Nonlinear Phenomena in Complex Systems, 2000, Vol.3, No.2, pp.208--213

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2000, Volume 3, Number 2, pp.208--213

A Biological Generator of Prime Numbers.
Eric Goles, Oliver Schulz, and Mario Markus

In the present work, we shall allow for the merging of two seemingly unrelated subjects, one being periodical insects and the other the theory of prime numbers. The fact that some species of cicadas (genus Magicicada) appear every 7, 13 or 17 years and that these periods are prime numbers has been regarded as a coincidence. Without intending to argue in favour or against this statement, we will show here that a simple evolutionary predator-prey model yields prime-periodic preys. Moreover, this result will be used as a number-theoretical tool, namely to generate large prime numbers. Furthermore, we will demonstrate how a spatio-temporal extension of the model renders spiral waves being reminiscent of those observed in excitable systems, host-parasitoid systems and prebiotic evolution.

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