Statements (50)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Prime_Number
|
| gptkbp:category |
gptkb:Number_Theory
gptkb:Prime_Numbers |
| gptkbp:defines |
Prime numbers of the form 2^p - 1, where p is a prime number
|
| gptkbp:discoveredBy |
gptkb:Euclid
gptkb:Marin_Mersenne |
| gptkbp:firstKnown |
3
31 7 127 |
| https://www.w3.org/2000/01/rdf-schema#label |
Mersenne Primes
|
| gptkbp:largestKnownDigits |
24,862,048
|
| gptkbp:largestKnownDiscoveryYear |
2018
|
| gptkbp:largestWin |
2^82,589,933 - 1
|
| gptkbp:namedAfter |
gptkb:Marin_Mersenne
|
| gptkbp:notation |
M_p = 2^p - 1
|
| gptkbp:numberKnownAsOf2024 |
51
|
| gptkbp:openProblem |
Are there infinitely many Mersenne primes?
|
| gptkbp:property |
Mersenne primes are used in perfect number research
Mersenne primes are used in mathematical competitions Mersenne primes are used in number theory education If 2^p - 1 is prime, then (2^{p-1})(2^p - 1) is a perfect number If 2^p - 1 is prime, then p must be prime Mersenne primes are a subset of prime numbers Mersenne primes are rare for large p Mersenne primes are used in computer science Mersenne primes are used in cryptography Mersenne primes are used in large prime searches Mersenne primes are used in mathematical databases Mersenne primes are used in mathematical journals Mersenne primes are used in mathematical outreach Mersenne primes are used in mathematical proofs Mersenne primes are used in mathematical research Mersenne primes are used in mathematical software Mersenne primes are used in primality testing No known odd perfect numbers Mersenne primes are used in recreational mathematics Mersenne primes are used in random number generation Mersenne primes are used in factorization algorithms Mersenne primes are used in mathematical conferences Mersenne primes are used in distributed computing projects All known even perfect numbers are related to Mersenne primes Not all numbers of the form 2^p - 1 with p prime are prime |
| gptkbp:relatedTo |
gptkb:Lucas–Lehmer_Primality_Test
Perfect Numbers |
| gptkbp:searchableBy |
gptkb:Great_Internet_Mersenne_Prime_Search_(GIMPS)
|
| gptkbp:sequence |
gptkb:A000668
|
| gptkbp:usedIn |
Perfect Numbers
|
| gptkbp:bfsParent |
gptkb:Number_Theory
|
| gptkbp:bfsLayer |
7
|