Emergence of Prime Numbers as the Result of Evolutionary Strategy

Paulo R. A. Campos, Viviane M. de Oliveira, Ronaldo Giro, and Douglas S. Galvão
Phys. Rev. Lett. 93, 098107 – Published 27 August 2004

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.

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  • Received 14 November 2003

DOI:https://doi.org/10.1103/PhysRevLett.93.098107

©2004 American Physical Society

Authors & Affiliations

Paulo R. A. Campos*, Viviane M. de Oliveira, Ronaldo Giro, and Douglas S. Galvão

  • Departamento de Física Aplicada, Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, 13083-970 Campinas SP, Brazil

  • *Electronic address: prac@ifi.unicamp.br Permanent address: Departamento de Física e Matemática, Universidade Federal Rural de Pernambuco, Dois Irmãos 52171-900, Recife-PE, Brazil

Comments & Replies

Campos et al. Reply:

Paulo R. A. Campos, Viviane M. de Oliveira, Ronaldo Giro, and Douglas S. Galvão
Phys. Rev. Lett. 95, 229802 (2005)

Comment on “Emergence of Prime Numbers as the Result of Evolutionary Strategy”

M. Markus, O. Schulz, and E. Goles
Phys. Rev. Lett. 95, 229801 (2005)

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Vol. 93, Iss. 9 — 27 August 2004

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