{"id":"goldbach-conjecture","domain":"number-theory","type":"Conjecture","title":"Goldbach Conjecture","slug":"goldbach-conjecture","url":"/mathematics/number-theory/goldbach-conjecture/","posed":"1742, Christian Goldbach (letter to Euler)","status":"open","summary":"Every even integer >2 is the sum of two primes. Strong form open; weak (ternary) form proven by Helfgott 2013. Verified computationally to 4x10^18.","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Helfgott, H.A. (2013). The ternary Goldbach conjecture is true. arXiv:1312.7748."},{"tier":1,"citation":"Chen, J.R. (1973). On the representation of a larger even integer. Scientia Sinica, 16, 157-176."},{"tier":2,"citation":"Oliveira e Silva, T. et al. (2014). Empirical verification of the even Goldbach conjecture. Mathematics of Computation, 83(288), 2033-2060."},{"tier":3,"citation":"Wells, D. (2005). Prime Numbers: The Most Mysterious Figures in Math."}],"relationships":[{"type":"built_on","target":"prime-number","label":"Prime Number"},{"type":"related_to","target":"twin-prime-conjecture","label":"Twin Prime Conjecture"},{"type":"tracked_in","target":"proof-status","label":"Proof Status Board"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"2.3"}