On the storage and retrieval of primes and other random numbers using n-dimensional geometry

TL;DR

This paper presents a geometric method to store and retrieve prime numbers efficiently by representing them as points in n-dimensional space and separating them with planes, enabling scalable and adaptable data management.

Contribution

The paper introduces a novel geometric approach for prime storage and retrieval that does not rely on prime-specific properties, allowing for scalable and adaptable data systems.

Findings

Prime numbers can be represented as points in n-dimensional space.

A small number of planes can separate all primes less than n digits.

The system allows incremental addition of primes without reinitialization.

Abstract

We show that if you represent all primes with less than n-digits as points in n-dimensional space, then they can be stored and retrieved conveniently using n-dimensional geometry. Also once you have calculated all the prime numbers less than n digits, it is very easy to find out if a given number having less than n-digits is or is not a prime. We do this by separating all the primes which are represented by points in n-dimension space by planes. It so turns out that the number of planes q, required to separate all the points represented by primes less than n-digit, are very few in number. Thus we obtain a very efficient storage and retrieval system in n-dimensional space. In addition the storage and retieval repository has the property that when new primes are added there is no need to start all over, we can begin where we last left off and add the new primes in the repository and add new planes that separate them as and when necessary. Also we can arrange matters such that the repository can begin to accept larger primes which has more digits say n' where n' > n. The algorithm does not make use of any property of prime numbers or of integers in general,except for the fact that any n-digit integer can be represented as a point in n-dimension space. Therefore the method can serve to be a storage and retrieval repository of any set of given integers, in practical cases they can represent information. Thus the algorithm can be used to devise a very efficient storage and retrieval system for large amounts of digital data.