Millennium Prize Problems

The Riemann Hypothesis: Why All Zeros Must Lie on a Single Line

Understanding the Riemann Hypothesis: Prime Numbers and Quantum Physics

Part 4: I discuss the connection between the zeros of the Riemann zeta function and the distribution of prime numbers. The zeros control the oscillations of the prime counting function, $\\pi(x)$. The prime counting function is roughly approximated by $li(x)$, which is the logarithmic integral and is basically the number one would expect. The difference between $\\pi(x)$ and $li(x)$ contributes a term like $\\cos(t \\log x)$. We note that if Riemann Hypothesis is true, prime numbers are spread s