Prime number generation and factor elimination

TL;DR

This paper introduces a multivariate polynomial function called the factor elimination function, which can generate prime numbers and explain their distribution, potentially leading to more efficient prime generation algorithms.

Contribution

The paper proposes a novel polynomial-based method for prime number generation and provides conditions for primality, offering new insights into prime distribution and algorithm efficiency.

Findings

The factor elimination function can generate prime numbers.

It explains irregularities in prime distribution.

It suggests pathways for efficient prime generation algorithms.

Abstract

We have presented a multivariate polynomial function termed as factor elimination function,by which, we can generate prime numbers. This function's mapping behavior can explain the irregularities in the occurrence of prime numbers on the number line. Generally the different categories of prime numbers found till date, satisfy the form of this function. We present some absolute and probabilistic conditions for the primality of the number generated by this method. This function is capable of leading to highly efficient algorithms for generating prime numbers.