What is the conjecture

https://www.erdosproblems.com/962

Let $k(n)$ be the maximal $k$ such that there exists $m\leq n$ such that each of the integers
$$m+1,\ldots,m+k$$
are divisible by at least one prime $>k$. Estimate $k(n)$.

Status: open

Choose either option

• I plan on working on this conjecture
• This issue is up for grabs: I would like to see this conjecture added by somebody else