19.6.7 ** Let $S=\{1,2, \cdots, 2005\}$, if any $n$ pairwise coprime numbers in $S$ contain at least one prime number, find the minimum value of $n$.


Parse 15 numbers (1 and the squares of 14 prime numbers)
$$
1,2^{2}, 3^{2}, 5^{2}, \cdots, 41^{2}, 43^{2}
$$

are all in $S$, every two numbers are coprime, but (1) contains no prime numbers. Therefore, $n \geqslant 16$.
On the other hand, let $A=\left\{a_{1}, a_{2}, \cdots, a_{16}\right\} \subseteq S$, and $a_{i}, a_{j}$ are coprime $(1 \leqslant i2005$, contradiction.
(2) $1 \in A$. Without loss of generality, assume $a_{16}=1$. Similarly, $a_{15} \geqslant 47^{2}>2005$, contradiction. Therefore, $A$ must contain a prime number. The minimum value of $n$ is 16.