Research ArticleOpen AccessGoogle Scholar indexed
Symmetrical Distribution of Primes and Their Gaps
School of Mechanical, Electrical & Information Engineering, Shandong University, Weihai, China
State Key Laboratory of Palaeobiology and Stratigraphy, Nanjing Institute of Geology and Palaeontology and Center for Excellence in Life and Paleoenvironment, Chinese Academy of Sciences, Nanjing, China
- 1 School of Mechanical, Electrical & Information Engineering, Shandong University, Weihai, China
- 2 State Key Laboratory of Palaeobiology and Stratigraphy, Nanjing Institute of Geology and Palaeontology and Center for Excellence in Life and Paleoenvironment, Chinese Academy of Sciences, Nanjing, China
Advances in Pure Mathematics·Volume 11 (2021)·Pages 447–456·Published 17 May 2021·DOI10.4236/apm.2021.115031
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Abstract
Primes are of great importance and interest in mathematics partially due to their hard-to-predict distribution. A corollary of the Goldbach Conjecture is that two primes are equally distanced from a mid-point integer. Here the authors demonstrate that most primes are bilateral symmetrically distributed on the both sides of the halves of super products (or their integer multiples) of primes. This pattern suggests that greater primes may be obtained more efficiently by subtracting smaller ones from constants equal to super products (or their integer multiples) of primes.
KeywordsPrime NumberDistributionBilateral SymmetrySuper ProductPairwise
- Devlin, K. (1999) Mathematics: The New Golden Age. Columbia University Press, New York.
- Luque, B. and Lacasa, L. (2009) The First-Digit Frequencies of Prime Numbers and Riemann Zeta Zeros. Proceedings of the Royal Society A, 564, 2197-2216. https://doi.org/10.1098/rspa.2009.0126
- Oliver, R.J.L. and Soundaranjan, K. (2016) Unexpected Biases in the Distribution of Consecutive Primes. PNAS, 113, E4446-E4454. https://doi.org/10.1073/pnas.1605366113
- Zhang, Y. (2013) Bounded Gaps between Primes. Annals of Mathematics, 179, 1121-1174. https://doi.org/10.4007/annals.2014.179.3.7
- Sha, Y.Y. (2017) Twin Prime Number Theorem. Global Journal of Science Frontier Research, 17, 41-45.
- GIMPS (2018) GIMPS Discovers Largest Known Prime Number: 2 82,589,933 -1. https://www.mersenne.org/primes/?press=M82589933
- Zhao, G., You, J., Sun, J. and Yin, G. (2015) Further Discussion of Prime Number Distribution Rule. Henan Science, 33, 506-508.
- Li, B. (2001) Distribution Rule of Prime Numbers. Journal of Jiaozuo University, 4, 45-46. https://doi.org/10.16214/j.cnki.cn41-1276/g4.2001.04.012
- Wang, X. (2021) The Genesis of Prime Numbers—Revealing the Underlying Periodicity of Prime Numbers. Advances in Pure Mathematics, 11, 12-18. https://scirp.org/journal/paperinformation.aspx?paperid=106566 https://doi.org/10.4236/apm.2021.111002
- Cai, T. (2019) Figurate Primes and Goldbach Conjecture. Advances in Mathematics (China), 48, 766-768.
- Guy, R.K. (2007) Unsolved Problems in Number Theory. Science Press, Beijing.
- Ghanouchi, J. (2013) About an Even as the Sum or the Difference of Two Primes. Bulletin of Mathematical Science and Applications, 5, 35-43. https://doi.org/10.18052/www.scipress.com/BMSA.5.35
- Qiu, Y. (2017) Symmetry Distribution Law of Prime Numbers of Positive Integers and Related Results. International Journal of Science and Engineering Applications, 6, 360-363. https://core.ac.uk/display/105342972
- Aiazzi, B., Baronti, S., Santurri, L. and Selva, M. (2019) An Investigation on the Prime and Twin Prime Number Functions by Periodical Binary Sequences and Symmetrical Runs in a Modified Sieve Procedure. Symmetry, 11, 775. https://doi.org/10.3390/sym11060775
- Hua, L.-G. (1979) Introduction to Number Theory. Science Press, Beijing.