  We present the results of a survey for trans-neptunian objects (TNOs) based
on Subaru archival images, originally collected by Sheppard et al. (2005) as
part of a search for irregular satellites of Uranus. The survey region covers
2.8 deg^2, centered on Uranus and observed near opposition on two adjacent
nights. Our survey reaches half its maximum detection efficiency at
R=25.69$\pm$0.01. The objects detected correspond to 82 TNOs, five Centaurs,
and five irregular satellites. We model the cumulative number of TNOs brighter
than a given apparent magnitude with both a single and double power law. The
best fit single power law, with one object per square degree at magnitude $R_0
=22.6_{-0.4}^{+0.3}$ and a slope of $\alpha = 0.51_{-0.6}^{+0.5}$, is
inconsistent with the results of similar searches with shallower limiting
magnitudes. The best fit double power law, with a bright-end slope $\alpha_1 =
0.7_{-0.1}^{+0.2}$, a faint-end slope $\alpha_2=0.3_{-0.2}^{+0.2}$, a
differential number density at R=23, $\sigma_{23} = 2.0_{-0.5}^{+0.5}$ and a
magnitude break in the slope at $R_{eq} = 24.3_{-0.1}^{+0.8}$, is more likely
than the single power law by a Bayes factor of ~26. This is the first survey
with sufficient depth and areal coverage to identify the magnitude at which the
break occurs without relying on the results of other surveys. ...
