A note on Quarks and numbers theory

TL;DR

This paper introduces a novel binary number representation of basis vectors for unitary groups, connects it with quark notation, and uncovers a new property of prime numbers through this analogy.

Contribution

It presents a new binary encoding of Cartan basis vectors and relates quark models to prime number properties, offering a fresh perspective in mathematical physics.

Findings

Binary representation of SU(3) basis vectors using quark notation

Identification of a new prime number property through analogy with mesons and quarks

Connection between group theory and prime number characteristics

Abstract

We express the basis vectors of Cartan fundamental representations of unitary groups by binary numbers. We determine the expression of Gel'fand basis of SU (3) based on the usual subatomic quarks notations and we represent it by binary numbers. By analogy with the mesons and quarks we find a new property of prime numbers.