1. either is satisfiable and any one of its prime implicants has a normalized length at least equal to (α_m^r(c)/(1 - e^-rc)) - and at most equal to (α_M^r(c)/(1 - e^-rc)) + , α_m^r(c) and α_M^r(c) being well-defined as functions of c,

2. or is unsatisfiable.

A first practical consequence is when testing the satisfiability of r-CNF formulae by procedures such as the well-known Davis, Putnam and Loveland Procedure, for almost every r-CNF formula, when it is satisfiable, the proportion of variables which must be assigned a value by such procedures, in order to find a solution, is at least equal to (α_m^r(c)/(1 - e^-rc)) - .

A second consequence is that almost every r-CNF formula, when it is satisfiable, has an exponential actual number of solutions (i.e. the number of solutions defined on the variables occurring in the formula) at least equal to 2^{(1 - e-rc} - α_M^r(c) - )n. Moreover for r = 2, 3 we show th for any c it is at least equal to 2^0.03n,2^0.012n, respectively.