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Prime Values of the Euler Polynomial

N. A. Carella

Abstract

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

Prime Values of the Euler Polynomial

Abstract

This note provides an effective lower bound for the number of primes in the quadratic progression as .

Paper Structure

This paper contains 6 sections, 5 theorems, 30 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Linear to Quadratic Identity
  3. Fibers and Multiplicities
  4. Estimate for the Main Term
  5. Estimate for the Error Term
  6. Main Result

Key Result

Theorem 1.1

Let $x \geq 1$ be a large number. Then,

Theorems & Definitions (10)

  • Conjecture 1.1
  • Theorem 1.1
  • Lemma 2.1
  • Lemma 3.1
  • proof : Proof
  • Lemma 4.1
  • proof : Proof
  • Lemma 5.1
  • proof : Proof
  • proof : Proof