2. Let the complex number $z$ satisfy
$\frac{2017 z-25}{z-2017}=3+4 \mathrm{i}$, where $\mathrm{i}$ is the imaginary unit, then the modulus of $z$ $|z|=$ $\qquad$
Let $w=3+4 \mathrm{i}$, then $\frac{2017 z-w \bar{w}}{z-2017}=w \Rightarrow 2017 z-w \bar{w}=z w-2017 w$ $\Rightarrow z=\frac{w \bar{w}-2017 w}{2017-w}=-w \cdot \frac{2017-\bar{w}}{2017-w}$, so $|z|=|-w| \cdot\left|\frac{2017-\bar{w}}{2017-w}\right|=5$.