  Let $N$ be a prime 3-manifold that is not a closed graph manifold. Building
on a result of Hongbin Sun and using a result of Asaf Hadari we show that for
every $k\in\Bbb{N}$ there exists a finite cover $\tilde{N}$ of $N$ such that
$|\operatorname{Tor} H_1(\tilde{N};\Bbb{Z})|>k$.
