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The double sum sum_(s >= 1) sum_p 1/(p^s log p^s) = 2.00666645... over theinverse of the product of prime powers p^s and their logarithms, is computed to24 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 looksat the fraction as the underivative of the Prime Zeta Function, and thenevaluates the integral by numerical methods.

Twenty Digits of Some Integrals of the Prime Zeta Function