Introduction to number theory lecture 47. The prime number theorem

This lecture is part of my Berkeley math 115 course “Introduction to number theory”
For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8

We give an overview of the prime number theorem, stating that the number of primes less than x is about x/log x

Zagier’s article about the proof: https://www.jstor.org/stable/2975232

The textbook is “An introduction to the theory of numbers” by Niven, Zuckerman, and Montgomery (5th edition).