Scientific and Technical Journal


ISSN Print 2221-3937
ISSN Online 2221-3805

In the work of computer simulation methods, the properties of prime numbers are investigated, as a dynamic evolving system. Methods for the classification of prime numbers based on Fermat's small theorem are constructed. It is proved that, based on the results of computer simulation, the bases for the development of analytic and algebraic number theory as dynamical systems were created.

DOI 10.15276/eltecs.28.104.2018.29
  1. Manin, Y. and Panchishkin, A. (2009), Introduction to the modern theory of numbers [Vvedenie v sovremennuyu teoriyu chisel], Moscow, MTSNMO, p 551.
  2. Crandall, R. and Pomerance, C. (2005), Prime Numbers A Computational Perspective, Portland, Springer, p. 664.
  3. Katok, A. and Hasselpat, B. (2005), Introduction to the theory of dynamical systems [Vvedenie v teoriyu dinamicheskih sistem s obzorom poslednih dostizheniy], Moscow, MTSNMO, p. 464.
  4. Sharkovsky, A. (2013), Attractors of trajectories and their basins [Attraktoryi traektoriy i ih basseynyi], Kiev, Naukova Dumka, p. 319.
  5., (2009), Tent map. [online] Available at: [Accessed 10 May 2018].
  6. Jeffrey, R. (2016), Conjugating the Tent and Logistic Maps, University Michigan, p. 78.
  7. Collet, P. and Eckmann J. Iterated Maps on the Interval as Dynamical Systems. Boston: Bizkhauser, p. 248.
  8. De L'eglise, M. and Dusart, P. and Roblot, X-F. (2004), Counting primes in residue classes, Mathematics of Computation, Volume 73, Number 247, pp. 1565-1575.
  9. Vostrov, G. and Opiata, R. (2017), Effective computability of the structure of the dynamic processes of the formation of primes. ELTECS No. 25 pp. 432-438.
  10. Vostrov, G., Khrinenko, A. (2018), Pseudorandom processes of the number sequence generation. ELTECS No. 26.
  11., (2003), Order of 4 mod n-th prime: least k such that prime(n) divides 4^k-1, n>=2. [online] Available at: [Accessed 10 May 2018].
  12. Vinogradov, I. (2006), Fundamentals of the theory of numbers [Osnovyi teorii chisel], Moscow, Lan, p. 176.
  13. Karatsuba, A. (1975), Fundamentals of analytic number theory, Science Fizmatlit, p. 183.
  14. Jennifer, J. (2014), Developing a 21st Century Global Library for Mathematics Research. [online] Available at: [Accessed 10 May 2018], Washington, D.C: The National Academies press. p. 142.
  15. Ambrose, C. (2014), On Artin's primitive root conjecture. Gottingen, p. 169.
Last download:
14 Feb 2019

[ © KarelWintersky ] [ All articles ] [ All authors ]
[ © Odessa National Polytechnic University, 2014-2018. Any use of information from the site is possible only under the condition that the source link! ]