A classic way to visualise prime numbers is in a spiral. Imagine a rope with all natural numbers (1, 2, 3, 4…) evenly spaced from each other. We roll the rope into a spiral with 1 at the center. Now we hide all non-prime numbers, leaving only the primes.

This animation extends this to three dimensions, by progressively stretching and twisting the spiral of prime numbers around itself into a ball of yarn. We see the first 50k prime numbers (up to 611953).

The size of the prime numbers corresponds to the distance to the previous prime. Twin primes (where n and n + 2 are both prime) are coloured blue. Pythagorean primes (where p = 4n + 1) are red. All other primes are yellow.