I think you will find it in Moon, J. W.; Moser, L.
Almost all (0,1) matrices are primitive. 
Studia Sci. Math. Hungar. 1 (1966) 153–156.
But I don't have time to visit the library to be sure and I don't see it online.

It is certainly in 
Burtin, Ju. D.
Asymptotic estimates of the diameter and the independence and domination numbers of a random graph. (Russian) 
Dokl. Akad. Nauk SSSR 209 (1973), 765–768.