  "Does there exist a naturally occurring counting device that might elucidate
the hidden structure of prime numbers ?" is a question that has fascinated
computer scientists and mathematical physicists for decades. While most recent
research in this area have explored the role of the Riemann zeta-function in
different formulations of statistical mechanics, condensed matter physics and
quantum chaotic systems, the resulting devices (quantum or classical) have only
existed in theory or the fabrication of the device has been found to be not
scalable to large prime numbers. Here we report for the first time that any
hypothetical prime number generator, to our knowledge, has to be a special case
of a dynamical system that is governed by the physics of Fowler-Nordheim (FN)
quantum-tunneling. In this paper we report how such a dynamical system can be
implemented using a counting process that naturally arises from sequential FN
tunneling and integration of electrons on a floating-gate (FG) device. The
self-compensating physics of the FG device makes the operation reliable and
repeatable even when tunneling-currents approach levels below 1 attoamperes. We
report measured results from different variants of fabricated prototypes, each
of which shows an excellent match with the asymptotic prime number statistics.
We also report similarities between the spectral signatures produced by the FN
device and the spectral statistics of a hypothetical prime number sequence
generator. We believe that the proposed floating-gate device could have future
implications in understanding the process that generates prime numbers with
applications in security and authentication.
