An elementary sieve

TL;DR

This paper reviews properties of numbers of the form 6n±1 and introduces a new sieve method to distinguish prime-generating numbers from composite ones, aiding in prime counting.

Contribution

It proposes a novel sieve based on 6n±1 numbers to identify primes and estimate their distribution up to a given limit.

Findings

Properties of 6n±1 numbers analyzed

A new sieve method introduced

Potential for prime counting up to h

Abstract

In this paper we review the properties of families of numbers of the form $6n\pm1$, with $n$ integer (in which there are all prime numbers greater than 3 and other compound numbers with particular properties) to later use them in a new sieve that allows the separation of numbers $n$ that generate primes from those that only generate compounds. In principle, this can be used to find the amount of prime numbers up to a given number $h$; this means, $\pi(h)$.