Title: Formalization of the prime number theorem and Dirichlet's theorem
Abstract: 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 $\pi(x)$ of primes less than $x$ is asymptotic to $x/\log x$, within the proof system Metamath.