MersennePrimeExponent

MersennePrimeExponent[n]

gives the n^(th) Mersenne prime exponent.

Details

  • A Mersenne prime exponent is a prime number p for which the Mersenne number is prime.
  • In MersennePrimeExponent[n], n must be a positive integer.
  • As of this version of the Wolfram Language, only 47 Mersenne prime exponents have definite ranking. Four more Mersenne prime exponents are known, but their ranking is still unknown. MersennePrimeExponent[n] will attempt to find Mersenne prime exponents for n larger than 47, but cannot be expected to return results in a reasonable time.

Examples

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Basic Examples  (1)

Return the first ten Mersenne prime exponents:

Construct the corresponding Mersenne primes:

Check that they are all primes:

Scope  (1)

MersennePrimeExponent automatically threads over lists:

Properties & Relations  (5)

Mersenne prime exponents generate even perfect numbers:

Triangular numbers of Mersenne primes generate even perfect numbers:

Hexagonal numbers related to Mersenne prime exponents generate even perfect numbers:

Mersenne prime exponents generate superperfect numbers:

A trinomial whose order is a Mersenne prime exponent is primitive modulo 2 if and only if it is irreducible:

Possible Issues  (1)

As of this version of the Wolfram Language, only 47 Mersenne prime exponents have definite ranking:

Four more Mersenne prime exponents are known, but their ranking is still unknown:

Introduced in 2016
 (10.4)