Sexy Prime Geometry is an experimental mathematical visualization based on a simple deterministic rule applied to the integers from 2 to 4,000.

A prime number p is treated as a sexy prime in this visualization when another prime exists at a distance of 6, i. e. when p−6 or p+6 is also prime.

The geometric construction starts at a fixed point and processes the integers sequentially. For every number n:

Sexy prime → +180° turn
All other integers → −90° turn

Each turn is represented by a circular arc of constant radius, and the endpoint of one arc becomes the starting point of the next. The animation therefore shows the geometry developing step by step as the integers are processed.

The resulting structure is not intended as a proof of a special property of sexy primes. Rather, it is a visual experiment: a simple arithmetic classification is translated into a sequence of geometric rotations, allowing patterns, symmetries and large-scale structures to emerge from the distribution of sexy primes.

Range: 2≤n≤4000
Sexy-prime rotation: +180°
Other integers: −90°
Arc radius: 1

The visualization was generated computationally in Python using a prime sieve and sequential circular-arc construction.