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 |
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Pages (from-to) | 289-294 |
Number of pages | 6 |
Journal | Experimental Mathematics |
Volume | 24 |
Issue number | 3 |
DOIs | |
Publication status | Published - 3 Jul 2015 |