Odd and even symmetric prime constellations

[1] Hoche R., Nicomachus, Nicomachi Geraseni Pythagorei Introductionis arithmeticae Libri II (Greek Ed.), Chapter XIII, Kessinger, USA, 1866. HocheR. Nicomachus, Nicomachi Geraseni Pythagorei Introductionis arithmeticae Libri II (Greek Ed.), Chapter XIII Kessinger USA 1866 Search in Google Scholar

[2] Caragiu M., Sequential Experiments with Primes, Springer, USA, 2017. CaragiuM. Sequential Experiments with Primes Springer USA 2017 Search in Google Scholar

[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. StepneyS. 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. Search in Google Scholar

[4] Uselton S.C., A study of semiprime arithmetic sequences, (Honors Thesis), Belmont University, USA, 2022. UseltonS.C. A study of semiprime arithmetic sequences, (Honors Thesis), Belmont University USA 2022 Search in Google Scholar

[5] Faber X., Granville A., Prime factors of dynamic sequences, Journal für Die Reine und Angewandte Mathematik, 661, 1–26, 2011. FaberX. GranvilleA. Prime factors of dynamic sequences Journal für Die Reine und Angewandte Mathematik 661 1 26 2011 Search in Google Scholar

[6] Numbers Aplenty, Semiprimes, https://www.numbersaplenty.com/set/semiprime/, Accessed: September 9, 2022. Numbers Aplenty, Semiprimes https://www.numbersaplenty.com/set/semiprime/, Accessed: September 9, 2022. Search in Google Scholar

[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. BorneK. AbdenimO.H. 20 Best Prime Numbers Books of All Time https://bookauthority.org/books/best-prime-numbers-books, Accessed: August 14, 2024. Search in Google Scholar

[8] Niven I., Zuckerman H.S., Montgomery H.L., An Introduction to the Theory of Numbers, John Wiley and Sons, USA, 1991. NivenI. ZuckermanH.S. MontgomeryH.L. An Introduction to the Theory of Numbers John Wiley and Sons USA 1991 Search in Google Scholar

[9] Hoffman P., The Man Who Loved Only Numbers: The Story of Paul Erdös and the Search for Mathematical Truth, Hyperison, USA, 1999. HoffmanP. The Man Who Loved Only Numbers: The Story of Paul Erdös and the Search for Mathematical Truth Hyperison USA 1999 Search in Google Scholar

[10] Granville A., Prime number patterns, The American Mathematical Monthly, 115(4), 279–296, 2008. GranvilleA. Prime number patterns The American Mathematical Monthly 115 4 279 296 2008 Search in Google Scholar

[11] Granville G.A., Primes in intervals of bounded length, Bulletin of the American Mathematical Society, 52(2), 171–222, 2015. GranvilleG.A. Primes in intervals of bounded length Bulletin of the American Mathematical Society 52 2 171 222 2015 Search in Google Scholar

[12] Baibekov S.N., Durmagambetov A.A., Infinite number of twin primes, Advances in Pure Mathematics, 6(13), 954–971, 2016. BaibekovS.N. DurmagambetovA.A. Infinite number of twin primes Advances in Pure Mathematics 6 13 954 971 2016 Search in Google Scholar

[13] Weisstein E.W., Twin primes, https://mathworld.wolfram.com/TwinPrimes.html, Accessed: September 12, 2023. WeissteinE.W. Twin primes https://mathworld.wolfram.com/TwinPrimes.html, Accessed: September 12, 2023. Search in Google Scholar

[14] Green B., Tao T., The primes contain arbitrarily long arithmetic progressions, Annals of Mathematics, 167, 481–547, 2008. GreenB. TaoT. The primes contain arbitrarily long arithmetic progressions Annals of Mathematics 167 481 547 2008 Search in Google Scholar

[15] Kai W., Mimura M., Munemasa A., Seki S.I., Yoshino K., Constellation in prime elements of number fields, arXiv:2012.15669v2, 2020. KaiW. MimuraM. MunemasaA. SekiS.I. YoshinoK. Constellation in prime elements of number fields arXiv:2012.15669v2, 2020 Search in Google Scholar

[16] Ericksen L., Primality testing and prime constellations, Šiauliai Mathematical Seminar, 3(11), 61–77, 2008. EricksenL. Primality testing and prime constellations Šiauliai Mathematical Seminar 3 11 61 77 2008 Search in Google Scholar

[17] Knill O., Some experiments in number theory, arXiv:1606.05971v1, 2016. KnillO. Some experiments in number theory arXiv:1606.05971v1, 2016 Search in Google Scholar

[18] Villegas F.R., Experimental Number Theory, Oxford University Press, UK, 2007. VillegasF.R. Experimental Number Theory Oxford University Press UK 2007 Search in Google Scholar

[19] Zhang G., Martelli F., Torquato S., The structure factor of primes, Journal of Physics A: Mathematical and Theoretical, 51(115001), 1–16, 2018. ZhangG. MartelliF. TorquatoS. The structure factor of primes Journal of Physics A: Mathematical and Theoretical 51 115001 1 16 2018 Search in Google Scholar

[20] https://oeis.org/wiki/Prime_constellations, Accessed: July 20, 2024. https://oeis.org/wiki/Prime_constellations, Accessed: July 20, 2024. Search in Google Scholar

[21] Zhang Y., Bounded gaps between primes, Annals of Mathematics, 179(3), 1121–1174, 2014. ZhangY. Bounded gaps between primes Annals of Mathematics 179 3 1121 1174 2014 Search in Google Scholar

[22] Polya G., Patterns of Plausible Inference, Princeton University Press, USA, 1968. PolyaG. Patterns of Plausible Inference Princeton University Press USA 1968 Search in Google Scholar

[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. HejhalD.A. FriedmanJ. GutzwillerM.C. OdlyzkoA.M. Emerging Applications of Number Theory (Chapter: Number Theory and Formal Languages) 109 547 570 Springer USA 1999 Search in Google Scholar

[24] https:www.reddit.com/r/learnmath/comments/lfnk5b/among_n_consecutive_numbers_one_i_always/?rdt=46836, Accessed: July 20, 2024. https:www.reddit.com/r/learnmath/comments/lfnk5b/among_n_consecutive_numbers_one_i_always/?rdt=46836, Accessed: July 20, 2024. Search in Google Scholar

[25] Di Pietro G., Numerical analysis approach to twin primes conjecture, Notes on Number Theory and Discrete Mathematics, 27(3), 175–183, 2021. DiPietro G. Numerical analysis approach to twin primes conjecture Notes on Number Theory and Discrete Mathematics 27 3 175 183 2021 Search in Google Scholar

[26] Rokne J., A hierarchy of double, quadruple and octuple primes, International Journal of Mathematics and Computer in Engineering, 2(2), 111–122, 2024. RokneJ. A hierarchy of double, quadruple and octuple primes International Journal of Mathematics and Computer in Engineering 2 2 111 122 2024 Search in Google Scholar

[27] Rokne J., Some observations on prime pairs quadruples and octuples, IEEE Canadian Review, 92, 8–11, 2023. RokneJ. Some observations on prime pairs quadruples and octuples IEEE Canadian Review 92 8 11 2023 Search in Google Scholar