  We obtain an asymptotic formula for the number of circles of curvature at
most T in any given bounded Apollonian circle packing. For an integral packing,
we obtain the upper bounds for the number of circles with prime curvature as
well as of pairs of circles with prime curvatures, which are sharp up constant
multiples. The main ingredient of our proof is the effective equidistribution
of expanding horospheres on geometrically finite hyperbolic 3-manifolds under
the assumption that the critical exponent of its fundamental group exceeds one.
