Twenty Digits of Some Integrals of the Prime Zeta Function

2008/11/28 by Mathar, Richard J.
#11A41 #11M06 #11Y60 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0811.4739

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.

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