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Bounds on the Number of Primes in Ramanujan Interval

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Submitted:

05 September 2021

Posted:

06 September 2021

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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.
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Subject: Computer Science and Mathematics  -   Algebra and Number Theory
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
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