  The synergistic formation of zero (exponentially small) resistance states
(ESRS) in high mobility two-dimensional electron systems (2DES) in a static
magnetic field B and exposed to strong microwave (MW) radiation exhibits
hysteresis and an anomalous logarithmic dependence on MW power. These
synergistically organized states appear to be associated with a new kind of
energy gap \Delta. Here I show that a microscopic quantum model that involves
the Prime Number Theorem explains the MW power dependence of the energy gap
\Delta. The explanation involves remarkable convergence with the most abstract
ideas of modern mathematics.
