Saouter, YannickTrudgian, TimDemichel, Patrick2014-04-112014-04-110025-5718http://hdl.handle.net/1885/11566We consider the least number x for which a change of sign of π(x) - li(x) occurs. First, we consider modifications of Lehman's method that enable us to obtain better estimates of some error terms. Second, we establish a new lower bound for the first x for which the difference is positive. Third, we use numerical computations to improve the final result.The second author was supported in part by ARC Grant DE120100173.14 pageshttp://www.sherpa.ac.uk/romeo/issn/0025-5718/author can archive pre-print (ie pre-refereeing); author can archive post-print (ie final draft post-refereeing); author can archive publisher's version/PDFSkewes' numberprime counting function2013