Spacing of the results of Fortran intrinsic random_number

Question about the behaviour in practice of the random_number intrinsic. The standard says pseudo-random numbers in the range 0<=r<1. I believe that in practice we always get random numbers from an equally spaced set in that range. I wonder if, in practice, I can count on it that the spacing in that set is the narrowest possible for the involved floating point type. Equivalently, may I expect (in practice) the largest possible result of random_number (r) for a given precision of the real variable r to be nearest(1.0,-1.0) for arguments of that same precision? (That is the nearest floating point number to 1.0 in the negative direction.)