A conjecture about prime numbers assuming the Riemann hypothesis

Abstract : 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 → +∞.
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https://hal.archives-ouvertes.fr/hal-01560672
Contributor : Rédoane Daoudi <>
Submitted on : Tuesday, July 11, 2017 - 6:37:03 PM
Last modification on : Wednesday, May 15, 2019 - 10:34:02 AM
Long-term archiving on : Wednesday, January 24, 2018 - 8:15:31 PM

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

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