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For the function $f(m,p,q,n)$, where $k,s,a$ general complex numbers and $q$any positive integer, we establish the sum of values of the Hurwitz-Lerch zetafunction $\Phi(f(m,p,q,n),k,a)$ taken at prime numbers $n$. Special cases ofthis sum are evaluated in terms of products of trigonometric functions andCatalan's constant $K$.

Sum of the Hurwitz-Lerch Zeta Function over Prime Numbers: Derivation and Evaluation