The probability of electron–positron pair production out of the vacuum of pulsars is calculated. Pair production is induced by a super-strong intrinsic magnetic field and a circularly polarized electromagnetic wave propagating along the magnetic field lines in the magnetized pair plasma near the polar caps of the pulsar. The dependence of the probability on the intensity of electromagnetic fields, the frequency of the electromagnetic radiation and the pair plasma of pulsars is discussed in detail. A significant conclusion is reached, namely that the electromagnetic radiation with frequencies close to the cyclotron frequency of an electron moving in the magnetized pair plasma plays an important role in the pair production. The attenuation of the luminosity of the pulsar radiation resulting from pair production is also examined.