Placer mining sorts grains of sand roughly by density, so it can separate out gold from the other minerals, which are mostly less dense by a factor of five or more. With somewhat more difficulty it can separate out other dense minerals like monazite, zircon, and even magnetite. A miner with a gold pan and some water might be able to pan the gold out of 200 mℓ of sand in some 30 seconds; if the mean sand grain is some 30 microns in diameter, this amounts to picking the dozen or two grains of gold out of several billion grains of sand, a rate of several hundred millions of grains per second. Impressive, for a human.
Various kinds of froth flotation, flocculation, and deflocculation of crushed rock work in a similar way to separate out massive numbers of grains by various physical properties.
Suppose that we instead use machine vision, X-ray diffraction, frequency-dependent complex electric permeability, and so forth to sort through individual grains. For example, nearly all granite has grains of zircon in it, precious for its use in the manufacture of the resilient refractory ceramic zirconia. If we break up the granite, perhaps we can use automated feedback systems to sort through at least a few thousand crystals per second per machine, needing only a few hundred thousand machines to compete with the 49er with his gold pan.
Of course, in 02020, the idea of constructing a few hundred thousand machines sounds absurd, but in fact I am typing this on a computer containing several tens of billions of transistors and capacitors, one which is already obsolete. So in fact such things are not impossible; MEMS simply has not focused on them thus far.