Very good post! For an excellent introduction to the prime number theorem (and the Riemann Hypothesis), I recommend Prime Numbers and the Riemann Hypothesis, b

Very good post! For an excellent introduction to the prime number theorem (and the Riemann Hypothesis), I recommend Prime Numbers and the Riemann Hypothesis, by Barry Mazur and William Stein. It is structured in small chapters, each illuminating one idea, and I find this fantastic.