Home›Open Questions›Can every even integer greater than two really always be written as the sum of two primes?Open QuestionsCan every even integer greater than two really always be written as the sum of two primes?Citation FormatsGeneral ReferenceGeneral Reference Citation TextMathematics Atlas. "Can every even integer greater than two really always be written as the sum of two primes?." Accessed August 30, 2026. https://dev-mathematics.interactiveatlas.org/open-questions-index/goldbach-conjecture-open-question.Copy General ReferenceAPA StyleAPA Style Citation TextMathematics Atlas. (n.d.). Can every even integer greater than two really always be written as the sum of two primes?. Retrieved August 30, 2026, from https://dev-mathematics.interactiveatlas.org/open-questions-index/goldbach-conjecture-open-questionCopy APA StyleBibTeXBibTeX Citation Text@misc{mathematicsatlas-can-every-even-integer-greater-than-two, author = {Mathematics Atlas}, title = {Can every even integer greater than two really always be written as the sum of two primes?}, year = {2026}, url = {https://dev-mathematics.interactiveatlas.org/open-questions-index/goldbach-conjecture-open-question}, note = {Accessed August 30, 2026} }Copy BibTeXOpen QuestionCross-Tradition ConnectionsSourcesComments (0)Reader Challenges (0 open reader challenges)Open QuestionVerified by computer for every even number checked so far, into the many quintillions, with no exception found, but no general proof covering all even numbers exists, nearly three centuries after Goldbach first proposed it.What would resolve this A general proof covering every even integer (or a single confirmed counterexample, an even number that is not the sum of two primes).OpenAnalytic number theoryMacTutor History of Mathematics ArchiveCross-Tradition ConnectionsQuestion OnGoldbach Conjecture, Conjectures Well-attested Source MacTutor History of Mathematics Archivetier 1SourcesMacTutor History of Mathematics Archivetier 1University of St Andrews, School of Mathematics and StatisticsView the SourceComments (0)No comments yet. Be the first to share a thought.Sign in to join the discussion.Reader Challenges (0 open reader challenges)No disputes yet. Spotted an error or a better source? Open the first one.Sign in to dispute this or suggest a correction.View At A Past YearThe atlas records no dated fact of its own for this entry, so there is no other year to choose.Show This Year