  We compute the contribution of the vacuum Virasoro representation to the
genus-two partition function of an arbitrary CFT with central charge $c>1$.
This is the perturbative pure gravity partition function in three dimensions.
We employ a sewing construction, in which the partition function is expressed
as a sum of sphere four-point functions of Virasoro vacuum descendants. For
this purpose, we develop techniques to efficiently compute correlation
functions of holomorphic operators, which by crossing symmetry are determined
exactly by a finite number of OPE coefficients; this is an analytic
implementation of the conformal bootstrap. Expanding the results in $1/c$,
corresponding to the semiclassical bulk gravity expansion, we find
that---unlike at genus one---the result does not truncate at finite loop order.
Our results also allow us to extend earlier work on multiple-interval Renyi
entropies and on the partition function in the separating degeneration limit.
