Emergence of Prime Numbers as the Result of Evolutionary Strategy
Abstract
We investigate by means of a simple theoretical model the emergence of prime numbers as life cycles, as those seen for some species of cicadas. The cicadas, more precisely the Magicicadas, spend most of their lives below the ground and then emerge and die in a short period of time. The Magicicadas display an uncommon behavior: their emergence is synchronized and these periods are usually prime numbers. In the current work, we develop a spatially extended model at which preys and predators coexist and can change their evolutionary dynamics through the occurrence of mutations. We verified that prime numbers as life cycles emerge as a result of the evolution of the population. Our results seem to be a first step in order to prove that the development of such strategy is selectively advantageous, especially for those organisms that are highly vulnerable to attacks of predators.
 Publication:

Physical Review Letters
 Pub Date:
 August 2004
 DOI:
 10.1103/PhysRevLett.93.098107
 arXiv:
 arXiv:qbio/0406017
 Bibcode:
 2004PhRvL..93i8107C
 Keywords:

 87.23.Kg;
 02.10.De;
 02.50.Ey;
 89.75.Fb;
 Dynamics of evolution;
 Algebraic structures and number theory;
 Stochastic processes;
 Structures and organization in complex systems;
 Quantitative Biology  Populations and Evolution
 EPrint:
 11 pages and 4 figures