Predicting Prime Numbers Using Cartesian Genetic Programming

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  author =       "James Alfred Walker and Julian Francis Miller",
  title =        "Predicting Prime Numbers Using Cartesian Genetic
  editor =       "Marc Ebner and Michael O'Neill and Anik\'o Ek\'art and 
                 Leonardo Vanneschi and Anna Isabel Esparcia-Alc\'azar",
  booktitle =    "Proceedings of the 10th European Conference on Genetic
  publisher =    "Springer",
  series =       "Lecture Notes in Computer Science",
  volume =       "4445",
  year =         "2007",
  address =      "Valencia, Spain",
  month =        "11-13 " # apr,
  pages =        "205--216",
  keywords =     "genetic algorithms, genetic programming, cartesian
                 genetic programming",
  ISBN =         "3-540-71602-5",
  isbn13 =       "978-3-540-71602-0",
  DOI =          "doi:10.1007/978-3-540-71605-1_19",
  abstract =     "Prime generating polynomial functions are known that
                 can produce sequences of prime numbers (e.g. Euler
                 polynomials). However, polynomials which produce
                 consecutive prime numbers are much more difficult to
                 obtain. In this paper, we propose approaches for both
                 these problems. The first uses Cartesian Genetic
                 Programming (CGP) to directly evolve integer based
                 prime-prediction mathematical formulae. The second uses
                 multi-chromosome CGP to evolve a digital circuit, which
                 represents a polynomial. We evolved polynomials that
                 can generate 43 primes in a row. We also found
                 functions capable of producing the first 40 consecutive
                 prime numbers, and a number of digital circuits capable
                 of predicting up to 208 consecutive prime numbers,
                 given consecutive input values. Many of the formulae
                 have been previously unknown.",
  notes =        "Part of \cite{ebner:2007:GP} EuroGP'2007 held in
                 conjunction with EvoCOP2007, EvoBIO2007 and

Genetic Programming entries for James Alfred Walker Julian F Miller