack)$Out$\bigl\lbrack2, 3, 5, 7, 13, 17\bigr\rbrack$

The first ten exponents $p$ with $2^p-1$ prime

live ↗

In$\mathrm{MersennePrimeExponent}(1..10)$Out$\bigl\lbrack2, 3, 5, 7, 13, 17, 19, 31, 61, 89\bigr\rbrack$

Possible issues #

Past the known table of Mersenne-prime exponents, the call stays unevaluated rather than guessing

live ↗

In$\mathrm{MersennePrimeExponent}(1\,000)$Out$\mathrm{MersennePrimeExponent}(1\,000)$

live ↗

In$\mathrm{TimeConstrained}(\mathrm{MersennePrimeExponent}(50), 10)$Out$\mathrm{MersennePrimeExponent}(50)$

About

Examples	7
Checked against	Wolfram Language 5 agree1 differ1 error
Crosswalk	Wolfram Language

See also: PerfectNumber, IsPrime