Analytic continuation of the prime zeta function

I want to plot the real part of the prime zeta function over the imaginary axis. This should be doable since the prime zeta function has an analytic continuation up to the imaginary axis. However, Mathematica doesn’t seem to know about it.

Plot[Re[PrimeZetaP[I x]], {x, 0, 10}] 

just gives an empty plot, and

x = 1
Re[PrimeZetaP[I x]]
x =.

doesn’t evaluate.

Is there some trick, or the explicit form of the analytic continuation? I can’t find it.