It is suggested that the anomalous leakage of ultra-cold neutrons from a neutron trap may be associated with the formation of dineutrons in it. It is shown that the gas of ultracold neutrons at temperatures T less than 10-3 K should form a dineutron Bose condensate even in the absence of dineutrons as free stable particles. The consequences arising from the assumption of the stability of dineutrons in neutron stars are considered. The conditions for the formation of a Bose condensate from dineutrons in them and in heavy nuclei are discussed