About the Formalization of some Results by Chebyshev in Number Theory

We discuss the formalization, in the Matita Interactive Theorem Prover, of a famous result by Chebyshev concerning the distribution of prime numbers, essentially subsuming, as a corollary, Bertrand's postulate. Even if Chebyshev's result has been later superseded by the stronger prime number theorem, his machinery, and in particular the two functions psi and theta still play a central role in the modern development of number theory. Differently from other recent formalizations of other results innumber theory, our proof is entirely arithmetical. It makes use of most part of the machinary of elementary arithmetics, and in particular of properties of prime numbers, gcd, products and summations, providing a natural benchmark for assessing the actual development of the arithmetical knowleddge base.