MersennePrimeExponentQ
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MersennePrimeExponentQ
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 allBasic Examples (2)Summary of the most common use cases
Scope (3)Survey of the scope of standard use cases
MersennePrimeExponentQ works over integers:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-tljmzg
Negative integers are not Mersenne prime exponents:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-uvzq00
Noninteger numbers are not Mersenne prime exponents:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-k7132b
Applications (8)Sample problems that can be solved with this function
Basic Applications (3)
Highlight Mersenne prime exponents:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-yh43l
Generate random Mersenne prime exponents:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-e15ejf
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-bwk494
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-cu2my6
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-dqedo
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-3xz21
Special Sequences (2)
Recognize Mersenne numbers, numbers of the form :
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-goll8y
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-exahzh
The number is a Mersenne number; is not:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-uwdrlw
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-clrb27
Recognize Gaussian Mersenne primes, prime numbers n such that is a Gaussian prime:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-czd2jj
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-b7rsdv
Number Theory (3)
A trinomial whose order is a Mersenne prime exponent is primitive modulo if and only if it is irreducible:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-c5g8uz
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-mlo7fy
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-6uqqsv
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-pt450w
If p is a Mersenne prime exponent, then is a perfect number:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-bxwgix
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-cgl01
Every even perfect number has the form , where p is a Mersenne prime exponent:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-grf6jv
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-gf48vx
Check that in the representation above p is 5:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-kpphrj
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-ceo7ld
Properties & Relations (10)Properties of the function, and connections to other functions
Mersenne prime exponents are prime numbers:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-hdqnbn
Composite numbers cannot be MersennePrimeExponents:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-blul38
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-c5un5t
The only even Mersenne prime exponent is :
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-oefyfe
MersennePrimeExponent gives Mersenne prime exponent:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-fl5q3k
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-dkw2m0
is a Mersenne prime, where p is a Mersenne prime exponent:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-db5157
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-j50oah
If p is a Mersenne prime exponent, then is a perfect number:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-l1ix6
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-elpe2o
Every even perfect number has the form , where p is a Mersenne prime exponent:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-h4lq3
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-jlb7jz
Check that in the representation above p is 5:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-nknu8g
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-ekfwh8
Triangular numbers of Mersenne primes are perfect numbers:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-i6f7h4
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-3vgv7
Hexagonal numbers related to Mersenne prime exponents are perfect numbers:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-mlidf
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-k4oip
Find Mersenne prime exponents:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-n63f3p
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-kuntq6
Possible Issues (1)Common pitfalls and unexpected behavior
Expressions that represent Mersenne prime exponents but do not evaluate explicitly will give False:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-j0etnt
It is necessary to use symbolic simplification first:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-d68e28
Neat Examples (1)Surprising or curious use cases
The minor planet 8191 Mersenne is named after Marin Mersenne:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-pulpqy
The number is a Mersenne prime:
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-x5v15r
https://wolfram.com/xid/0czdeuzsar0knzrjkcj-265pc4
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
]}
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
]}