Prime values of a sparse polynomial sequence

TL;DR

This paper investigates the distribution of prime numbers within a sparse polynomial sequence, specifically estimating the count of primes of the form x^3 + 2y^3 when y is small, addressing a key challenge in prime number theory.

Contribution

It provides an estimate for the number of primes in the sparse sequence x^3 + 2y^3 with small y, advancing understanding of primes in polynomial sequences.

Findings

Estimated the number of primes of the form x^3 + 2y^3 with small y

Addressed the challenge of prime distribution in sparse polynomial sequences

Contributed to prime number theory by analyzing specific polynomial forms

Abstract

A distinguishing feature of certain intractable problems in prime number theory is the sparsity of the underlying sequence. Motivated by the general problem of finding primes in sparse polynomial sequences, we give an estimate for the number of primes of the shape $x^3 + 2y^3$ where $y$ is small.