An explicit lower bound for large gaps between some consecutive primes

Keiju Sono

Let $p_n$ denote the $n$th prime and for any fixed positive integer $k$ and $X\ge 2$, put \[ G_{k}(X):=\max _{p _{n+k}\leq X} \min \{ p_{n+1}-p_{n}, \ldots , p_{n+k}-p_{n+k-1} \…