Statements (68)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:definedIn |
A natural number greater than 1 that has no positive divisors other than 1 and itself
|
| gptkbp:distributionDescribedBy |
gptkb:Prime_number_theorem
|
| gptkbp:firstPrime |
2
|
| gptkbp:hasInfinitelyMany |
True
|
| gptkbp:hasLargestKnownPrime |
Mersenne prime (as of 2024)
|
| gptkbp:hasNoPrimeDivisors |
True
|
| gptkbp:hasPrimeCountingFunction |
π(x)
|
| gptkbp:hasPrimeGap |
Yes
|
| gptkbp:hasSubgroup |
Integers
Natural numbers |
| gptkbp:hasUniqueFactorization |
True
|
| gptkbp:hasUnsolvedProblems |
gptkb:Twin_prime_conjecture
gptkb:Goldbach_conjecture gptkb:Riemann_hypothesis gptkb:Polignac's_conjecture gptkb:Legendre's_conjecture Cramér's conjecture Distribution of primes Infinitude of Chen primes Infinitude of Fermat primes Infinitude of Mersenne primes Infinitude of Sophie Germain primes Infinitude of Wagstaff primes Infinitude of Wieferich primes Infinitude of Wilson primes Infinitude of circular primes Infinitude of cousin primes Infinitude of emirp primes Infinitude of irregular primes Infinitude of palindromic primes Infinitude of prime chains Infinitude of prime constellations Infinitude of prime cousins Infinitude of prime k-tuplets Infinitude of prime ladders Infinitude of prime quadruplets Infinitude of prime quintuplets Infinitude of prime septuplets Infinitude of prime sextuplets Infinitude of prime sexy pairs Infinitude of prime spirals Infinitude of prime triplets Infinitude of prime twins Infinitude of safe primes Infinitude of sexy primes Infinitude of twin primes Prime gaps Primes in arithmetic progression |
| https://www.w3.org/2000/01/rdf-schema#label |
Prime number
|
| gptkbp:isEven |
2
|
| gptkbp:isGreaterThan |
1
|
| gptkbp:isOdd |
All primes except 2
|
| gptkbp:OEIS |
A000040
|
| gptkbp:opposedBy |
Composite number
|
| gptkbp:relatedTo |
gptkb:Mersenne_primes
gptkb:Goldbach_conjecture gptkb:Sophie_Germain_primes Twin primes |
| gptkbp:sequence |
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...
|
| gptkbp:studiedIn |
gptkb:Number_theory
|
| gptkbp:symbol |
p (commonly used)
|
| gptkbp:usedFor |
gptkb:RSA_encryption
Random number generation Hash functions |
| gptkbp:usedIn |
Cryptography
|
| gptkbp:bfsParent |
gptkb:Prime_ideal
|
| gptkbp:bfsLayer |
7
|