An interactive, visual guide to one of the most beautiful theorems in mathematics: Dirichlet's theorem on primes in arithmetic progressions.
If you pick any starting number and step size that share no common factor, the sequence contains infinitely many primes — and they're spread equally among all valid starting points. Dirichlet proved this in 1837 by inventing entirely new mathematics.
This explorable explanation breaks the proof down into 8 sections with 20+ interactive visualizations, making it accessible to a motivated middle school student.
- Hook — pick a progression, watch primes appear
- Primes — factor trees, Euclid's argument, prime density
- Arithmetic Progressions — the mod-q grid, coprimality, Euler's totient
- Modular Arithmetic — remainder clocks, multiplication tables, group structure
- Dirichlet Characters — complex arrows, phasor sweeps, orthogonality, the extraction formula
- L-Functions — harmonic series, the s-dial, Euler product, the key formula
- Non-Vanishing — the product trick, pole/zero playground, the non-negative series trap
- The Full Picture — proof map, equidistribution, exploration sandbox
npm install
npm run devnpm run deployBuilds and pushes to the gh-pages branch for GitHub Pages hosting.
Maksym Lysenko and Claude Opus 4.6
MIT