The distribution of natural numbers divisible by 2,3,5,11,13 and 17 on the Square Root Spiral

TL;DR

This paper analyzes how natural numbers divisible by specific prime factors are distributed on the Square Root Spiral, revealing they lie on quadratic polynomial-defined spiral graphs with distinct spatial orientations.

Contribution

It identifies the quadratic polynomial equations governing the spiral graphs for numbers divisible by 2, 3, 5, 11, 13, and 17, and classifies these graphs into specific Spiral Graph Systems.

Findings

Numbers divisible by the same prime factor lie on specific spiral graphs.

These spiral graphs are defined by quadratic polynomials.

Spiral graphs can be grouped into systems with defined spatial orientations.

Abstract

The natural numbers divisible by the Prime Factors 2, 3, 5, 11, 13 and 17 lie on defined spiral graphs, which run through the Square Root Spiral. A mathematical analysis shows, that these spiral graphs are defined by specific quadratic polynomials. Basically all natural number which are divisible by the same prime factor lie on such spiral graphs. And these spiral graphs can be assigned to a certain number of Spiral Graph Systems, which have a defined spatial orientation to each other. This document represents a supplementation to my detailed introduction study to the Square Root Spiral, and it contains the missing diagrams and analyses, showing the distribution of the natural numbers divisible by 2, 3, 5, 11, 13 and 17 on the Square Root Spiral. My introduction study to the Square Root Spiral can be found in the arxiv-archive. The title of this study : The ordered distribution of the natural numbers on the Square Root Spiral.