The Prime Number Theorem

How thinly the primes are spread: Gauss's guess, the 1896 proof through the zeta function, Riemann's zeros behind the error, and what remains open

The Prime Number Theorem — the density of primes and 1/ln x, Chebyshev's function, prime counts against li(x) and Riemann's R(x), the explicit formula rebuilt from zeta zeros, the critical strip, the race between π(x) and li(x), prime gaps and the nth prime