Let $A>0$ be fixed. Uniformly for all sufficiently large $x$, all $q \le (\log x)^A$, and all reduced residue classes $a\pmod q$,
\begin{align*}
\sum_{\substack{n\le x;\ n\equiv a \pmod q}}\Lambda(n)=\frac{x}{\varphi(q)}+O_A\left(xe^{-c_A\sqrt{\log x}}\right)
\end{align*}
with constants depending on $A$.