AR players can take advantage of two aspects of the Stars! game to produce an essentially unlimited amount of minerals.
First, ARs can remote mine their own planets. Unlike planetary mines, there is no limit to the number of mining ships that can mine a single planet.
Second, the homeworld of each race never drops below 30% mineral concentrations as long as it is inhabited.
Combining these two, an AR can have an enormous number of remote miners (limited only by their ability to build them) mining their homeworld, and the minerals will never run out.
Other PRTs cannot do this because either they occupy the planet, in which case they can only use planetary mines, or it is unoccupied in which case the 30% minimum concentrations don't apply.
Note that there is a limit of 1200kt of each mineral per mining fleet, beyond which additional miners don't produce any minerals. For this reason, the ships in a mineral fountain must be split into a number of fleets, each below that limit.