An Arithmetic Metric

TL;DR

This paper introduces a novel arithmetic-based metric for measuring the distance between natural numbers, focusing on their intrinsic properties rather than their numerical positions.

Contribution

It proposes a new distance measure rooted in the arithmetic characteristics of numbers, offering an alternative to traditional numerical metrics.

Findings

The metric captures meaningful differences between numbers based on their prime and composite structure.

It provides a different perspective on number relationships beyond standard numerical proximity.

Potential applications in number theory and related computational fields.

Abstract

What is the distance between 11 (a prime number) and 12 (a highly composite number)? If your answer is 1, then ask yourself "is this reasonable?" In this work, we will introduce a distance between natural numbers based on their arithmetic properties, instead of their position on the real line.