Computational estimation of the constant

The paper describes a computational estimation of the constant characterizing the bounds of . It is known that as

with , while the truth of the Riemann hypothesis would also imply that . In the range , two sets of estimates of are computed, one for increasingly small minima and another for increasingly large maxima of . As increases, the estimates in the first set rapidly fall below and gradually reach values slightly below , while the estimates in the second set rapidly exceed and gradually reach values slightly above . The obtained numerical results are discussed and compared to the implications of recent theoretical work of Granville and Soundararajan.