A formally verified proof of the prime number theorem

Details A formally verified proof of the prime number theorem A formally verified proof of the prime number theorem

2005-09-09

arxiv.org/abs/cs/0509025v3

Computer Science

Artificial Intelligence

23 pages

Scientific paper

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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