An elementary sieve

Damian Gulich; Gustavo Funes; Leopoldo Garavaglia; Beatriz Ruiz; Mario Garavaglia

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arXiv · 0708.3709

An elementary sieve

Damian Gulich·Gustavo Funes·Leopoldo Garavaglia·Beatriz Ruiz·Mario Garavaglia

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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, $π(h)$.

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Damian Gulich, Gustavo Funes, Leopoldo Garavaglia, Beatriz Ruiz, Mario Garavaglia. 2007-08-28. An elementary sieve. https://arxiv.org/abs/0708.3709

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