Have a personal or library account? Click to login
Odd and even symmetric prime constellations Cover

References

  1. Hoche R., Nicomachus, Nicomachi Geraseni Pythagorei Introductionis arithmeticae Libri II (Greek Ed.), Chapter XIII, Kessinger, USA, 1866.
  2. Caragiu M., Sequential Experiments with Primes, Springer, USA, 2017.
  3. Stepney S., Euclid's proof that there are an infinite number of primes, https://www-users.cs.york.ac.uk/susan/cyc/p/primeprf.htm, Accessed: September 3, 2022.
  4. Uselton S.C., A study of semiprime arithmetic sequences, (Honors Thesis), Belmont University, USA, 2022.
  5. Faber X., Granville A., Prime factors of dynamic sequences, Journal für Die Reine und Angewandte Mathematik, 661, 1–26, 2011.
  6. Numbers Aplenty, Semiprimes, https://www.numbersaplenty.com/set/semiprime/, Accessed: September 9, 2022.
  7. Borne K., Abdenim O.H., 20 Best Prime Numbers Books of All Time, https://bookauthority.org/books/best-prime-numbers-books, Accessed: August 14, 2024.
  8. Niven I., Zuckerman H.S., Montgomery H.L., An Introduction to the Theory of Numbers, John Wiley and Sons, USA, 1991.
  9. Hoffman P., The Man Who Loved Only Numbers: The Story of Paul Erdös and the Search for Mathematical Truth, Hyperison, USA, 1999.
  10. Granville A., Prime number patterns, The American Mathematical Monthly, 115(4), 279–296, 2008.
  11. Granville G.A., Primes in intervals of bounded length, Bulletin of the American Mathematical Society, 52(2), 171–222, 2015.
  12. Baibekov S.N., Durmagambetov A.A., Infinite number of twin primes, Advances in Pure Mathematics, 6(13), 954–971, 2016.
  13. Weisstein E.W., Twin primes, https://mathworld.wolfram.com/TwinPrimes.html, Accessed: September 12, 2023.
  14. Green B., Tao T., The primes contain arbitrarily long arithmetic progressions, Annals of Mathematics, 167, 481–547, 2008.
  15. Kai W., Mimura M., Munemasa A., Seki S.I., Yoshino K., Constellation in prime elements of number fields, arXiv:2012.15669v2, 2020.
  16. Ericksen L., Primality testing and prime constellations, Šiauliai Mathematical Seminar, 3(11), 61–77, 2008.
  17. Knill O., Some experiments in number theory, arXiv:1606.05971v1, 2016.
  18. Villegas F.R., Experimental Number Theory, Oxford University Press, UK, 2007.
  19. Zhang G., Martelli F., Torquato S., The structure factor of primes, Journal of Physics A: Mathematical and Theoretical, 51(115001), 1–16, 2018.
  20. https://oeis.org/wiki/Prime_constellations, Accessed: July 20, 2024.
  21. Zhang Y., Bounded gaps between primes, Annals of Mathematics, 179(3), 1121–1174, 2014.
  22. Polya G., Patterns of Plausible Inference, Princeton University Press, USA, 1968.
  23. Hejhal D.A., Friedman J., Gutzwiller M.C., Odlyzko A.M., Emerging Applications of Number Theory (Chapter: Number Theory and Formal Languages), 109, 547–570, Springer, USA, 1999.
  24. https:www.reddit.com/r/learnmath/comments/lfnk5b/among_n_consecutive_numbers_one_i_always/?rdt=46836, Accessed: July 20, 2024.
  25. Di Pietro G., Numerical analysis approach to twin primes conjecture, Notes on Number Theory and Discrete Mathematics, 27(3), 175–183, 2021.
  26. Rokne J., A hierarchy of double, quadruple and octuple primes, International Journal of Mathematics and Computer in Engineering, 2(2), 111–122, 2024.
  27. Rokne J., Some observations on prime pairs quadruples and octuples, IEEE Canadian Review, 92, 8–11, 2023.
Language: English
Page range: 267 - 292
Submitted on: Apr 29, 2024
Accepted on: Sep 5, 2024
Published on: Sep 20, 2024
Published by: Harran University
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2024 Jon Rokne, published by Harran University
This work is licensed under the Creative Commons Attribution 4.0 License.