Twenty Digits of Some Integrals of the Prime Zeta Function
Abstract
The double sum sum(s >= 1) sump 1/(ps log ps) = 2.00666645... 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.
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