  Using 1200 CPUs of the National Supercomputer TH-A1 and a parallel integral
algorithm based on the 3500th-order Taylor expansion and the 4180-digit
multiple precision data, we have done a reliable simulation of chaotic solution
of Lorenz equation in a rather long interval [0,10000] (Lorenz time unit). Such
a kind of mathematically reliable chaotic simulation has never been reported.
It provides us a numerical benchmark for mathematically reliable long-term
prediction of chaos. Besides, it also proposes a safe method for mathematically
reliable simulations of chaos in a finite but long enough interval. In
addition, our very fine simulations suggest that such a kind of mathematically
reliable long-term prediction of chaotic solution might have no physical
meanings, because the inherent physical micro-level uncertainty due to thermal
fluctuation might quickly transfer into macroscopic uncertainty so that
trajectories for a long enough time would be essentially uncertain in physics.
