4. Let $a_{n}=4^{2 n+1}$
$$
+3^{n+2}(n=1,2,3 \text {. }
$$
$\cdots)$, $p$ is the smallest prime that can divide infinitely many terms of
$a_{1}, a_{2}, a_{3}, \cdots$, $q$ is the smallest prime that can divide every term of $a_{1}, a_{2}, a_{3}, \cdots$, then $p$ - $q$ is ( ).
(A) $5 \times 7$
(B) $7 \times 13$
(C) $13 \times 13$
(D) None of the above answers

直接输出翻译结果，保留了源文本的换行和格式。