Schoenfeld, Lowell Sharper bounds for the Chebyshev functions \(\theta(x)\) and \(\Psi(x)\). II. (English) Zbl 0326.10037 Math. Comput. 30, 337-360 (1976). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 13 ReviewsCited in 119 Documents MSC: 11N05 Distribution of primes 11A25 Arithmetic functions; related numbers; inversion formulas 65D20 Computation of special functions and constants, construction of tables × Cite Format Result Cite Review PDF Full Text: DOI Digital Library of Mathematical Functions: §27.12 Asymptotic Formulas: Primes ‣ Multiplicative Number Theory ‣ Chapter 27 Functions of Number Theory Online Encyclopedia of Integer Sequences: The Chebyshev primes of index 1. The Riemann primes of the psi type and index 1. The Riemann primes of the theta type and index 1. a(n) is the least r > 1 for which the interval (r*n, r*(n+1)) contains no prime, or a(n)=0 if no such r exists. a(n) is the least r > 1 for which the interval (r*(2*n-1), r*(2*n+1)) contains no prime, or 0 if no such r exists. Successive records of function f(x) = log(abs(pi(x) - R(x)))/log(x) where pi(x) is the number of primes <= x and R(x) is Riemann’s prime counting function.