On the Additive and Subtractive Representation of Even Numbers from Primes

Ali Shehu; Jetmira Uka

doi:10.20944/preprints202110.0087.v8

Preprint Article Version 8 Preserved in Portico This version is not peer-reviewed

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)
Version 3 : Received: 4 December 2021 / Approved: 7 December 2021 / Online: 7 December 2021 (20:52:47 CET)
Version 4 : Received: 12 January 2022 / Approved: 14 January 2022 / Online: 14 January 2022 (14:43:54 CET)
Version 5 : Received: 29 June 2022 / Approved: 30 June 2022 / Online: 30 June 2022 (03:50:17 CEST)
Version 6 : Received: 9 July 2022 / Approved: 11 July 2022 / Online: 11 July 2022 (04:28:25 CEST)
Version 7 : Received: 21 July 2022 / Approved: 22 July 2022 / Online: 22 July 2022 (03:38:39 CEST)
Version 8 : Received: 4 August 2022 / Approved: 5 August 2022 / Online: 5 August 2022 (03:41:27 CEST)

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 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.

Sieve of Eratosthenes; Goldbach conjecture; Polignac conjecture; Twin Prime conjecture

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

Comment 1

Received: 5 August 2022
Commenter: Ali Shehu
Commenter's Conflict of Interests: Author

Comment: Some minor adjustments were made.

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On the Additive and Subtractive Representation of Even Numbers from Primes

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