Recent studies have suggested that the characteristics of prompt gammas (PGs) emitted from excited nuclei during proton therapy are advantageous for determining beam range during treatment delivery. Since PGs are only emitted while the beam is on, the feasibility of using PGs for online treatment verification depends greatly on the design of highly efficient detectors. The purpose of this work is to characterize how PG detection changes as a function of distance from the patient as a means of guiding the design and usage of clinical PG imaging detectors. Using a Monte Carlo model (GEANT4.9.4) we studied the detection rate (PGs per incident proton) of a high purity germanium detector for both the total PG emission and the characteristic 6.13 MeV PG emission from (16)O emitted during proton irradiation. The PG detection rate was calculated as a function of distance from the isocenter of the proton treatment nozzle for: (1) a water phantom irradiated with a proton pencil beam and (2) a prostate patient irradiated with a scanning beam proton therapy treatment field (lateral field size: ∼6 cm × 6 cm, beam range: 23.5 cm). An analytical expression of the PG detection rate as a function of distance from isocenter, detector size, and proton beam energy was then developed. The detection rates were found to be 1.3 × 10(-6) for oxygen and 3.9 × 10(-4) for the total PG emission, respectively, with the detector placed 11 cm from isocenter for a 40 MeV pencil beam irradiating a water phantom. The total PG detection rate increased by ∼85 ± 3% for beam energies greater than 150 MeV. The detection rate was found to be approximately 2.1 × 10(-6) and 1.7 × 10(-3) for oxygen and total PG emission, respectively, during delivery of a single pencil beam during a scanning beam treatment for prostate cancer. The PG detection rate as a function of distance from isocenter during irradiation of a water phantom with a single proton pencil beam was described well by the model of a point source irradiating a cylindrical detector of a known diameter over the range of beam energies commonly used for proton therapy. For the patient studies, it was necessary to divide the point source equation by an exponential factor in order to correctly predict the falloff of the PG detection rate as a function of distance from isocenter.