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returns True if n is a Mersenne prime exponent, and False otherwise.

Details

  • MersennePrimeExponentQ is typically used to test whether an integer is a Mersenne prime exponent.
  • A positive integer n is a Mersenne prime exponent if the Mersenne number is prime.
  • MersennePrimeExponentQ[n] returns False unless n is manifestly a Mersenne prime exponent.

Examples

open allclose all

Basic Examples  (2)Summary of the most common use cases

Test whether a number is a Mersenne prime exponent:

Out[1]=1

The number is not a Mersenne prime exponent:

Out[1]=1

Scope  (3)Survey of the scope of standard use cases

MersennePrimeExponentQ works over integers:

Out[2]=2

Negative integers are not Mersenne prime exponents:

Out[1]=1

Noninteger numbers are not Mersenne prime exponents:

Out[1]=1

Applications  (8)Sample problems that can be solved with this function

Basic Applications  (3)

Highlight Mersenne prime exponents:

Out[4]=4

Generate random Mersenne prime exponents:

Out[2]=2
Out[3]=3

Digits of a Mersenne prime :

Out[1]=1
Out[2]=2

Special Sequences  (2)

Recognize Mersenne numbers, numbers of the form :

Out[4]=4

The number is a Mersenne number; is not:

Out[2]=2
Out[3]=3

Recognize Gaussian Mersenne primes, prime numbers n such that is a Gaussian prime:

Out[2]=2

Number Theory  (3)

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

Out[1]=1
Out[3]=3
Out[4]=4

If p is a Mersenne prime exponent, then is a perfect number:

Out[1]=1
Out[2]=2

Every even perfect number has the form , where p is a Mersenne prime exponent:

Out[1]=1
Out[2]=2

Check that in the representation above p is 5:

Out[3]=3
Out[4]=4

Properties & Relations  (10)Properties of the function, and connections to other functions

Mersenne prime exponents are prime numbers:

Out[5]=5

Composite numbers cannot be MersennePrimeExponents:

Out[1]=1
Out[2]=2

The only even Mersenne prime exponent is :

Out[1]=1

MersennePrimeExponent gives Mersenne prime exponent:

Out[1]=1
Out[3]=3

is a Mersenne prime, where p is a Mersenne prime exponent:

Out[1]=1
Out[2]=2

If p is a Mersenne prime exponent, then is a perfect number:

Out[1]=1
Out[2]=2

Every even perfect number has the form , where p is a Mersenne prime exponent:

Out[1]=1
Out[2]=2

Check that in the representation above p is 5:

Out[3]=3
Out[4]=4

Triangular numbers of Mersenne primes are perfect numbers:

Out[2]=2

Hexagonal numbers related to Mersenne prime exponents are perfect numbers:

Out[2]=2

Find Mersenne prime exponents:

Out[1]=1
Out[2]=2

Possible Issues  (1)Common pitfalls and unexpected behavior

Expressions that represent Mersenne prime exponents but do not evaluate explicitly will give False:

Out[4]=4

It is necessary to use symbolic simplification first:

Out[5]=5

Neat Examples  (1)Surprising or curious use cases

The minor planet 8191 Mersenne is named after Marin Mersenne:

Out[1]=1

The number is a Mersenne prime:

Out[2]=2
Out[3]=3
Wolfram Research (2016), MersennePrimeExponentQ, Wolfram Language function, https://reference.wolfram.com/language/ref/MersennePrimeExponentQ.html.
Wolfram Research (2016), MersennePrimeExponentQ, Wolfram Language function, https://reference.wolfram.com/language/ref/MersennePrimeExponentQ.html.

Text

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

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

CMS

Wolfram Language. 2016. "MersennePrimeExponentQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MersennePrimeExponentQ.html.

Wolfram Language. 2016. "MersennePrimeExponentQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MersennePrimeExponentQ.html.

APA

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

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

BibTeX

@misc{reference.wolfram_2024_mersenneprimeexponentq, author="Wolfram Research", title="{MersennePrimeExponentQ}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/MersennePrimeExponentQ.html}", note=[Accessed: 08-January-2025 ]}

@misc{reference.wolfram_2024_mersenneprimeexponentq, author="Wolfram Research", title="{MersennePrimeExponentQ}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/MersennePrimeExponentQ.html}", note=[Accessed: 08-January-2025 ]}

BibLaTeX

@online{reference.wolfram_2024_mersenneprimeexponentq, organization={Wolfram Research}, title={MersennePrimeExponentQ}, year={2016}, url={https://reference.wolfram.com/language/ref/MersennePrimeExponentQ.html}, note=[Accessed: 08-January-2025 ]}

@online{reference.wolfram_2024_mersenneprimeexponentq, organization={Wolfram Research}, title={MersennePrimeExponentQ}, year={2016}, url={https://reference.wolfram.com/language/ref/MersennePrimeExponentQ.html}, note=[Accessed: 08-January-2025 ]}