Fibonacci primes

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 20, 2014, Number 2, Pages 6—9
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Authors and affiliations

J. V. Leyendekkers
Faculty of Science, The University of Sydney
NSW 2006, Australia

A. G. Shannon
Faculty of Engineering & IT, University of Technology
Sydney, NSW 2007, Australia

Abstract

Fibonacci composites with prime subscripts, Fp, have factors (kp ± 1) in which k is even. The class of p governs the class of k in the modular ring Z5, and the digit sum of p, Fp and a function of Fp provide an approximate check on primality.

Keywords

  • Fibonacci numbers
  • Modular rings
  • Digit sums
  • Prime numbers
  • Simson’s identity

AMS Classification

  • 11B39
  • 11B50

References

  1. Atanassov, K. T., A. G. Shannon. The Digital Root Function for Fibonacci-type Sequences. Advanced Studies in Contemporary Mathematics. Vol. 21, 2011, No. 3, 251–254.
  2. Gardiner, A. Digital Roots, Rings and Clock Arithmetic. The Mathematical Gazette. Vol. 66 (437), 1982, 184–188.
  3. Leyendekkers, J. V., A. G. Shannon. Fibonacci and Lucas Primes. Notes on Number Theory and Discrete Mathematics. Vol. 19, 2013, No. 2, 49–59.
  4. Leyendekkers, J. V., A. G. Shannon. The Pascal-Fibonacci Numbers. Notes on Number Theory and Discrete Mathematics. Vol. 19, 2013, No. 3, 5–11.
  5. Ribenboim, Paulo. My Numbers, My Friends: Popular Lectures on Number Theory. Berlin, Springer-Verlag, 2000.
  6. Shannon A. G., A. F. Horadam. Generalized staggered sums. The Fibonacci Quarterly, Vol. 29, 1991, No. 1, 47–51.

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Cite this paper

APA

Leyendekkers, J., & Shannon, A. (2014). Fibonacci primes. Notes on Number Theory and Discrete Mathematics, 20(2), 6-9.

Chicago

Leyendekkers, JV, and AG Shannon. “Fibonacci Primes.” Notes on Number Theory and Discrete Mathematics 20, no. 2 (2014): 6-9.

MLA

Leyendekkers, JV, and AG Shannon. “Fibonacci Primes.” Notes on Number Theory and Discrete Mathematics 20.2 (2014): 6-9. Print.

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