A function to calculate all relative prime numbers up to the product of the first n primes

TL;DR

The paper introduces a novel function based on prime modular numbers that efficiently calculates all numbers up to the product of the first n primes which are coprime to those primes, offering a new perspective on prime number computation.

Contribution

It establishes an isomorphism between a finite domain and prime modular numbers, enabling non-sequential calculation of coprime numbers up to the product of the first n primes.

Findings

Provides an inverse function for prime modular numbers.

Enables non-sequential calculation of coprime numbers.

Offers insights into the structure of relative prime numbers.

Abstract

We prove an isomorphism between the finite domain from 1 up to the product of the first n primes and the new defined set of prime modular numbers. This definition provides some insights about relative prime numbers. We provide an inverse function from the prime modular numbers into this finite domain. With this function we can calculate all numbers from 1 up to the product of the first n primes that are not divisible by the first n primes. This function provides a non sequential way for the calculation of prime numbers.