Example 11 Write 10 consecutive natural numbers, each of which is a composite number.
Solution: Construct the following decimal natural numbers:
$$
11!+2,11!+3, \cdots, 11!+11 \text {. }
$$

Obviously, they satisfy the requirements of the problem.
In general, for any given $n \in \mathbf{N}$, we can write $n$ consecutive natural numbers, all of which are composite:
$$
\begin{array}{l}
(n+1)!+2,(n+1)!+3, \cdots \\
(n+1)!+(n+1)
\end{array}
$$