On the nth record gap between primes in an arithmetic progression

Alexei Kourbatov

Let $q>r\ge 1$ be coprime integers. Let $R(n,q,r)$ be the $n$th record gap between primes in the arithmetic progression $r$, $r+q$, $r+2q,\dots ,$ and denote by $N_{q,r}(x)$ the num…