13. B. If five pairwise coprime distinct integers $a_{1}, a_{2}, a_{3}, a_{4}, a_{5}$ are randomly selected from $1,2, \cdots, n$, and one of these integers is always a prime number, find the maximum value of $n$.
13. B. When $n \geqslant 49$, take the integers $1, 2^{2}, 3^{2}, 5^{2}, 7^{2}$. These five integers are five pairwise coprime distinct integers, but none of them are prime.

When $n=48$, in the integers $1, 2, \cdots, 48$, take any five pairwise coprime distinct integers $a_{1}, a_{2}, a_{3}, a_{4}, a_{5}$. If $a_{1}, a_{2}, a_{3}, a_{4}, a_{5}$ are all not prime, then at least four of $a_{1}, a_{2}, a_{3}, a_{4}, a_{5}$ are composite (let these be $a_{1}, a_{2}, a_{3}, a_{4}$).

Let the smallest prime factors of $a_{1}, a_{2}, a_{3}, a_{4}$ be $p_{1}, p_{2}, p_{3}, p_{4}$, respectively.

Since $a_{1}, a_{2}, a_{3}, a_{4}$ are pairwise coprime, $p_{1}, p_{2}, p_{3}, p_{4}$ are pairwise distinct.
Let $p$ be the largest of $p_{1}, p_{2}, p_{3}, p_{4}$. Then $p \geqslant 7$.
Since $a_{1}, a_{2}, a_{3}, a_{4}$ are composite, there must exist an $a_{i} \geqslant p^{2} \geqslant 7^{2}=49$, which is a contradiction.

Therefore, at least one of $a_{1}, a_{2}, a_{3}, a_{4}, a_{5}$ must be prime.
In conclusion, the maximum value of the positive integer $n$ is 48.