The Collision Invariant

A hidden symmetry in prime number collisions. This audio overview walks through the collision invariant, a finite signed integer attached to every prime by long division.

The digit function floor(br/p) sorts remainders into bins. The collision count depends only on the prime's last two digits. Complement pairs sum to exactly -1. The table's mean is exactly -1/2. Every prime larger than b^2 has a home in this finite periodic table.

Paper: https://arxiv.org/abs/2604.00045
Blog post: https://alexpetty.com/the-collision-invariant/
Code: https://github.com/alexspetty/nfield

Alexander S. Petty, 2026

Видео The Collision Invariant канала Petty's Notebook