Statements (67)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:definedIn |
Natural numbers greater than 1 with exactly two positive divisors: 1 and itself
|
| gptkbp:distributionDescribedBy |
gptkb:Prime_number_theorem
|
| gptkbp:firstPrime |
2
|
| https://www.w3.org/2000/01/rdf-schema#label |
Prime Numbers
|
| gptkbp:infinitudeProvedBy |
gptkb:Euclid
|
| gptkbp:onlyEvenPrime |
2
|
| gptkbp:property |
Infinite set
Building blocks of natural numbers Can be found by Sieve of Eratosthenes Central to modern encryption Density decreases as numbers grow Distribution related to logarithmic integral Fundamental Theorem of Arithmetic applies Gaps between primes can be arbitrarily large Irreducible in integers Many open questions remain No divisors other than 1 and itself No largest prime No simple formula for nth prime Prime gaps studied in mathematics Prime-counting function π(x) Randomly distributed Tested by primality tests Every integer greater than 1 is a product of primes |
| gptkbp:relatedTo |
gptkb:Mersenne_primes
gptkb:Goldbach_conjecture gptkb:Riemann_hypothesis gptkb:Sophie_Germain_primes Composite numbers Twin primes |
| gptkbp:sequence |
A000040
|
| gptkbp:sequenceBeginsWith |
2
11 13 17 19 23 29 3 31 37 41 43 47 5 61 7 71 73 79 53 59 67 83 89 97 |
| gptkbp:smallestPrime |
2
|
| gptkbp:symbol |
p
π(x) |
| gptkbp:usedIn |
gptkb:Mathematics
gptkb:Number_theory Computer science Cryptography |
| gptkbp:bfsParent |
gptkb:XDC_Network
gptkb:Motor_City_Drum_Ensemble |
| gptkbp:bfsLayer |
7
|