We show the T-g-scaled temperature dependence of the minimum number of molecules capable of undergoing a rearrangement, z*, in the Adam and Gibbs model of relaxation of glass-formers is strikingly similar to that of n and m = [d log tau(alpha)/d(T-g/T)]. Here (1-n) and tau(alpha) are, respectively, the exponent and the effective relaxation time in the Kohlrausch correlation function, exp[-(t/tau(alpha))(1-n)], of the primary alpha-relaxation, z* is obtained from the excess (configurational) entropy, S-c, of the Kauzmann paradox and T-g is the glass temperature. As functions of T-g/T, z*, n and m all assume their minimal values at high temperatures. On decreasing temperature they all increase monotonically with a more rapid change in the vicinity of some temperature T-B above T-g. Moreover, from the data of a number of small molecule glass-formers in which the high temperature limit of S-c can be determined accurately, we find that at the glass temperature, T-g, z*(T-g) obtained from thermodynamic data correlates with the steepness index m = [d log tau(alpha)/d(T-g/T)](T=Tg) and the Kohlrausch exponents (1 - n(T-g)). The similarity of the temperature dependencies of n, m, and z* makes plausible the explanation that the temperature dependences of the kinetic quantities, n and m, originate from that of z*, which is a pure thermodynamics quantity.