A proof of Bertrand's postulate

Andrea Asperti, Wilmer Ricciotti

Abstract


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Even if Chebyshev's result has been later superseded by the stronger prime number theorem, his machinery, and in particular the two functions psi and theta still play a central role in the modern development of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.

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DOI: 10.6092/issn.1972-5787/3406

Copyright (c) 2012 Andrea Asperti, Wilmer Ricciotti

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