Linnik's theorem
= Linnik's theorem
{c}
{title2=$p(a,q)\ll q^L\quad((a,q)=1)$}
{wiki}
There is an absolute finite exponent $L$ bounding the least <prime> in any reduced arithmetic progression by a constant times $q^L$. The <multiplicative large sieve inequality> is one of the tools in proofs of this theorem.