## A New Simple Recursive Algorithm for Finding Prime Numbers Using Rosser's Theorem

**Authors:** Rédoane Daoudi

In our previous work (The distribution of prime numbers: overview of n.ln(n), (1) and (2)) we defined a new method derived from Rosser's theorem (2) and we used it in order to approximate the nth prime number. In this paper we improve our method to try to determine the next prime number if the previous is known. We use our method with five intervals and two values for n (see Methods and results). Our preliminary results show a reduced difference between the real next prime number and the number given by our algorithm. However long-term studies are required to better estimate the next prime number and to reduce the difference when n tends to infinity. Indeed an efficient algorithm is an algorithm that could be used in practical research to find new prime numbers for instance.

**Comments:** 7 Pages.

**Download:** **PDF**

### Submission history

[v1] 2017-02-21 06:04:58

**Unique-IP document downloads:** 15 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.*

*
*