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Relevant bibliographies by topics / Goldbach's conjecture

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Academic literature on the topic 'Goldbach's conjecture'

Author: Grafiati

Published: 5 June 2025

Last updated: 2 August 2025

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Journal articles on the topic "Goldbach's conjecture"

1

Bosco, Adriko. "Goldbach's Conjecture." International Journal of Science and Research (IJSR) 10, no. 10 (2021): 988–91. https://doi.org/10.21275/mr21928021925.

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Teng, Liao. "The Proof of the Fermar's Last Theorem, Mersenne's Prime Conjecture and Poincare Conjecture in Euclidean Geometry." Journal of Robotics and Automation Research 5, no. 3 (2024): 01–09. https://doi.org/10.33140/jrar.05.03.07.

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In order to strictly prove from the point of view of pure mathematics Goldbach's 1742 Goldbach conjecture and Hilbert's twinned prime conjecture in question 8 of his report to the International Congress of Mathematicians in 1900, and the French scholar Alfond de Polignac's 1849 Polignac conjecture, By using Euclid's principle of infinite primes, equivalent transformation principle, and the idea of normalization of set element operation, this paper proves that Goldbach's conjecture, twin primes conjecture and Polignac conjecture are completely correct. In order to strictly prove a conjecture ab

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Mercedes, Orús–Lacort, Orús Román, and Christophe Jouis Christophe Joui. "Analyzing twin primes, Goldbach's strong conjecture and Polignac's conjecture." Annals of Mathematics and Physics 7, no. 1 (2024): 076–84. http://dx.doi.org/10.17352/amp.000110.

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Here we analyze three well-known conjectures: (i) the existence of infinitely many twin primes, (ii) Goldbach's strong conjecture, and (iii) Polignac's conjecture. We show that the three conjectures are related to each other. In particular, we see that in analysing the validity of Goldbach's strong conjecture, one must consider also the existence of an infinite number of twin primes. As a consequence of how we approach this analysis, we also observe that if this conjecture is true, then so is Polignac's conjecture. Our first step is an analysis of the existence of infinitely many twin prime nu

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Shannon, Anthony G., and J. V. Leyendekkers. "ON GOLDBACH'S CONJECTURE." JOURNAL OF ADVANCES IN MATHEMATICS 11, no. 9 (2016): 5661–65. http://dx.doi.org/10.24297/jam.v11i9.830.

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This paper considers some aspects of Goldbach's conjecture as a conjecture and estimates the number of prime pairs in some intervals in order to portray a compelling picture of some of the computational issues generated by the conjecture.

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Bahbouhi, Bouchaib. "New Mathematical Rules and Methods for the Strong Conjecture of Goldbach to be Verified." Journal of Robotics and Automation Research 6, no. 1 (2025): 01–36. https://doi.org/10.33140/jrar.06.01.04.

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This article emphasizes the most fundamental rules to verify Goldbach's strong conjecture that an even number is the sum of two primes. One rule states that for an even number E to split into two primes there must be two equidistant prime numbers p and p' such that E/2 - p = p' - E/2. The strong conjecture also applies to biprime numbers that are x2 – y2 . Two prime numbers equidistant with respect to an integer n have a specific property of Modulo when divided by the gap that separates them from n. The paper further proposes methods to convert even and odd numbers into sums of two and three p

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Bahbouhi, Bouchaib. "Proving Goldbach's Strong Conjecture by Analyzing Gaps Between Prime Numbers and their Digits." Journal of Mathematical Techniques and Computational Mathematics 4, no. 1 (2025): 01–18. https://doi.org/10.33140/jmtcm.04.01.04.

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The main idea of this article lies in the fact that Goldbach's strong conjecture is associated with the progression of natural integers from 0 to infinity, which results in precise gaps between prime numbers. The gap of 6 is the most regular between primes 6x + 1 on the one hand and primes 6x – 1 on the other. In this article, using the equations 3x ± 5 and analyzing the 6-based gaps between primes while determining the initial conditions that make a prime appear after or before an integer, this article argues for the truth of Goldbach's strong conjecture. Two new concepts are introduced for t

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Bahbouhi, Bouchaib. "Verification of Goldbach's Strong and Weak Conjectures at Infinity Using Basic and Accessible Mathematics." Journal of Robotics and Automation Research 6, no. 1 (2025): 01–11. https://doi.org/10.33140/jrar.06.01.02.

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This article uses two basic arguments: an even number denoted E' is either E' = 2n x E (E being even) or it is the sum of two or more even numbers. In the first case, E' = 2 n x E, this paper shows that primes p < E/2 and if E = p + q (q being prime and > E/2) and if E' = p + qx (qx being prime) then qx = (2n - 1)p + 2n q with n idicating the rank of the multiple such that n = 0 for E, n = 1 for 2 x E, n = 2 for 22 x E and so on. Therefore, 2n x E = p + (2n - 1)p + 2n q. E' and E must share one common prime p < E/2 for this equation to be verified. The primes qx follow an exponential

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Romanov, Vadim N. "Proof of Goldbach's binary conjecture." International Journal of Engineering Research and Applications 07, no. 07 (2017): 01–04. http://dx.doi.org/10.9790/9622-0707010104.

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Savvas, Minus, and Apostolos Doxiadis. "Uncle Petros and Goldbach's Conjecture." World Literature Today 74, no. 3 (2000): 684. http://dx.doi.org/10.2307/40156047.

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Farkas, Gábor, and Zsófia Juhász. "A generalization of Goldbach's conjecture." Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio computatorica, no. 46 (2017): 39–53. https://doi.org/10.71352/ac.46.039.

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Dissertations / Theses on the topic "Goldbach's conjecture"

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Härdig, Johan. "Goldbach's Conjecture." Thesis, Uppsala universitet, Algebra och geometri, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-420658.

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Farrugia, James A. "Brun's 1920 Theorem on Goldbach's Conjecture." DigitalCommons@USU, 2018. https://digitalcommons.usu.edu/etd/7153.

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One form of Goldbach’s Conjecture asserts that every even integer greater than 4is the sum of two odd primes. In 1920 Viggo Brun proved that every sufficiently large even number can be written as the sum of two numbers, each having at most nine prime factors. This thesis explains the overarching principles governing the intricate arguments Brun used to prove his result. Though there do exist accounts of Brun’s methods, those accounts seem to miss the forest for the trees. In contrast, this thesis explains the relatively simple structure underlying Brun’s arguments, deliberately avoiding most o

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Malaquias, Maurício dos Santos Matos. "Bingo de Goldbach." Universidade Federal de Goiás, 2018. http://repositorio.bc.ufg.br/tede/handle/tede/8593.

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Submitted by Liliane Ferreira (ljuvencia30@gmail.com) on 2018-06-21T11:05:12Z No. of bitstreams: 2 Dissertação - Maurício dos Santos Matos Malaquias - 2018.pdf: 2856630 bytes, checksum: a00fba48e864a23964adc8e7b38bb34b (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-06-27T10:52:48Z (GMT) No. of bitstreams: 2 Dissertação - Maurício dos Santos Matos Malaquias - 2018.pdf: 2856630 bytes, checksum: a00fba48e864a23964adc8e7b38bb34b (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e98

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Dalpizol, Luiz Gustavo. "O conjunto excepcional do problema de Goldbach." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2018. http://hdl.handle.net/10183/180946.

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Seja E(X) a cardinalidade dos números pares menores ou iguais a X que não podem ser escritos como soma de dois primos. O objetivo central desta dissertação é apresentar uma demonstração de uma estimativa para E(X) dada por Hugh L. Montgomery e Robert C. Vaughan em [22]. Mais precisamente, estabeleceremos a existência de uma constante positiva (efetivamente computável) tal que E(X) X1 ; para todo X su cientemente grande.<br>Let E(X) the cardinality of even numbers not exceeding X which cannot be written as a sum of two primes. The main goal of this dissertation is to present a proof of an estim

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Pereira, Andressa de Lima. "Números primos e a conjectura de Goldbach." reponame:Repositório Institucional da UFABC, 2017.

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Orientador: Prof. Dr. Mauricio Firmino Silva Lima<br>Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional, 2017.<br>Este trabalho apresenta os números primos, para isso é abordado seu papel na história da matemática, verificando sua atual relevância para a criptografia, analisadas as principais propriedades e resultados e sugere uma sequência didática para abordar o tema com alunos da educação básica. Também, são discutidos os avanços obtidos no estudo da conjectura de Goldbach, a partir da análise de trabalhos

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Settimi, Valentina. "On some additive problems with primes and powers of a fixed integer." Doctoral thesis, Università degli studi di Padova, 2011. http://hdl.handle.net/11577/3421684.

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This PhD thesis is devoted to study two problems in additive number theory with prime summands; the first one (Chapter 2) is about the approximation of a given real number using a linear form with one prime, two squares of primes and k powers of two, while the second one (Chapter 3) is about estimating the exceptional set of the integers representable as a sum of two primes and powers of a fixed integer g.<br>In questa Tesi di Dottorato vengono studiati due problemi di teoria additiva dei numeri con addendi primi; il primo risultato (Capitolo 2) riguarda l'approssimabilità di un dato numero re

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Dias, Cristina Helena Bovo Batista [UNESP]. "Números primos e divisibilidade: estudo de propriedades." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/99839.

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Made available in DSpace on 2014-06-11T19:30:22Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-01-28Bitstream added on 2014-06-13T20:07:43Z : No. of bitstreams: 1 dias_chbb_me_rcla.pdf: 477138 bytes, checksum: 4be306af49ba1d1e9a1fd7538c7a63be (MD5)<br>O objetivo deste trabalho é apresentar os fundamentos da divisibilidade, estudar as propriedades dos números primos, sua associação com fatoriais e com progressões aritm éticas, além de apresentar alguns resultados equivalentes à Conjetura de Goldbach<br>The objective of this paper is to present the fundamentals of divisibility, study t

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Dias, Cristina Helena Bovo Batista. "Números primos e divisibilidade : estudo de propriedades /." Rio Claro, 2013. http://hdl.handle.net/11449/99839.

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Orientador: Eliris Cristina Rizziolli<br>Banca: Aldicio José Miranda<br>Banca: Thiago de Melo<br>O PROFMAT - Programa de Mestrado Profissional em Matemática em Rede Nacional é coordenado pela Sociedade Brasileira de Matemática e realizado por uma rede de Instituições de Ensino Superior<br>Resumo: O objetivo deste trabalho é apresentar os fundamentos da divisibilidade, estudar as propriedades dos números primos, sua associação com fatoriais e com progressões aritm éticas, além de apresentar alguns resultados equivalentes à Conjetura de Goldbach<br>Abstract: The objective of this paper is to pre

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Sousa, José Emanuel. "Conjetura de Goldbach: uma visão aritmética." Master's thesis, 2013. http://hdl.handle.net/10400.3/2881.

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Dissertação de Mestrado, Matemática para Professores, 1 de Novembro de 2013, Universidade dos Açores.<br>Esta dissertação insere-se no Mestrado em Matemática para Professores, da Universidade dos Açores, e centra-se no estudo da Conjetura de Goldbach visando apresentar e aprofundar de forma sistemática e sintetizada este problema da Matemática, ainda em aberto, do ponto de vista da Teoria Aritmética dos Números. Sendo a Conjetura de Goldbach considerada a mais famosa conjetura, ainda por resolver, sobre os números primos, uma parte considerável do capítulo 1 é dedicada aos mesmos, bem como a o

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HUANG, KAI-JYUN, and 黃凱焌. "Exploring Goldbach Conjecture by Statistical Software and JAVA." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/51241799253538347207.

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碩士<br>國立屏東教育大學<br>應用數學系<br>101<br>This study used computer programs and statistical software to discuss Goldbach conjecture: each even number greater than 2 can be broken down into two prime numbers and their sum must be equal to the even number. The first chapter described the motivation and purpose, as well as the history of Goldbach conjecture and its developments. The second chapter used JAVA program to operate the number of ways to write an even number as the sum of two primes. The third chapter used SPSS19 to analyze the relations between the numbers of ways to write an even number as th

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Books on the topic "Goldbach's conjecture"

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Doxiadēs, Apostolos K. Uncle Petros and Goldbach's conjecture. Bloomsbury, 2000.

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Doxiadēs, Apostolos K. Uncle Petros and Goldbach's conjecture. Faber and Faber, 2000.

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Hu, Zhenwu. Gedebahe cai xiang zheng ming zhi tuo zhan yan jiu: Development research of proof of Goldbach's conjecture. [Publisher not identified], 2016.

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1930-, Wang Yuan, ed. Goldbach conjecture. 2nd ed. World Scientific, 2002.

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Doxiadēs, Apostolos K. Apo tēn paranoia stous algorithmous: Hē Dekatē Hevdomē Nychta kai alles diadromes. 2nd ed. Ikaros, 2006.

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Doxiadēs, Apostolos K. Zio Petros e la congettura di Goldbach. Tascabili Bompiani, 2001.

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Chen, Qing-Hui. Decoding the code in Golg[sic]bach conjecture: The law and proof of Goldbach conjecture. Goldbach Conjecture Research, 2006.

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Pogorzelski, H. A. Transtheoretic foundations of mathematics (general summary of results). Research Institute for Mathematics, 2004.

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Pogorzelski, H. A. Transtheoretic foundations of mathematics (general summary of results). Research Institute for Mathematics, 2004.

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Doxiadēs, Apostolos K. Ho theios Petros kai hē eikasia tou Gkolntmpach: Mythistorēma. 4th ed. Ekdoseis Kastaniōtē, 1992.

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Book chapters on the topic "Goldbach's conjecture"

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Clawson, Calvin C. "Goldbach’s Conjecture." In Mathematical Mysteries. Springer US, 1996. http://dx.doi.org/10.1007/978-1-4899-6080-1_13.

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Karatsuba, Anatolij A., and Melvyn B. Nathanson. "The Goldbach Conjecture." In Basic Analytic Number Theory. Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-58018-5_10.

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Booth, David, and Renatus Ziegler. "On the Goldbach Conjecture." In Finsler Set Theory: Platonism and Circularity. Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-9031-1_18.

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Vaughan, Robert C. "Goldbach’s Conjectures: A Historical Perspective." In Open Problems in Mathematics. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-32162-2_16.

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Deshouillers, J. M., H. J. J. te Riele, and Y. Saouter. "New experimental results concerning the Goldbach conjecture." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0054863.

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Huang, Jing-Jing, and Huixi Li. "On the Connection Between the Goldbach Conjecture and the Elliott-Halberstam Conjecture." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-67996-5_17.

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Benschop, Nico F. "Additive Structure of Z(.) mod m k (Squarefree) and Goldbach’s Conjecture." In Associative Digital Network Theory. Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-1-4020-9829-1_9.

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Farkas, Hershel M. "A Matrix Related to the Theorem of Fermat and the Goldbach Conjecture." In From Fourier Analysis and Number Theory to Radon Transforms and Geometry. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4075-8_9.

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Paiva, Carlos Daniel Chaves, Rildo Alves do Nascimento, Isaías José de Lima, et al. "The search for Goldbach's conjecture proof: Exploring your achievements." In Frontiers of Knowledge: Multidisciplinary Approaches in Academic Research. Seven Editora, 2024. http://dx.doi.org/10.56238/sevened2024.026-018.

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Christian Goldbach was a Russian mathematician who lived in the eighteenth century. Although he saw mathematics more as a hobby, he published several works on Number Theory. It is in one of his correspondences with Euler that his conjecture arises, which states that every even number greater than 2 can be expressed as the sum of two prime numbers (equal or not). Despite having a very simple statement, its demonstration requires advanced mathematical knowledge, so much so that to this day it remains without a definitive proof. Obviously, several mathematicians have devoted many years of their l

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Wilson, Robin. "7. Conjectures and theorems." In Number Theory: A Very Short Introduction. Oxford University Press, 2020. http://dx.doi.org/10.1093/actrade/9780198798095.003.0007.

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‘Conjectures and theorems’ investigates a number of topics, such as the distribution of prime numbers, and two unsolved problems, Goldbach’s conjecture and the twin prime conjecture. The factorization of positive integers into primes is unique, but this does not hold for certain other systems of numbers. A more in-depth look at unique factorization gives deeper results, including a proposed result of Gauss. Mathematicians in the 1950s and 1960s confirmed that he was correct, as shown in the so-called ‘Baker-Heegner-Stark theorem’.

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Conference papers on the topic "Goldbach's conjecture"

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Ge, Linfu. "The Proof and Decryption of Goldbach Conjecture." In IS4SI Summit 2023. MDPI, 2023. http://dx.doi.org/10.3390/cmsf2023008052.

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Burqan, Aliaa. "New algebraic insights to the Goldbach conjecture." In 5TH INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES (ICMS5). AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0228106.

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Al-Ameen, Talal, and Imad Muhi. "A Rudimentary Proof on Goldbach Conjectures." In 2022 IEEE 2nd International Conference on Information Communication and Software Engineering (ICICSE). IEEE, 2022. http://dx.doi.org/10.1109/icicse55337.2022.9828990.

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Wang, Yu. "The Mathematical Modeling and Proof of the Goldbach Conjecture." In 2018 3rd International Conference on Modelling, Simulation and Applied Mathematics (MSAM 2018). Atlantis Press, 2018. http://dx.doi.org/10.2991/msam-18.2018.6.

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Junchi, Li. "From the Goldbach Conjecture Cipher to the Han Ge CODE." In 2019 IEEE 4th International Conference on Big Data Analytics (ICBDA). IEEE, 2019. http://dx.doi.org/10.1109/icbda.2019.8712839.

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Reports on the topic "Goldbach's conjecture"

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Friedland, Gerald. On the Goldbach Conjecture. Office of Scientific and Technical Information (OSTI), 2018. http://dx.doi.org/10.2172/1476233.

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Friedland, G. On the Goldbach Conjecture. Office of Scientific and Technical Information (OSTI), 2018. http://dx.doi.org/10.2172/1417954.

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