A new simple recursive algorithm for finding prime numbers using Rosser's theorem

Rédoane Daoudi (1)

1 Université de Poitiers - Faculté de Sciences fondamentales et appliquées

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.

Mots clés: Prime numbers; Algorithm prime numbers; Rosser's theorem

Domaines: Théorie des nombres [math.NT]

Rédoane Daoudi. A new simple recursive algorithm for finding prime numbers using Rosser's theorem. 2017. ⟨hal-01472833⟩