  We give explicit numerical values with 100 decimal digits for the Mertens
constant involved in the asymptotic formula for $\sum\limits_{\substack{p\leq x
p\equiv a \bmod{q}}}1/p$ and, as a by-product, for the Meissel-Mertens constant
defined as $\sum_{p\equiv a \bmod{q}} (\log(1-1/p)+1/p)$, for $q \in \{3$, ...,
$100\}$ and $(q, a) = 1$.

Number Theory