On compositeness of special types of integers

TL;DR

This paper investigates special types of integers, disproves a conjecture about the infinitude of primes of a certain form, and explores related conjectures in number theory.

Contribution

It provides a counterexample to Juricevic's conjecture and analyzes the nature of primes of special forms in the context of Lehmer triples.

Findings

Disproved Juricevic's conjecture on primes of a special form.

Established results on the structure of Lehmer triples.

Explored the implications for the distribution of primes of special types.

Abstract

In paper on a classification of Lehmer triples, Juricevic conjectured that there are infinitely many primes of special form. We disprove one of his conjectures and consider the other one.