Twenty Digits of Some Integrals of the Prime Zeta Function

Details Twenty Digits of Some Integrals of the Prime Zeta Function Twenty Digits of Some Integrals of the Prime Zeta Function

2008-11-28

arxiv.org/abs/0811.4739v2

Mathematics

Number Theory

Title change. Additional table at the end of section 2.4

Scientific paper

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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