3. Let $m$ be the largest integer that cannot be expressed as the sum of three distinct composite numbers. Then $m=$ $\qquad$

Set $m$ is the largest integer that cannot be represented as the sum of three distinct composite numbers. Then $m=$ $\qquad$
3.17 .

The smallest three composite numbers are 4, 6, and 8, and $4+6+8=18$. Therefore, 17 is an integer that cannot be expressed as the sum of three distinct composite numbers.

When $m>18$, if $m=2k>18$, then $m=4+6+2 \times (k-5)$; if $m=2k-1>18$, then $m=4+9+2(k-7)$.

Therefore, any integer greater than 18 can be expressed as the sum of three distinct composite numbers. Hence, $m=17$.