2. For an integer $n(n \geqslant 4)$, find the smallest integer $f(n)$ such that for any positive integer $m$, in any $f(n)$-element subset of the set $\{m, m+1, \cdots, m+n-1\}$, there are at least three pairwise coprime elements.
$(2004$, National High School Mathematics League Competition)
Prompt: Prove: Among any five numbers chosen from six consecutive numbers, there must be three numbers that are pairwise coprime.
Answer: $n=6k+m(0 \leqslant m<6)$,
$$
f(n)=4k+m+1-\left[\frac{m}{4}\right] .
$$