Twenty Digits of Some Integrals of the Prime Zeta Function
Number Theory
2018-09-19 v3
Abstract
The double sum sum_(s >= 1) sum_p 1/(p^s log p^s) = 2.00666645... over the inverse of the product of prime powers p^s and their logarithms, is computed to 24 decimal digits. The sum covers all primes p and all integer exponents s>=1. The calculational strategy is adopted from Cohen's work which basically looks at the fraction as the underivative of the Prime Zeta Function, and then evaluates the integral by numerical methods.
Cite
@article{arxiv.0811.4739,
title = {Twenty Digits of Some Integrals of the Prime Zeta Function},
author = {Richard J. Mathar},
journal= {arXiv preprint arXiv:0811.4739},
year = {2018}
}
Comments
Constants with higher powers of logarithms in the prime sums added