Get started
Keyword

prime counting function

Description: The prime-counting function gives the number of prime integers less than or equal to a specified number in number theory.
Wikidata ID: wiki/Q251922
OpenAlex ID: keywords/prime-counting-function
Approximate formulas for some functions of prime numbers
1962 · J. Barkley Rosser, Lowell Schoenfeld · Illinois Journal of Mathematics · 1,551
PDF
Handbuch der Lehre von der Verteilung der Primzahlen
1911 · Landau, Edmund, 1877-1938. · Monatshefte für Mathematik · 677
The Distribution of Prime Numbers
1933 · Bouras, Mohammed · Nature · 470
PDF
Handbook of number theory
1996 · D. S. Mitrinović, József Sándor, et al. · CERN Document Server (European Organization for Nuclear Research) · 272
Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x)
1975 · J. Barkley Rosser, Lowell Schoenfeld · Mathematics of Computation · 270
Irregularities of distribution, VII
1972 · Wolfgang Schmidt · Acta Arithmetica · 270
PDF
The Logarithmic Integral I
1988 · Paul Koosis · Cambridge University Press eBooks · 264
Approximate Formulas for Some Functions of Prime Numbers
1963 · D. S., J. Barkley Rosser, et al. · Mathematics of Computation · 225
An Elementary Proof of the Prime-Number Theorem
1949 · Atle Selberg · Annals of Mathematics · 212
Explicit Bounds for Some Functions of Prime Numbers
1941 · Barkley Rosser · American Journal of Mathematics · 194
Estimation de la fonction de Tchebychef θ sur le k-ième nombre premier et grandes valeurs de la fonction ω(n) nombre de diviseurs premiers de n
1983 · Guy Robin · Acta Arithmetica · 173
PDF
Primes in arithmetic progressions
1996 · Olivier Ramaré, Robert Rumely · Mathematics of Computation · 159
PDF
An Elementary Problem Equivalent to the Riemann Hypothesis
2002 · Jeffrey C. Lagarias · American Mathematical Monthly · 149
The 𝑘^{𝑡ℎ} prime is greater than 𝑘(ln𝑘+lnln𝑘-1) for 𝑘≥2
1999 · Pierre Dusart · Mathematics of Computation · 146
PDF
Simple Analytic Proof of the Prime Number Theorem
1980 · D. J. Newman · American Mathematical Monthly · 137
Sharper bounds for the Chebyshev functions 𝜃(𝑥) and 𝜓(𝑥)
1975 · J. Barkley Rosser, Lowell Schoenfeld · Mathematics of Computation · 134
PDF
Pure and Applied Mathematics
2015 · Barry Mazur, William Stein · Cambridge University Press eBooks · 133
Shifted primes without large prime factors
1998 · R. Baker, G. Harman · Acta Arithmetica · 130
PDF
Explicit estimates of some functions over primes
2016 · Pierre Dusart · The Ramanujan Journal · 129
Sharper bounds for the Chebyshev functions 𝜃(𝑥) and 𝜓(𝑥). II
1976 · Lowell Schoenfeld · Mathematics of Computation · 121
PDF
On Chebyshev-Type Inequalities for Primes
1982 · M. Nair · American Mathematical Monthly · 112
Autour de la fonction qui compte le nombre de nombres premiers
1998 · Pierre Dusart · 110
Pair Correlation of Zeros and Primes in Short Intervals
1987 · Daniel A. Goldston, Hugh L. Montgomery · Birkhäuser Boston eBooks · 109
Elementary methods in the study of the distribution of prime numbers
1982 · Harold G. Diamond · Bulletin of the American Mathematical Society · 103
PDF
The Prime Number Theorem
2003 · G. J. O. Jameson · Cambridge University Press eBooks · 99
Works count: 3,034
Citation count: 15,010
Year
Topic
Type