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Prime-counting function

In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some real number x. It is denoted by π(x) (unrelated to the number π).

Growth rate, Formulas for prime-counting functions & Algorithms for evaluating π(x)

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Overview

Growth rate

Table of π(x), ⁠x/log x ⁠, and li(x)

  • OEIS On-Line Encyclopedia of Integer Sequences
  • J. Franke Jens Franke

Algorithms for evaluating π(x)

Other prime-counting functions

Formulas for prime-counting functions

Inequalities

The Riemann hypothesis

Advanced semantic analysis

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Map overview Semantic statistics

Prime-counting function

Nodes66
Edges65
Triples39
Avg. degree1.97
Density0.030303
Components1

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Prime-counting function

Top relations

related to External links · 16
Prime-counting function → Adrian, Bibcode, Chris Caldwell, Dudek, International Journal, ISSN, Number Theory, On, Riemann, S1793042115500426, S2CID, Silva, Tables, The Nth Prime Page, The Prime Pages, Tomás Oliveira
related to Growth rate · 14
Prime-counting function → An, Atle Selberg, Charles, Gauss, It, Jacques Hadamard, Legendre, Of, Paul Erdős, Proofs, Riemann, The, This, Vallée Poussin
related to Formulas for prime-counting functions · 7
Prime-counting function → Analytic, Chebyshev, Formulas, Mangoldt, Riemann, They, We
is a · 1
Prime-counting function → function counting the number of prime numbers less than or equal to some real number x
related to Other prime-counting functions · 1
Prime-counting function → Other

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Important terminology

number function log prime riemann li displaystyle proved sum numbers equal prime-counting pi zeta π0 frac left right value less

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Prime-counting functionis afunction counting the number of prime numbers less than or equal to some real number x0.90text
Prime-counting functionrelated to External linksChris Caldwell0.60section
Prime-counting functionrelated to External linksThe Nth Prime Page0.60section
Prime-counting functionrelated to External linksThe Prime Pages0.60section
Prime-counting functionrelated to External linksTomás Oliveira0.60section
Prime-counting functionrelated to External linksSilva0.60section
Prime-counting functionrelated to External linksTables0.60section
Prime-counting functionrelated to External linksDudek0.60section
Prime-counting functionrelated to External linksAdrian0.60section
Prime-counting functionrelated to External linksOn0.60section
Prime-counting functionrelated to External linksRiemann0.60section
Prime-counting functionrelated to External linksInternational Journal0.60section

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