4. Let $P=\{$ natural numbers no less than 3 $\}$. Define the function $f$ on $P$ as follows: if $n \in P, f(n)$ represents the smallest natural number that is not a divisor of $n$, then $f(360360)=$ $\qquad$ .
4. 16 .

Since $360360=2^{3} \times 3^{2} \times 5 \times 7 \times 11 \times 13$, we know that the divisors of 360360 in ascending order are $1,2,3,4,5,6,7,8,9,10$, $11,12,13,14,15,18,20, \cdots$, the smallest natural number that is not a divisor of 360360 is 16. Therefore, $f(360360)=16$.