Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:concerns |
gptkb:Asymptotic_analysis
Prime numbers |
| gptkbp:field |
gptkb:Number_theory
|
| gptkbp:form |
∑_{p ≤ n} 1/p ~ log log n as n → ∞
∏_{p ≤ n} (1 - 1/p) = e^{-γ}/log n (1 + o(1)) as n → ∞ ∏_{p ≤ n} (1 - 1/p)^{-1} ~ e^{γ} log n as n → ∞ |
| https://www.w3.org/2000/01/rdf-schema#label |
Mertens' Theorem
|
| gptkbp:implies |
Divergence of the sum of reciprocals of primes
|
| gptkbp:namedAfter |
gptkb:Franz_Mertens
|
| gptkbp:publicationYear |
1874
|
| gptkbp:publishedIn |
gptkb:Journal_für_die_reine_und_angewandte_Mathematik
|
| gptkbp:relatedTo |
gptkb:Prime_number_theorem
gptkb:Harmonic_series Mertens function |
| gptkbp:state |
The sum of the reciprocals of the primes up to n is asymptotic to log log n
|
| gptkbp:bfsParent |
gptkb:Number_Theory
|
| gptkbp:bfsLayer |
7
|