Primes In Cubic Arithmetic Progressions

TL;DR

This paper proves that there are infinitely many primes of the form n^3 + 2 and estimates their distribution, advancing understanding of primes in cubic polynomial sequences.

Contribution

It provides a proof that the primes of the form n^3 + 2 are infinite and estimates their counting function's growth.

Findings

Primes of the form n^3 + 2 are infinite.

Estimated order of magnitude of their counting function.

Established the distribution pattern of cubic primes.

Abstract

This work proposes a proof of the simplest cubic primes counting problem. It shows that the subset of primes {p = n^3 + 2 is prime : n => 1} is an infinite subset of primes. Further, the expected order of magnitude of the cubic primes counting function is established.