Frequency Distribution of Prime Numbers between an Integer and its Square: A Case Study

TL;DR

This paper investigates the distribution of prime numbers between an integer and its square, proposing potential patterns that could impact fields like encryption and algorithm design.

Contribution

It introduces mathematical equations suggesting a pattern in prime occurrence between a number and its square, challenging the belief that primes are patternless.

Findings

Identification of potential patterns in prime distribution

Mathematical equations supporting the pattern hypothesis

Implications for encryption and algorithms

Abstract

The chronicle of prime numbers travel back thousands of years in human history. Not only the traits of prime numbers have surprised people, but also all those endeavors made for ages to find a pattern in the appearance of prime numbers has been captivating them. Until recently, it was firmly believed that prime numbers do not maintain any pattern of occurrence among themselves. This statement is conferred not to be completely true. This paper is also an attempt to discover a pattern in the occurrence of prime numbers. This work intends to introduce some mathematical well-known equations that point to the existence of a simplistic pattern in the number of primes within the range of a number and its square. We assume that the rigorous evaluation of the perceived pattern may benefit in many aspects such as applications of encryption, algorithms concerning prime numbers, and many more.