2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224097We reduce the leading term in Lehman's theorem. This improved estimate allows us to refine the main theorem of Bays and Hudson. Entering $2,000,000$ Riemann zeros, we prove that there exists $x$ in the interval $[exp(727.951858), exp(727.952178)]$ for which $π(x)-\li(x) > 3.2 \times 10^{151}$. There are at least $10^{154}$ successive integers $x$ in this interval for which $π(x)>\li(x)$. This interval is strictly a sub-interval of the interval in Bays and Hudson, and is narrower by a factor of about 12.Final version, to be published in the International Journal of Number Theory [copyright World Scientific Publishing Company][www.worldscinet.com/ijnt]Number Theory11N05; 11Y35; 11M26text