Let $f(u)$ be the largest $v$ such that no $m\in (u,v)$ is composed entirely of primes dividing $uv$. Estimate $f(u)$.

Let $f(u)$ be the largest $v$ such that no $m\in (u,v)$ is composed entirely of primes dividing $uv$. Estimate $f(u)$.

The estimate $u + 2 \le f(u) \le u^2$ holds for every $u \ge 2$. The upper bound is attained when $u$ is prime, and the lower bound when $u = 2^k - 2$ with $k \ge 2$; Cambie further showed that $f(n) = (1 + o(1))n$ for almost all $n$.