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A formally verified proof of the prime number theorem

Jeremy Avigad·Kevin Donnelly·David Gray·Paul Raff
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Abstract

The prime number theorem, established by Hadamard and de la Vall'ee 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 Erd"os in 1948. We describe a formally verified version of Selberg's proof, obtained using the Isabelle proof assistant.

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Jeremy Avigad, Kevin Donnelly, David Gray, Paul Raff. 2006-04-06. A formally verified proof of the prime number theorem. https://arxiv.org/abs/cs/0509025

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