Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alternativeTo |
lim n→∞ π(n) log n / n = 1
|
| gptkbp:approximationFormula |
π(n) ~ n / log n
|
| gptkbp:describes |
asymptotic distribution of prime numbers
|
| gptkbp:field |
number theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Prime number theorem
|
| gptkbp:implies |
density of primes decreases as numbers grow larger
|
| gptkbp:provenBy |
gptkb:Charles_Jean_de_la_Vallée-Poussin
gptkb:Jacques_Hadamard |
| gptkbp:relatedTo |
gptkb:Gauss's_conjecture
gptkb:Riemann_zeta_function gptkb:Legendre's_conjecture |
| gptkbp:state |
the number of primes less than or equal to n is approximately n / log n
|
| gptkbp:uses |
complex analysis
|
| gptkbp:yearProved |
1896
|
| gptkbp:π(n) |
number of primes less than or equal to n
|
| gptkbp:bfsParent |
gptkb:Dirichlet's_theorem_on_arithmetic_progressions
gptkb:Prime_zeta_function gptkb:Number_theory gptkb:Riemann_zeta_function_(when_χ_is_trivial) gptkb:Zeta_function |
| gptkbp:bfsLayer |
5
|