Statements (35)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
gptkb:Prime_Number |
| gptkbp:alsoKnownAs |
safe prime precursor
|
| gptkbp:application |
cryptography
public key cryptography |
| gptkbp:category |
gptkb:Number_theory
Prime numbers Mathematical sequences |
| gptkbp:defines |
A prime number p such that 2p + 1 is also prime
|
| gptkbp:distribution |
Estimated to be about C x n/(log n)^2 for primes less than n, where C is the twin prime constant
|
| gptkbp:example |
2
11 23 29 3 41 5 113 53 83 89 |
| gptkbp:hasConjecture |
There are infinitely many Sophie Germain primes
|
| https://www.w3.org/2000/01/rdf-schema#label |
Sophie Germain primes
|
| gptkbp:namedAfter |
gptkb:Sophie_Germain
|
| gptkbp:openProblem |
Are there infinitely many Sophie Germain primes?
|
| gptkbp:property |
If p is a Sophie Germain prime, then 2p+1 is a safe prime
If p > 3 is a Sophie Germain prime, then p ≡ 2 (mod 3) If p is a Sophie Germain prime, then 2p+1 is also prime All Sophie Germain primes greater than 3 are congruent to 2 mod 3 |
| gptkbp:relatedTo |
safe prime
|
| gptkbp:sequence |
gptkb:A005384
|
| gptkbp:studiedIn |
number theory
|
| gptkbp:bfsParent |
gptkb:Unsolved_Problems_in_Number_Theory
gptkb:Prime_Number |
| gptkbp:bfsLayer |
6
|