The Riemann Hypothesis

The function

$$\Li(x) = \int_{2}^{x} \frac{1}{\log(x)} dx.$$

is also a good approximation to $\pi(x)$.

The famous Riemann Hypothesis is equivalent to the assertion that

$$\pi(x) = \Li(x) +O(\sqrt{x}\log(x)).$$

(This is another $1000000 prize problem.)

      pi(10^22)     = 201467286689315906290
      Li(10^22)     = 201467286691248261498.1505...    (using Maple)
      Log(x)/(x-1)  = 201381995844659893517.7648...    (pari)