1. Let $S_{n} 、 T_{n}$ be the sums of the first $n$ terms of the arithmetic sequences $\left\{a_{n}\right\} 、\left\{b_{n}\right\}$, respectively, and for any positive integer $n$, we have
$$
\frac{S_{n}}{T_{n}}=\frac{2 n+6}{n+1} \text {. }
$$

If $\frac{a_{m}}{b_{m}}$ is a prime number, then the value of the positive integer $m$ is ( ).
(A) 2
(B) 3
(C) 5
(D) 7
- 1. A.

Given the conditions
$$
S_{n}=k n(2 n+6), T_{n}=k n(n+1) \text {. }
$$

When $m=1$, $\frac{a_{1}}{b_{1}}=\frac{S_{1}}{T_{1}}=\frac{8}{2}=4$, which does not satisfy the condition in the problem, so it is discarded.
When $m \geqslant 2$,
$$
\frac{a_{m}}{b_{m}}=\frac{S_{m}-S_{m-1}}{T_{m}-T_{m-1}}=\frac{4 m+4}{2 m}=2+\frac{2}{m} \text {. }
$$

Thus, only when $m=2$, $\frac{a_{m}}{b_{m}}=3$ is a prime number. Therefore, the required positive integer $m=2$.