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Displaying primes as a 3D array of spheres

I am currently learning my way through Mathematica and have stumbled upon a strange problem. It is asking me to implement PrimeQ into ...
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Hurwitz-Lerch transcendent

I want to compute the following sum over primes: $$\sum\limits_{p \text{ prime}}\sum\limits_{k=1}^\infty(\log(p^k))\left(\frac{1}{2p^k} - \Phi[-1,1,p^k]\right),$$ where $\Phi[z,s,a]$ is the ...