On prime-generating linear polynomials and x^2+1

TL;DR

This paper uses elementary methods and Dirichlet's theorem to prove that certain linear polynomials and the polynomial x^2+1 generate infinitely many primes, providing new insights into prime distribution.

Contribution

It offers elementary proofs that linear polynomials and x^2+1 produce infinitely many primes, expanding understanding of prime-generating polynomials.

Findings

Linear polynomials generating primes also generate infinitely many primes

x^2+1 generates infinitely many primes

Elementary proof techniques applied to prime distribution

Abstract

In this paper we use Dirichlet's theorem in order to elementally prove two theorems. The first says that since a polynomial ax+b generates one prime, it also generates infinites. The second theorem (which is proved in a very simillar way to the first) says that x^2+1 generates infinitely many primes.