We report on the fabrication and characterization of photoconductive ultraviolet detectors based on insulating single-crystal GaN. The active layer (GaN) was deposited over basal-plane sapphire substrates using a unique switched atomic-layer-epitaxy process. The sensors were measured to have a responsivity of 2000 A/W at a wavelength of 365 nm under a 5-V bias. The responsivity remained nearly constant for wavelengths from 200 to 365 nm and dropped by three orders of magnitude within 10 nm of the band edge (by 375 nm). We estimate our sensors to have a gain of 6×103 (for wavelength 365 nm) and a bandwidth in excess of 2 kHz. The photosignal exhibited a linear behavior over five orders of incident optical power, thereby implying a very large dynamic range for these GaN-based ultraviolet sensors.