The strong goldbach conjecture and the function g(n): An analysis of prime distribution
DOI:
https://doi.org/10.33448/rsd-v14i6.48924Keywords:
Mathematics, Conjecture, Goldbach, Primes.Abstract
Goldbach's Conjecture, an ancient and important problem in number theory, states that every even number greater than 2 can be expressed as the sum of two prime numbers. Although many advances have been made in the search for a solution to this conjecture, it remains unsolved to this day. The goal of the article is to analyze the relationship between Goldbach's Conjecture and the distribution of prime numbers, two fundamental questions in number theory. The main results and theories used by mathematicians to try to solve the conjecture will be presented, as well as discussing how the study of prime number distribution can lead to significant advances in this search. The importance of the research lies in solving one of the greatest mysteries in mathematics, as well as in the implications of the conjecture in other areas of science and technology. Additionally, the research contributes to the advancement of number theory and the understanding of prime number distribution, a fundamental problem in mathematics.
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References
APostol, T. M. (1998). Introdução à teoria analítica dos números. Editora LTC.
Bertone, A. M. A. (2014). Introdução à Teoria dos Números. UFU.
Bernardes, R. M. (2020). Ensaio matemático sobre a conjectura de goldbach. https://www.conic-semesp.org.br/anais/files/2020/trabalho-1000005615.pdf.
Bertone, A. M. A. (2014). Introdução à Teoria dos Números. Uberlândia, MG: UFU.
Derbyshire, J. (2012). Obsessão prima. Editora Record.
Eves, H. (2011). Introdução à história da Matemática. (5ed). Editora da Unicamp.
Gil, A. C. (2017). Como elaborar projetos de pesquisa. (6ed). Editora Atlas.
Goldston, D. A. & Suriajaya, A. I. (2023). On an average Goldbach representation formula of Fujii. Nagoya Mathematical Journal, Cambridge. 250, 511–32. https://www.cambridge.org/core/journals/nagoya-mathematical-journal/article/abs/on-an-average-goldbach-representation-formula-of-fujii/9C6EF5AA639674AD7AFF4A9F91BD72E3
Granville, A. (2015). Prime Number Patterns. The American Mathematical Monthly. 122(4), 299–315.
Hardy, G. H. & Wright, E. M. (2008). An introduction to the theory of numbers. (6.ed). Oxford University Press.
Helfgott, H. A. (2023). The ternary Goldbach conjecture is true. Annals of Mathematics Studies. 203. https://arxiv.org/abs/1312.7748.
Ikeda, K. & Suriajaya, A. I. (2025). The average number of Goldbach representations over multiples of q. https://arxiv.org/abs/2405.04315v4.
Lima, R. F. (2016). Introdução à geometria diferencial. Macapá: SBM.
Maiers, R. R. (2005). Teoria dos números. Universidade de Brasília. http://www.mat.unb.br/~maierr/tnotas.pdf.
Montgomery, H. & Vaughan, R. C. (2006). Multiplicative Number Theory I: Classical Theory. Cambridge: Cambridge University Press.
Niven, I., Zckerman, H. S. & Montgomery, H. L. (2009). Uma introdução à teoria dos números. Editora LTC.
Oliveira e Silva, T., Herzog, S. & Pardi, S. (2014). Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4 x 10^18. Mathematics of Computation, Providence. 83(288), 2033–60. doi:10.1090/S0025-5718-2013-02787-1.
Pereira A. S. et al. (2018). Metodologia da pesquisa científica. [free e-book]. Editora UAB/NTE/UFSM.
Ribas, R. A. (2011). Teoria dos Números: uma introdução para o ensino superior. Editora Livraria da Física.
Rieu, C. (2015). Criptografia e números primos: fundamentos e aplicações. Editora Bookman.
Sousa, J. E. (2013). Conjetura de Goldbach - Uma visão aritmética. 130f. Departamento de Matemática da Universidade dos Açores, 2013. https://repositorio.uac.pt/bitstream/10400.3/2881/1/DissertMestradoJoseEmanuelSousa2013.pdf.
Yin, R.K. (2015). O estudo de caso. Editora Bookman.
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Copyright (c) 2025 Alice Maria Rodrigues Barros; Dayana Maria Silva Silvestre; Evódia Patrícia S. Veríssimo; Gizelly Juliane de O. S. Eloi Batista; Hallana Thaysa Costa Barros
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