Numerical calculation of an $x$ for which $\pi(x) > li(x)$ Littlewood 1914 proved that there are an infinite number of $x$ for which $\pi(x) > li(x)$. Skewes 1933 provided the first numerical upper bound on $x$ (http://en.wikipedia.org/wiki/Skewes%27_number).
Bays and Hudson 2000 lowered the upper bound to a number with 317 decimal digits and lower values obtained since then still have 317 digits. Apparently no numerical value of an $x$ has yet been calculated.
Since software, such as C++ with GMP, or Java's BigInteger, can perform calculations on arbitrarily large numbers then why has no $x$ yet been calculated? Is it simply that the calculation using existing algorithms and existing hardware would take a prohibitively long time?  

While determining the primality of a single large integer of that size is not difficult using modern resources, determining the primality of all integers up to $10^{317}$ is computationally infeasible at this time.
Note that the current highest $n$ such that $\pi(n)$ is exactly known is $n=10^{27}$, computed by David Baugh and Kim Walisch in 2015. The computation took 23.03 CPU core years and the peak memory usage was 235 gigabytes! You can read more about the discovery here.
