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