Edinburgh Research Explorer· 2013
A proof of Bertrand's postulate
- 97citations
- 2013year
Short summary
Bertrand's postulate has been formally proven using the Matita Interactive Theorem Prover, leveraging Chebyshev's machinery for prime number distribution.
AI-generated from the title and abstract; the full text is not read.
Key points
- Bertrand's postulate has been formally proven using the Matita Interactive Theorem Prover.
- The proof is based on Chebyshev's work concerning the distribution of prime numbers.
- It employs elementary arithmetic, including properties of primes, GCD, products, and summations.
- The formalization serves as a benchmark for arithmetical knowledge bases in theorem provers.
AI-generated from the title and abstract; the full text is not read.
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 Even if Chebyshev's result has been later superseded by the stronger prime number theorem, his machinery, and in particular the two functions psi and theta still play a central role in the modern development of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.
The authors' abstract, as published at the source. Edinburgh Research Explorer, 2013 · DOI ↗
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Field: Theoretical Computer Science
Theoretical Computer ScienceMathematics