14.4 .39 Find five different positive integers such that they are pairwise coprime, and the sum of any $n(\leqslant$ 5) of them is a composite number.
Parse 5 can be generalized to a more general natural number $m(\geqslant n) . m$ numbers $a_{i}-i \cdot m!+1, i=1,2, \cdots$, $m$ (1) satisfy the condition. When $m=5$, $121,241,361,481,601$ are the five numbers sought.

Now prove that the numbers in (1) satisfy the condition: The sum of any $n(\leqslant m)$ numbers in (1) is $k \cdot m!+n(k \in \mathbf{N})$ which is divisible by $n$, hence composite. Also, $\left(a_{i}, a_{j}\right)=(i m!+1, j m!+1)=((j-i) m!, j m!+1)$, $1 \leqslant i<j \leqslant m .(m!, j \cdot m!+1)=(m!, 1)=1,(j-i, j \cdot m!+1)=(j-i$, 1) $=1$, so $\left(a_{i}, a_{j}\right)=1$.