Is it possible to find $n-1$ consecutive composite integers
Given an integer $n\geq 2$ ,can we always find an integer $m$ such that each of the $n-1$ consecutive integers $m+2,m+3,.....,m+n$ are composite?
Try the numbers: $$ k!+2,\,k!+3,\ldots,k!+k $$ and you have $k-1$ consecutive composite integers.