How many primes are there below x? The answer hides behind the greatest unsolved problem in math.
π(x) counts primes ≤ x. The Prime Number Theorem says π(x) ≈ x / ln(x).
A better estimate is the logarithmic integral Li(x).
The Riemann Hypothesis (unsolved, $1 million prize) says the error between π(x) and Li(x) is bounded by O(√x·log x). Below, watch all three plotted together.