Number Theory

    

Proof of the Conjectures of Legendre, Andrica, Oppermann and Their Generalizations

Authors: Philippe Sainty

Proofs of the conjectures of Legendre, Andrica, Oppermann, Brocard and their generalizations using Lgk function sequences: x--> sqrt(pk/pk+1).sqrt(x).ln(x) , pk , kth prime number , x between pk and pk+1; we use reasoning by recurrence and absurdity; we obtain gaps framings between two consecutive primes, as well as the number of primes between N² and (N+1)². Generalizations with Lqk : x-->racineqième(pk/pk+1)*racineqième(x)*ln(x).

Comments: 21 Pages.

Download: PDF

Submission history

[v1] 2024-09-01 22:27:37

Unique-IP document downloads: 205 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