Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Prime_Number
|
| gptkbp:application |
computer science
cryptography random number generation |
| gptkbp:category |
integer sequence
special prime numbers |
| gptkbp:definedIn |
prime number of the form 2^p - 1 where p is prime
|
| gptkbp:discoveredBy |
gptkb:Great_Internet_Mersenne_Prime_Search_(GIMPS)
|
| gptkbp:firstKnown |
3
31 7 127 |
| gptkbp:largestWin |
2^82,589,933-1 (as of 2018)
|
| gptkbp:namedAfter |
gptkb:Marin_Mersenne
|
| gptkbp:notation |
M_p = 2^p - 1
|
| gptkbp:OEIS |
gptkb:A000668
|
| gptkbp:openProblem |
infinitude of Mersenne primes
|
| gptkbp:property |
if 2^p-1 is prime, then p must be prime
not all numbers of the form 2^p-1 with p prime are prime |
| gptkbp:relatedTo |
gptkb:Euclid–Euler_theorem
gptkb:Lucas–Lehmer_primality_test |
| gptkbp:sequence |
3, 7, 31, 127, 8191, 131071, 524287, 2147483647, ...
|
| gptkbp:studiedIn |
number theory
|
| gptkbp:usedIn |
perfect numbers
|
| gptkbp:bfsParent |
gptkb:Marin_Mersenne
|
| gptkbp:bfsLayer |
6
|