Home›Open Questions›Do infinitely many twin prime pairs really exist, or does the last one eventually appear?Open QuestionsDo infinitely many twin prime pairs really exist, or does the last one eventually appear?Citation FormatsGeneral ReferenceGeneral Reference Citation TextMathematics Atlas. "Do infinitely many twin prime pairs really exist, or does the last one eventually appear?." Accessed August 30, 2026. https://mathematics.interactiveatlas.org/open-questions-index/twin-prime-conjecture-open-question.Copy General ReferenceAPA StyleAPA Style Citation TextMathematics Atlas. (n.d.). Do infinitely many twin prime pairs really exist, or does the last one eventually appear?. Retrieved August 30, 2026, from https://mathematics.interactiveatlas.org/open-questions-index/twin-prime-conjecture-open-questionCopy APA StyleBibTeXBibTeX Citation Text@misc{mathematicsatlas-do-infinitely-many-twin-prime-pairs-real, author = {Mathematics Atlas}, title = {Do infinitely many twin prime pairs really exist, or does the last one eventually appear?}, year = {2026}, url = {https://mathematics.interactiveatlas.org/open-questions-index/twin-prime-conjecture-open-question}, note = {Accessed August 30, 2026} }Copy BibTeXOpen QuestionCross-Tradition ConnectionsSourcesComments (0)Reader Challenges (0 open reader challenges)Open Question2013's breakthrough (Yitang Zhang, later sharpened by the Polymath collaborative project to a gap of 246) proved infinitely many prime pairs exist within SOME bounded gap, but closing that gap all the way down to exactly two, the original conjecture, remains open.What would resolve this A proof narrowing the proven bounded gap (currently 246) all the way to 2, or a fundamentally different argument establishing the gap-2 case directly.OpenAnalytic number theoryMacTutor History of Mathematics ArchiveCross-Tradition ConnectionsQuestion OnTwin Prime 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