  Given a prime $p$, a group is called residually $p$ if the intersection of
its $p$-power index normal subgroups is trivial. A group is called virtually
residually $p$ if it has a finite index subgroup which is residually $p$. It is
well-known that finitely generated linear groups over fields of characteristic
zero are virtually residually $p$ for all but finitely many $p$. In particular,
fundamental groups of hyperbolic 3-manifolds are virtually residually $p$. It
is also well-known that fundamental groups of 3-manifolds are residually
finite. In this paper we prove a common generalization of these results: every
3-manifold group is virtually residually $p$ for all but finitely many $p$.
This gives evidence for the conjecture (Thurston) that fundamental groups of
3-manifolds are linear groups.
