Statements (45)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
integer sequence
|
| gptkbp:definedIn |
numbers of the form 2^n - 1
|
| gptkbp:eighthMersennePrime |
2147483647
|
| gptkbp:fifthMersennePrime |
8191
|
| gptkbp:first_terms |
1
15 3 31 63 7 127 255 511 1023 |
| gptkbp:firstMersennePrime |
3
|
| gptkbp:fourthMersennePrime |
127
|
| https://www.w3.org/2000/01/rdf-schema#label |
Mersenne numbers
|
| gptkbp:namedAfter |
gptkb:Marin_Mersenne
|
| gptkbp:OEIS |
gptkb:A000225
|
| gptkbp:property |
M_n = 2^n - 1
all even perfect numbers are related to Mersenne primes Mersenne numbers are used in GIMPS (Great Internet Mersenne Prime Search) Mersenne numbers are used in distributed computing projects Mersenne numbers are used in random number generation Mersenne numbers are a subset of repunit numbers in base 2 Mersenne numbers are always odd for n > 0 Mersenne numbers are used in computer science Mersenne numbers are used in primality testing Mersenne numbers grow exponentially binary representation is all 1s if 2^n - 1 is prime, n must be prime if n is composite, 2^n - 1 is composite |
| gptkbp:relatedTo |
gptkb:Mersenne_primes
gptkb:Lucas–Lehmer_test perfect numbers |
| gptkbp:secondMersennePrime |
7
|
| gptkbp:sequence |
M_n = 2^n - 1
|
| gptkbp:seventhMersennePrime |
524287
|
| gptkbp:sixthMersennePrime |
131071
|
| gptkbp:thirdMersennePrime |
31
|
| gptkbp:usedIn |
cryptography
number theory perfect numbers |
| gptkbp:bfsParent |
gptkb:Lucas–Lehmer_primality_test
|
| gptkbp:bfsLayer |
8
|