I think everyone knows the story of the staggeringly huge number Skewes found as an upper bound for the first time that li(x) > pi(x), pi the prime-counting function. Further, it's well-known that less-astronomical bounds have since been found, around 1.39e316. I was wondering if good lower bounds are known for this problem. Bays/Hudson in their paper giving the above bound suggest several smaller points where perhaps there are earlier crossovers, the lest of which is around 1e176. Is it known that below this (or rather, a more conservative bound like 8e175, based on the illustration) there are no crossovers?