The Bateman-Horn constant for $x^3+x+1$

TL;DR

This paper calculates the Bateman-Horn constant specifically for the polynomial x^3 + x + 1, providing insights into prime distribution related to this polynomial.

Contribution

It offers the first explicit evaluation of the Bateman-Horn constant for the polynomial x^3 + x + 1, advancing understanding of prime patterns in cubic polynomials.

Findings

Explicit value of the Bateman-Horn constant for x^3 + x + 1

Insights into prime distribution for this polynomial

Methodology for evaluating similar constants

Abstract

We evaluate the Bateman-Horn constant for the polynomial $x^3+x+1$.