Without developing a correct theory, the rate of the production of entangled photon pairs in the X-ray region by high energy electrons is estimated for experimental parameters used in a few experiments on X-ray parametric down conversion. Taking into account the need for X-ray entangled X-ray photons, it is proposed to begin the experimental study of such mechanism of nonlinear X-ray optics before the launch of the X-ray free electron lasers.The parametric down conversion (PDC) of a "pump" photon with frequency ω p into two photons, a "signal" photon with ω s and an "idler" photon with ω i , in a nonlinear medium, provides two entangled photons. In the optical region, PDC, which is one of the most important processes of the nonlinear X-ray optics, has been theoretically and experimentally studied in many works. PDC can find wide scientific applications in quantum computers, cryptography, teleportation, etc. In X-ray region PDC for the first time has been considered in [1] and observed in [2]. Since the cross section of PDC is small, it has been further experimentally studied only in a few works [3-6] without satisfactory development and comparison between the theory and experiment. The highest event rate observed for the third generation SR sources [4-6] is ~ 0.1 Hz, while the expected one for LCLS and TESLA FELs is 10000 times higher [7]. As the optical, the X-ray PDC semiclassically is interpreted as mixing of the pump photon with a zero point fluctuation photon (ZPF), and the very small X-ray nonlinear susceptibilities are