Mario Carneiro
Abstract
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We present the formalization of Dirichlet's theorem on the infinitude of primes in arithmetic progressions, and Selberg's elementary proof of the prime number theorem, which asserts that the number $π(x)$ of primes less than $x$ is asymptotic to $x/\log x$, within the proof system Metamath.
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We present the formalization of Dirichlet's theorem on the infinitude of primes in arithmetic progressions, and Selberg's elementary proof of the prime number theorem, which asserts that the number $π(x)$ of primes less than $x$ is asymptotic to $x/\log x$, within the proof system Metamath.
Key concepts: Prime number theorem, Analytic number theory, Mathematics, Multiplicative number theory, Dirichlet distribution, Prime number, Dirichlet series, Prime (order theory)