Thermal Hawking emission from black holes is a remarkable consequence of the unification of quantum physics and gravitation. Black holes of a few solar masses are the only ones which can form in the present universe. However, having temperatures million times smaller than the ambient cosmic background radiation they cannot evaporate. Primordial black holes of M ̃ 1014g would evaporate over a Hubble age and considerable ongoing effort is on to detect such explosions. I point out, however, that at the early universe epochs when such black holes form, the ambient radiation temperature considerably exceeds their corresponding Hawking temperature. This results in rapid continual accretion (absorption) of ambient radiation by these holes. Consequently by the end of the radiation era their masses grow much greater so that their lifetimes (scaling as M3) would now be enormously greater than the Hubble age implying undetectably small emission.