I will give the following $$\sum_{p\leq x}\frac{1}{p^s} \approx \frac{1}{1-s}\frac{x^{1-s}}{\log x}$$ for $0\leq s < 1$ and $$\sum_{p\leq x}\frac{1}{p} \approx \log \log x$$ for $s = 1$.
Willie Wu
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