This talk considers logical formulas built on the single binary connector of implication and a finite number of variables. When the number of variables becomes large, we prove the following quantitative results: {\em asymptotically, all classical tautologies are \textit{simple tautologies}}. It follows that {\em asymptotically, all classical tautologies are intuitionistic}. We investigate the proportion between the number of formulas of size $n$ that are tautologies against the number of all formulas of size $n$. After isolating the special class of formulas called simple tautologies, of density $1/k+O(1/k2)$, we exhibit some families of non-tautologies whose cumulated density is $1-1/k-O(1/k2)$. It follows that the fraction of tautologies, for large $k$, is very close to the lower bound determined by simple tautologies. A consequence is that classical and intuitionistic logics are close to each other when the number of propositional variables is large.