  We present large scale simulations for a one-dimensional chain of hard-point
particles with alternating masses. We correct several claims in the recent
literature based on much smaller simulations. Both for boundary conditions with
two heat baths at different temperatures at both ends and from heat current
autocorrelations in equilibrium we find heat conductivities kappa to diverge
with the number N of particles. These depended very strongly on the mass
ratios, and extrapolation to N -> infty resp. t -> infty is difficult due to
very large finite-size and finite-time corrections. Nevertheless, our data seem
compatible with a universal power law kappa ~ N^alpha with alpha approx 0.33.
This suggests a relation to the Kardar-Parisi-Zhang model. We finally show that
the hard-point gas with periodic boundary conditions is not chaotic in the
usual sense and discuss why the system, when kept out of equilibrium, leads
nevertheless to energy dissipation and entropy production.
