TY - JOUR AU - Asperti, Andrea AU - Ricciotti, Wilmer PY - 2012/01/01 Y2 - 2024/03/29 TI - A proof of Bertrand's postulate JF - Journal of Formalized Reasoning JA - JFR VL - 5 IS - 1 SE - Articles DO - 10.6092/issn.1972-5787/3406 UR - https://jfr.unibo.it/article/view/3406 SP - 37-57 AB - We discuss the formalization, in the Matita Interactive Theorem Prover, of some results by Chebyshev concerning the distribution of prime numbers, 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 Even if Chebyshev's result has been later superseded by the stronger prime number theorem, his machinery, and in particular the two functions psi and theta still play a central role in the modern development of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. The proof makes use of most part of the machinery 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 knowledge base. ER -