  The formation of "zero" (exponentially small) resistance states (ESRS) in
high mobility two-dimensional electron systems (2DES) in a static magnetic
field B and subjected to strong microwave (MW) radiation has attracted great
theoretical interest. These states appear to be associated with a new kind of
energy gap $\Delta$. Here I show that the energy gap $\Delta$ is explained by a
microscopic quantum model that involves the Prime Number Theorem, hitherto
reserved for only mathematical contexts.
