Visualizing prime numbers through direction-encoded random walks
How It Works
We take a walk where each integer from 1 upward determines the direction. Primes bend the path.
Prime digit walk: digits of each prime control turns Prime residue walk: prime mod 4 encodes direction Twin prime walk: forward on twin primes Sieve walk: turn when hitting a prime
The resulting paths reveal hidden structure in prime distributions — Dirichlet's theorem, twin prime clustering, and more.
Primes found—
Steps taken—
Net displacement—
Largest prime gap—
The "residue mod 4" walk reflects Dirichlet's theorem: primes ≡1 and ≡3 (mod 4) appear equally often (≈50% each).