  We create mechanically stable (MS) packings of bidisperse disks using an
algorithm in which we successively grow or shrink soft repulsive disks followed
by energy minimization until the overlaps are vanishingly small. We focus on
small systems because this enables us to enumerate nearly all distinct MS
packings. We measure the probability to obtain a MS packing at packing fraction
$\phi$ and find several notable results. First, the probability is highly
nonuniform. When averaged over narrow packing fraction intervals, the most
probable MS packing occurs at the highest $\phi$ and the probability decays
exponentially with decreasing $\phi$. Even more striking, within each
packing-fraction interval, the probability can vary by many orders of
magnitude. By using two different packing-generation protocols, we show that
these results are robust and the packing frequencies do not change
qualitatively with different protocols.
