Preprint
Article

On the Additive and Subtractive Representation of Even Numbers from Primes

This version is not peer-reviewed.

Submitted:

04 December 2021

Posted:

07 December 2021

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Abstract
We demonstrate a new quantitative method to the sieve of Eratosthenes, which is an alternative to the sieve of Legendre. In this method, every element of a given set is sifted out once only, and therefore, this method is free of the Mobius function and of the consequential parity barrier. Using this method, we prove that every sufficiently large even number is the sum of two primes, and that every even number is the difference of two primes in infinitely many ways.
Keywords: 
Sieve of Eratosthenes; Goldbach’s conjecture; Polignac’s conjecture; Twin Prime conjecture
Subject: 
Computer Science and Mathematics  -   Algebra and Number Theory
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.

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