Resumen en inglés

Given a real positive number x, the quantity of prime numbers less than or equal to x is denoted by π(x). In this work, we will present an elementary proof of famous prime number theorem, which asserts that the quantity π(x) is asymptotically equivalent to the quotient x/ ln x as x → ∞. To do this demonstration, we will use elementary techniques of analytic number theory to demonstrate Selberg’s asymptotic formula, from which we will derive the elementary proof of the prime number theorem.