Ramanujan and Labos primes, their generalizations and classifications of primes

TL;DR

This paper explores Ramanujan and Labos primes, their generalizations, and classifications, introducing sieves and posing conjectures to deepen understanding of these special prime sets.

Contribution

It introduces generalized Ramanujan and Labos primes, develops sieves for their identification, and proposes new conjectures and open problems in prime classification.

Findings

Identification of generalized Ramanujan and Labos primes

Construction of sieves for these primes

Formulation of conjectures and open problems

Abstract

Considering Ramanujan primes and the symmetric to them so-called Labos primes, we study their parallel properties, we study all primes with these properties (generalized Ramanujan and Labos primes) and construct two kinds of sieves for them. Finally, we give a further natural generalization of these constructions and pose some conjectures and open problems.