Find the largest prime below $10^9$. How many primes numbers are there before this one? Which one is next? Compare to the prime-counting function $\pi(x)$ that counts how many primes there are below $x$ and which Gauss approximated to $x/\ln(x)$.
Answer: This is $999\,999\,937$, the $50\,847\,534$th prime number, for which the prime-counting function $\pi(x)$ compares to Gauss' approximation $\pi(x)\approx x/\ln x=48\,254\,942$ to withing 5% accuracy.
well, more things today?