On solving a curious inequality of ramanujan

Adrian W. Dudek; David J. Platt

doi:10.1080/10586458.2014.990118

On solving a curious inequality of ramanujan

Adrian W. Dudek^*, David J. Platt

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

Ramanujan proved that the inequality [equation presented] holds for all sufficiently large values of x. Using an explicit estimate for the error in the prime number theorem, we show unconditionally that it holds if x ≥ exp (9658). Furthermore, we solve the inequality completely on the Riemann hypothesis and show that x = 38 358 837 682 is the largest integer counterexample.

Original language	English
Pages (from-to)	289-294
Number of pages	6
Journal	Experimental Mathematics
Volume	24
Issue number	3
DOIs	https://doi.org/10.1080/10586458.2014.990118
Publication status	Published - 3 Jul 2015

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10.1080/10586458.2014.990118

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title = "On solving a curious inequality of ramanujan",

abstract = "Ramanujan proved that the inequality [equation presented] holds for all sufficiently large values of x. Using an explicit estimate for the error in the prime number theorem, we show unconditionally that it holds if x ≥ exp (9658). Furthermore, we solve the inequality completely on the Riemann hypothesis and show that x = 38 358 837 682 is the largest integer counterexample.",

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AB - Ramanujan proved that the inequality [equation presented] holds for all sufficiently large values of x. Using an explicit estimate for the error in the prime number theorem, we show unconditionally that it holds if x ≥ exp (9658). Furthermore, we solve the inequality completely on the Riemann hypothesis and show that x = 38 358 837 682 is the largest integer counterexample.

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KW - prime counting function

KW - primesieve

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On solving a curious inequality of ramanujan

Abstract

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