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MersennePrimeExponent[n]

gives the n^(th) Mersenne prime exponent.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Properties & Relations  
Possible Issues  
See Also
Related Guides
History
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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 49 Mersenne prime exponents have definite ranking. Three 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 49, 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 49 Mersenne prime exponents have definite ranking:

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

Wolfram Research (2016), MersennePrimeExponent, Wolfram Language function, https://reference.wolfram.com/language/ref/MersennePrimeExponent.html (updated 2025).

Text

Wolfram Research (2016), MersennePrimeExponent, Wolfram Language function, https://reference.wolfram.com/language/ref/MersennePrimeExponent.html (updated 2025).

CMS

Wolfram Language. 2016. "MersennePrimeExponent." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/MersennePrimeExponent.html.

APA

Wolfram Language. (2016). MersennePrimeExponent. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MersennePrimeExponent.html

BibTeX

@misc{reference.wolfram_2025_mersenneprimeexponent, author="Wolfram Research", title="{MersennePrimeExponent}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/MersennePrimeExponent.html}", note=[Accessed: 13-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_mersenneprimeexponent, organization={Wolfram Research}, title={MersennePrimeExponent}, year={2025}, url={https://reference.wolfram.com/language/ref/MersennePrimeExponent.html}, note=[Accessed: 13-August-2025]}