Counting Primes

The prime number theorem

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• $\pi(x)$ counts the primes up to $x$.
• Prime number theorem: $\pi(x) \approx x / \ln x$.
• Near $n$, about 1 in $\ln n$ numbers is prime.

Steps

1. Thinning out
2. Primes below a million
3. Below one hundred
4. Average gap
5. Twin primes below 100
6. Random big primes