Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

On the Additive and Subtractive Representation of Even Numbers from Primes

Version 1 : Received: 1 October 2021 / Approved: 5 October 2021 / Online: 5 October 2021 (14:48:18 CEST)
Version 2 : Received: 24 November 2021 / Approved: 25 November 2021 / Online: 25 November 2021 (20:28:09 CET)

How to cite: Shehu, A.; Uka, J. On the Additive and Subtractive Representation of Even Numbers from Primes. Preprints 2021, 2021100087 (doi: 10.20944/preprints202110.0087.v2). Shehu, A.; Uka, J. On the Additive and Subtractive Representation of Even Numbers from Primes. Preprints 2021, 2021100087 (doi: 10.20944/preprints202110.0087.v2).

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

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

Comments (1)

Comment 1
Received: 25 November 2021
Commenter: Ali Shehu
Commenter's Conflict of Interests: Author
Comment: Improved on some of the notation used.
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