6. Let $m, n$ be positive integers. If there exists a positive integer $k$ such that $\log _{2} m, \log _{2} n$ and $\log _{2} k$ can be the lengths of the three sides of a triangle, then $k$ is called a “good number”. It is known that there are exactly 100 good numbers $k$. Then the maximum possible value of $m n$ is ( ).
(A) 100
(B) 101
(C) 134
(D) 2007
6.C.

Assume $m \geqslant n$. From the problem, we have
$$
\begin{array}{l}
\log _{2} m-\log _{2} n\frac{m}{n}, m n-101 \leqslant \frac{m}{n},
\end{array}
$$

which implies $\frac{100}{1-\frac{1}{n^{2}}}<m n \leqslant \frac{101}{1-\frac{1}{n^{2}}}$.
It is easy to see that when $n=2$, $\frac{101}{1-\frac{1}{n^{2}}}$ reaches its maximum value $\frac{404}{3}$, at this time,
$$
\frac{400}{3}<m n \leqslant \frac{404}{3} \text {. }
$$

Therefore, when $m=67, n=2$, $m n$ reaches its maximum value 134.