Forgive my question if its elementary, I'm very new in number theory.
We know from Merten's theorem
$$\sum_{p\leq x} \frac{1}{p} = \ln \ln x + B + O\left(\frac{1}{\ln(x)}\right)$$
Here $B= \sum_p \left(\ln(1-1/p)+1/p\right)$
My question is how to get similar estimate for :
$$\sum_{p\leq x} \frac{1}{p^{1/2}}$$