Irregularities in the distribution of primes and twin primes

Abstract

The maxima and minima of sL(x) n(x), iR(x) n(x), and sL2(x) n2(x) in various intervals up to x = 8 x 10 are tabulated. Here n(x) and n2(x) are respectively the number of primes and twin primes not exceeding x, L(x) is the logarithmic integral, R(x) is Riemanns approximation to ir(x), and L2(x) is the Hardy-Littlewood approximation to ti"2(;c). The computation of the sum of inverses of twin primes less than 8 x 10 gives a probable value; 1.9021604 5 x 10-7 for Bruns constant. Show more