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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. https://doi.org/10.20944/preprints202109.0097.v1 Feliksiak, J. Bounds on the Number of Primes in Ramanujan Interval. Preprints 2021, 2021090097. https://doi.org/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
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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