The search for Goldbach's conjecture proof: Exploring your achievements - Paiva, Carlos Daniel Chaves; do Nascimento , Rildo Alves; de Lima, Isaías José; Alexandre, José Joel; Gomes, Francisco Bergson Araujo; Tomé , Joelder Lincoln Gomes; Alves , Cleilson Silva; de Brito, Ivan Eudes Gonçalves; Martins, Geovânio Felipe Oliveira; de Moura, Carlos Henrique Lima; de Oliveira, Adalgisa Maria; Oliveira, Santana da Rocha; et al. (Seven Editora, 2024)
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 lives to the study of Goldbach's conjecture. In this sense, the objective of this research is to list the advances achieved by such mathematicians over time. In addition, we will seek to better understand the historical context in which the conjecture arises. In the end, we will try to highlight the most significant results that at first can be the basis for further research. DOI:https://doi.org/10.56238/sevened2024.026-018