Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

A necessary and sufficient condition for proof of the Binary Goldbach conjecture. Proofs of Binary Goldbach, Andrica and Legendre conjectures. Notes on the Riemann hypothesis. (Edition 8D)

Version 1 : Received: 11 September 2023 / Approved: 14 September 2023 / Online: 15 September 2023 (04:23:12 CEST)
Version 2 : Received: 21 September 2023 / Approved: 3 October 2023 / Online: 7 October 2023 (08:13:27 CEST)
Version 3 : Received: 17 November 2023 / Approved: 20 November 2023 / Online: 30 November 2023 (05:11:18 CET)

A peer-reviewed article of this Preprint also exists.

Buya, S.B.; Nchima, J.B. A Necessary and Sufficient Condition for Proof of the Binary Goldbach Conjecture. Proofs of Binary Goldbach, Andrica and Legendre Conjectures. Notes on the Riemann Hypothesis. International Journal of Pure and Applied Mathematics Research 2024, 4, 12–27, doi:10.51483/ijpamr.4.1.2024.12-27. Buya, S.B.; Nchima, J.B. A Necessary and Sufficient Condition for Proof of the Binary Goldbach Conjecture. Proofs of Binary Goldbach, Andrica and Legendre Conjectures. Notes on the Riemann Hypothesis. International Journal of Pure and Applied Mathematics Research 2024, 4, 12–27, doi:10.51483/ijpamr.4.1.2024.12-27.

Abstract

In this research a neccessary and sufficient condition for the proof of the Binary Goldbach conjecture is established. It is established that the square of all natural numbers greater or equal to 2 have an additive partition equal to the sum of the square of a natural number greater or equal to zero and a Goldbach partition semiprime. All Goldbach partition semiprimes are odd except 4. This finding is in itself proof all composite even numbers have at least Goldbach partition. The result of the proof of the Binary Goldbach conjecture is used to prove the Andrica and Legendre conjectures. The Riemann hypothesis is examined and sources of non trivial zeroes outside the critical strip are discussed. An example example of a non-trivial zero outside the critical strip is given

Keywords

Proof of Binary Golbdach conjecture; Proof of Andrica conjecture; Proof of Legendre conjecture; Goldbach partition semiprime; Disproof of Riemann hypothesis

Subject

Computer Science and Mathematics, Algebra and Number Theory

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.

Leave a public comment
Send a private comment to the author(s)
* All users must log in before leaving a comment
Views 0
Downloads 0
Comments 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.