I wanted to evaluate the following sum psi(2n+1)/(2n+1)-psi(2n)/(2n) where n ranges from 1 to infinity and psi is the Chebyshev second function. So I wrote the following code.

Sum[ Sum[Floor[Log[Prime[k], 2x+1]] Log[Prime[k]]/(2x+1), {k, 1, PrimePi[2x+1]}]- Sum[Floor[Log[Prime[k], 2x]] Log[Prime[k]]/(2x), {k, 1, PrimePi[2x]}]] ,1]

But it didn't show the answer. Can anybody tell me the answer?