Prime Values of the Euler Polynomial

TL;DR

This paper establishes an effective lower bound on the quantity of primes of the form n^2+1 up to a large number x, advancing understanding of prime distribution in quadratic progressions.

Contribution

It provides a new effective lower bound for the count of primes in the quadratic progression n^2+1, improving previous results in this area.

Findings

Derived an explicit lower bound for primes of the form n^2+1

Enhanced understanding of prime distribution in quadratic sequences

Contributed to the theory of primes in polynomial progressions

Abstract

This note provides an effective lower bound for the number of primes in the quadratic progression $p=n^2+1 \leq x$ as $x \to \infty$.