4. Find the largest odd number that cannot be expressed as the sum of three distinct composite numbers.

 untranslated text:
4.求一个不能用三个不相等的合数之和表示的最大奇数。
The smallest sum of three unequal composite numbers is
$$
4+6+8=18 \text{.}
$$

We prove that 17 is the largest odd number that cannot be expressed as the sum of three unequal composite numbers.

In fact, it is only necessary to prove that any odd number $2k-1$ not less than 19 can always be expressed as the sum of three unequal composite numbers.
Since $2k-1=4+9+(2k-14)$.
For $k \geqslant 10$, we have $2k-14 \geqslant 6$, so 4, 9, and $2k-14$ are three unequal composite numbers.
Therefore, 17 is the largest odd number satisfying the condition.