A NUMERICAL VERIFICATION OF THE STRONG GOLDBACH CONJECTURE UP TO 9 × 10 ^18

  • Sankei Daniel Meru University of Science & Technology
  • Loyford Njagi Meru University of Science & Technology
  • Josephine Mutembei Meru University of Science & Technology
DOI: https://doi.org/10.5281/zenodo.10391440
Keywords: Goldbach Conjecture, Goldbach partition, Even numbers, Odd numbers, Prime numbers, Natural numbers.

Abstract

The Goldbach Conjecture states that every even integer ≥ 4 can be written as a sum of two prime numbers. It is known to be true for all even numbers up to 4 × 1018[1]. Using the new formulation of a set of even numbers as [9], and the fact that, an even number of this formulation can be partitioned into all pairs of odd numbers [10], we present a computational algorithm that confirms the Strong Goldbach Conjecture holds true for all even numbers not larger than 9 × 1018.

Downloads

Download data is not yet available.

References

1. Oliveira e Silva, T., Herzog, S., & Pardi, S. (2014). Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4⋅ 10¹⁸. Mathematics of Computation, 83(288), 2033-2060.
2. William-West, T. O. (2016). An Approach to Goldbach’s Conjecture. J Math Sci Math Educ, 11, 16.
3. Wang, X. (2022). A Concise Proof of Goldbach Conjecture.
4. Weisstein, E. W. (2002). Goldbach conjecture. https://mathworld. wolfram. com/.
5. Ghanim, M. (2018). Confirmation of the Goldbach binary conjecture. Global Journal of Advanced Engineering Technologies and Sciences, 5(5), 1-15.
6. O'Regan, G. (2022). A Guide to Business Mathematics. CRC Press.
7. Härdig, J. (2020). Goldbach's Conjecture.
8. Papadimitriou, C. H. (2003). Computational complexity. In Encyclopedia of computer science (pp. 260-265).
9. Sankei, D., Njagi, L., & Mutembei, J. (2023). A New Formulation of a Set of Even Numbers. European Journal of Mathematics and Statistics, 4(4), 78–82. https://doi.org/10.24018/ejmath.2023.4.4.249
10. Sankei, D., Njagi, L., & Mutembei, J. (2023). Partitioning an even number of the new formulation into all pairs of odd numbers. Journal of Mathematical Problems, Equations and Statistics, 4(2), 35-37. https://doi.org/10.22271/math.2023.v4.i2a.104
11. https://www.numberempire.com/primenumbers.php
12. Marshall, S. (2017). Elementary Proof of the Goldbach Conjecture.
Published
2023-12-15
How to Cite
Daniel, S., Njagi, L., & Mutembei, J. (2023). A NUMERICAL VERIFICATION OF THE STRONG GOLDBACH CONJECTURE UP TO 9 × 10 ^18. GPH - International Journal of Mathematics, 6(11), 28-37. https://doi.org/10.5281/zenodo.10391440
Issue
Vol 6 No 11 (2023): GPH - International Journal of Mathematics
Section
Articles

Copyright (c) 2023 Sankei Daniel, Loyford Njagi, Josephine Mutembei

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Author(s) and co-author(s) jointly and severally represent and warrant that the Article is original with the author(s) and does not infringe any copyright or violate any other right of any third parties, and that the Article has not been published elsewhere. Author(s) agree to the terms that the GPH Journal will have the full right to remove the published article on any misconduct found in the published article.