On the Natural Numbers that cannot be Expressed as a Sum of Two Primes

Peter Szabó

doi:10.20944/preprints202408.1416.v3

Preprint Article Version 3 This version is not peer-reviewed

Version 1 : Received: 19 August 2024 / Approved: 20 August 2024 / Online: 20 August 2024 (12:03:53 CEST)
Version 2 : Received: 5 September 2024 / Approved: 5 September 2024 / Online: 5 September 2024 (10:42:32 CEST)
Version 3 : Received: 25 October 2024 / Approved: 26 October 2024 / Online: 28 October 2024 (02:15:03 CET)

In the article, we define a sequence F: F(0) = 2, F(1) = 10, F(2) = 16, F(3) = 22, F(4) = 26, F(4) = 28, · · · , F(i) = F(i − 1) + l, where the number l ≤ 8 is defined by using prime numbers and matrix algebra. The sequence includes only even numbers and can be used to define a series of numbers F(i) + 1, the non-Goldbach sequence, that contains all numbers that cannot be written as the sum of two primes. The result is related to Goldbach’s conjecture. The famous Goldbach conjecture states that every even integer greater than 2 can be expressed as the sum of two primes.

circulant matrix; prime number; the Goldbach conjecture; the ternary Goldbach conjecture

Computer Science and Mathematics, Algebra and Number Theory

Not displayed online.

Please leave your comment to this article below.

Mathematical equations can be typed in either LaTeX formats \\[ ... \\] or $$ ... $$, or MathML format <math> ... </math>. Try the LaTeX or MathML example.

Type equation:

Preview:

Copy equation into message below

Close menu

Please click a symbol to insert it into the message box below:

Please enter the link here:

Optionally, you can enter text that should appear as linked text:

Copy link into message below

Close menu

Please enter or paste the URL to the image here (please only use links to jpg/jpeg, png and gif images):

Copy image into message below

Close menu

Type author name or keywords to filter the list of references in this group (you can add a new citation under Bibliography):

No existing citations in Discussion Group

Wikify editor is a simple editor for wiki-style mark-up. It was written by MDPI for Sciforum in 2014. The rendering of the mark-up is based on Wiky.php with some tweaks. Rendering of mathematical equations is done with MathJax. Please send us a message for support or for reporting bugs.

Close menu

Please declare any conflicts of interest you may have with this paper, financial or otherwise.

I do not have a conflict of interest

I would like to declare a conflict of interest

Display my name on the website

Captcha

Renew

I accept the following conditions:

Comments must follow the standards of professional discourse and should focus on the scientific content of the article. Insulting or offensive language, personal attacks and off-topic remarks will not be permitted. Comments must be written in English. Preprints reserves the right to remove comments without notice. Readers who post comments are obliged to declare any competing interests, financial or otherwise.

* All users must log in before leaving a comment

Notify me about updates to this article or when a peer-reviewed version is published.

On the Natural Numbers that cannot be Expressed as a Sum of Two Primes

Abstract

Keywords

Subject

Comments (0)