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Prime number generation using memetic programming

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Abstract

For centuries, the study of prime numbers has been regarded as a subject of pure mathematics in number theory. Recently, this vision has changed and the importance of prime numbers has increased rapidly, especially in information technology, e.g., public key cryptography algorithms, hash tables, and pseudo-random number generators. One of the most popular topics to attract attention is to find a formula that maps the set of natural numbers into the set of prime numbers. However, to date there is no known formula that produces all primes. In this article, we use a hybrid evolutionary algorithm, called the memetic programming (MP) algorithm, to generate mathematical formulas that produce distinct primes. Using the MP algorithm, we succeeded in discovering an interesting set of formulas that produce sets of distinct primes.

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References

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  2. Mabrouk E, Hedar A, Fukushima M (2008) Memetic programming with adaptive local search using tree data structures. In: Chbeir R et al (eds) Proceedings of the 5th International Conference on Soft Computing as Transdisciplinary Science and Technology (CSTST08), Cergy-Pontoise, Paris, France, October 27–31, 2008, pp 258–264

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  4. Walker JA, Miller JF (2007) Predicting prime numbers using Cartesian genetic programming. In: Ebner M et al (eds) Proceedings of the 10th European Conference on Genetic Programming (EuroGP), Valencia, Spain, April 11–13, 2007, pp 205–216

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Authors and Affiliations

  1. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Emad Mabrouk & Masao Fukushima

  2. Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt

    Emad Mabrouk

  3. School of Computing, University of Portsmouth, Portsmouth, UK

    Julio César Hernández-Castro

Authors
  1. Emad Mabrouk
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  2. Julio César Hernández-Castro
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  3. Masao Fukushima
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Corresponding author

Correspondence to Masao Fukushima.

Additional information

This work was presented in part at the 16th International Symposium on Artificial Life and Robotics, Oita, Japan, January 27–29, 2011

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Mabrouk, E., Hernández-Castro, J.C. & Fukushima, M. Prime number generation using memetic programming. Artif Life Robotics 16, 53–56 (2011). https://doi.org/10.1007/s10015-011-0890-3

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  • DOI: https://doi.org/10.1007/s10015-011-0890-3

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