  We use Fermi Gamma-ray Space Telescope detections and upper limits on
non-recycled pulsars obtained from the Large Area Telescope (LAT) to constrain
how the gamma-ray luminosity L depends on the period P and the period
derivative \dot{P}. We use a Bayesian analysis to calculate a best-fit
luminosity law, or dependence of L on P and \dot{P}, including different
methods for modeling the beaming factor. An outer gap (OG) magnetosphere
geometry provides the best-fit model, which is L \propto P^{-a} \dot{P}^{b}
where a=1.36\pm0.03 and b=0.44\pm0.02, similar to but not identical to the
commonly assumed L \propto \sqrt{\dot{E}} \propto P^{-1.5} \dot{P}^{0.5}. Given
upper limits on gamma-ray fluxes of currently known radio pulsars and using the
OG model, we find that about 92% of the radio-detected pulsars have gamma-ray
beams that intersect our line of sight. By modeling the misalignment of radio
and gamma-ray beams of these pulsars, we find an average gamma-ray beaming
solid angle of about 3.7{\pi} for the OG model, assuming a uniform beam. Using
LAT-measured diffuse fluxes, we place a 2{\sigma} upper limit on the average
braking index and a 2{\sigma} lower limit on the average surface magnetic field
strength of the pulsar population of 3.8 and 3.2 X 10^{10} G, respectively. We
then predict the number of non-recycled pulsars detectable by the LAT based on
our population model. Using the two-year sensitivity, we find that the LAT is
capable of detecting emission from about 380 non-recycled pulsars, including
150 currently identified radio pulsars. Using the expected five-year
sensitivity, about 620 non-recycled pulsars are detectable, including about 220
currently identified radio pulsars. We note that these predictions
significantly depend on our model assumptions.
