Number Theory

    

Goldbach Prime Pairs and Its Distribution for Integers of Form $ 2(n+1)^{2} $

Authors: Imran Ansari

In this article, detailed study on the distribution of the Goldbach prime pairs for the even integers of form $ 2(n + 1)^2 $ were carried out. The experimental proof of the formulated conjectures were given using the algorithm. The results suggest that, there will always be Goldbach prime pair for expression, $ (n)(n-1) < p_{f} < (n+1)^{2} < p'_{f} < 2(n+1)^{2} - (n)(n-1) $, were $ n = 1, 2, 3, ....$ Additionally, the gap between Goldbach first prime pair, that is, $ (p'_{f} - p_{f})$ was found to be always less than its corresponding $n$ value after $n = 2538 $, hence, $Gap(p'_{f} - p_{f}) << n$, where, $n = 2539, 2540, 2541, ....$

Comments: 21 Pages.

Download: PDF

Submission history

[v1] 2024-10-29 20:15:03
[v2] 2024-11-01 08:12:04
[v3] 2025-03-08 21:34:56

Unique-IP document downloads: 478 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus