@MISC{Mathar08twentydigits, author = {Richard J. Mathar}, title = {Twenty digits of the . . .}, year = {2008} }

Share

OpenURL

Abstract

The double sum P P s≥1 p 1/(ps log ps) = 2.006666... over the inverse of the product of prime powers ps 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.