A conjecture about prime numbers assuming the Riemann hypothesis

Rédoane Daoudi (1)

1 Université de Poitiers - Faculté de Sciences fondamentales et appliquées

In this paper we propose a conjecture about prime numbers. Based on the result of Pierre Dusart stating that the n th prime number is smaller than n(ln n+ln ln n−0.9484) for n ≥ 39017 we propose that the n th prime number is smaller than n(ln n + ln ln n − 1 +) when n → +∞.

Mots clés: Prime numbers; Dusart; Riemann hypothesis; conjecture

Domaines: Théorie des nombres [math.NT]

Rédoane Daoudi. A conjecture about prime numbers assuming the Riemann hypothesis. 2017. ⟨hal-01560672⟩