Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Bounds on the Number of Primes in Ramanujan Interval

Version 1 : Received: 5 September 2021 / Approved: 6 September 2021 / Online: 6 September 2021 (13:21:06 CEST)

How to cite: Feliksiak, J. Bounds on the Number of Primes in Ramanujan Interval. Preprints 2021, 2021090097 (doi: 10.20944/preprints202109.0097.v1). Feliksiak, J. Bounds on the Number of Primes in Ramanujan Interval. Preprints 2021, 2021090097 (doi: 10.20944/preprints202109.0097.v1).

Abstract

The Ramanujan primes are the least positive integers Rn having the property that if m ≥ Rn, then πm − π(m/2) ≥ n. This document develops several bounds related to the Ramanujan primes, sharpening the currently known results. The theory presented is by no means exhaustive, however it provides insights for future research work. Alternatively, we may say that it is a road map which may be followed to make further discoveries.

Keywords

Prime counting function Supremum/Infimum; prime numbers distribution; Ramanujan Interval; Ramanujan primes

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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