Infinite Primes, Quadratic Polynomials, and Fermat’s Criterion

EasyChair Preprint no. 11402

Abstract

In this study, we explore the existence of an infinite number of primes
represented by the quadratic polynomial 4(Mp − 2)2 + 1 . We propose
a hypothesis that considers Fermat primes as a criterion for the infinitude
of such primes, where Mp represents Mersenne primes. Additionally,
we provide an elementary argument supporting the presence of infinitely
many primes in the form , as these primes are a subset of primes of the
same form x2 + 1 . Furthermore, we present a basic argument demonstrating
the infinity of Mersenne primes. This paper contributes to the
understanding of prime numbers and their intriguing relationships with
quadratic polynomials and Fermat primes.

Keyphrases: natural number, Prime, Real

@Booklet{EasyChair:11402,
  author = {Budee U Zaman},
  title = {Infinite Primes, Quadratic Polynomials, and Fermat’s Criterion},
  howpublished = {EasyChair Preprint no. 11402},

  year = {EasyChair, 2023}}