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Low noise receivers based on superconducting niobium nitride (NbN) hot electron bolometer (HEB) mixers have been designed, fabricated and measured in the terahertz (THz) frequency range for applications in astronomy and cosmology. The NbN HEB mixer consists of a planar antenna and an NbN bridge connecting across the antenna's inner terminals on high-resistivity Si substrates. Double sideband (DSB) receiver noise temperatures of 920 K at 1.6 THz and 1630 K at 2.5 THz have been obtained at 4.2 K without corrections. Effects of Parylene C AR coating on the lens have been studied; with such a coating a lowest DSB receiver noise temperature of 1135 K at 2.5 THz has been obtained at 4.2 K.