1975/01/01 by Richard P. Brent · 1 citation
Mathematics · #Analytic Number Theory Research #History and Theory of Mathematics #Mathematics and Applications #Mathematics #Twin prime #Pi #Riemann hypothesis #Combinatorics #Constant (computer programming) #Prime number theorem #Maxima #Logarithm #Distribution (mathematics) #Mathematical analysis #Prime number #Geometry
paper · doi:10.2307/2005460
openalex publication_date 1975/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
The maxima and minima of ⟨ L(x)⟩ - π (x),⟨ R(x)⟩ - π (x), and ⟨ L2(x)⟩ - π 2(x) in various intervals up to x = 8 × 1010 are tabulated. Here π (x) and π 2(x) are respectively the number of primes and twin primes not exceeding x,L(x) is the logarithmic integral, R(x) is Riemannâs approximation to π (x), and L2(x) is the Hardy-Littlewood approximation to π 2(x). The computation of the sum of inverses of twin primes less than 8 × 1010 gives a probable value 1.9021604 ± 5 × 10 - 7 for Brunâs constant.