A formally verified proof of the prime number theorem-Reference-Cited by-同舟云学术

A formally verified proof of the prime number theorem

Published:2007-12 Issue:1 Volume:9 Page:2
ISSN:1529-3785
Container-title:ACM Transactions on Computational Logic
language:en
Short-container-title:ACM Trans. Comput. Logic

Author:

Avigad Jeremy¹,Donnelly Kevin²,Gray David¹,Raff Paul³

Affiliation:

1. Carnegie Mellon University, Pittsburgh, PA

2. Boston University

3. Rutgers University

Abstract

The prime number theorem, established by Hadamard and de la Vallée Poussin independently in 1896, asserts that the density of primes in the positive integers is asymptotic to 1/ln x . Whereas their proofs made serious use of the methods of complex analysis, elementary proofs were provided by Selberg and Erdös in 1948. We describe a formally verified version of Selberg's proof, obtained using the Isabelle proof assistant.

Publisher

Association for Computing Machinery (ACM)

Subject

Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science

Link

https://dl.acm.org/doi/pdf/10.1145/1297658.1297660

Reference16 articles.

1. Number theory and elementary arithmetic†

2. Avigad J. and Donnelly K . 2004 . Formalizing O notation in Isabelle/HOL. In Proceedings of the 2nd International Joint Conference on Automated Reasoning (IJCAR) D. Basin and M. Rusinowitch Eds. vol. 3097 Lecture Notes in Artificial Intelligence Springer-Verlag 357--371. Avigad J. and Donnelly K. 2004. Formalizing O notation in Isabelle/HOL. In Proceedings of the 2nd International Joint Conference on Automated Reasoning (IJCAR) D. Basin and M. Rusinowitch Eds. vol. 3097 Lecture Notes in Artificial Intelligence Springer-Verlag 357--371.

3. Avigad J. and Friedman H. 2006. Combining decision procedures for the reals. Logic. Meth. Comput. Sci. 2 (4:4) 1--42. Avigad J. and Friedman H. 2006. Combining decision procedures for the reals. Logic. Meth. Comput. Sci. 2 (4:4) 1--42.

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