Generalizations of the Rowland theorem

TL;DR

This paper generalizes Rowland's theorem by providing new equivalent formulations and extends the results to generate primes greater than a fixed prime, broadening the understanding of prime generation.

Contribution

It introduces new formulations of Rowland's theorem enabling generalizations and prime generation beyond a fixed prime.

Findings

New equivalent theorems to Rowland's results

A method to generate primes larger than a given prime

Extended understanding of prime generation mechanisms

Abstract

We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.