  The long-term stability of the Solar System is an issue of significant
scientific and philosophical interest. The mechanism leading to instability is
Mercury's eccentricity being pumped up so high that Mercury either collides
with Venus or is scattered into the Sun. Previously, only three
five-billion-year $N$-body ensembles of the Solar System with thousands of
simulations have been run to assess long-term stability. We generate two
additional ensembles, each with 2750 members, and make them publicly available
at \texttt{https://archive.org/details/@dorianabbot}. We find that accurate
Mercury instability statistics can be obtained by (1) including only the Sun
and the 8 planets, (2) using a simple Wisdom-Holman scheme without correctors,
(3) using a basic representation of general relativity, and (4) using a time
step of 3.16 days. By combining our Solar System ensembles with previous
ensembles we form a 9,601-member ensemble of ensembles. In this ensemble of
ensembles, the logarithm of the frequency of a Mercury instability event
increases linearly with time between 1.3 and 5 Gyr, suggesting that a single
mechanism is responsible for Mercury instabilities in this time range and that
this mechanism becomes more active as time progresses. Our work provides a
robust estimate of Mercury instability statistics over the next five billion
years, outlines methodologies that may be useful for exoplanet system
investigations, and provides two large ensembles of publicly available Solar
System integrations that can serve as testbeds for theoretical ideas as well as
training sets for artificial intelligence schemes.
