Number Theory

   

On the Firoozbakht’s and Cramér‎’s Conjectures as N→∞

Authors: Reza Farhadian

Let p_n be the nth prime number. We prove that p_(n+1)<〖p_n〗^((n+1)/n ((logp_(n+1))/(logp_n )) ) for every n≥1. This inequality is weaker than the Firoozbakht’s conjecture p_(n+1)<〖p_n〗^((n+1)/n).Afterward we prove that the new inequality is equivalent to Firoozbakht’s conjecture, as n→∞, and hence the Cramér’s conjecture p_(n+1)-p_n=O(log^2 p_n ) to be hold, because the Firoozbakht’s conjecture is stronger than the Cramér’s conjecture, see [5].

Comments: 5 Pages.

Download: PDF

Submission history

[v1] 2017-02-26 13:00:05

Unique-IP document downloads: 30 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