A positive integer $n$ is called $k$-rough if all of the prime factors of $n$ strictly exceed $k$. For $k$ fixed and $n$ large enough, what's the shortest interval $[n,n+t]$ that contains a $k$-rough number ?

A positive integer $n$ is called $k$-rough if all of the prime factors of $n$ strictly exceed $k$. For $k$ fixed and $n$ large, what's the shortest interval $[n,n+t]$ that contains a $k$-rough number ?