Home›Open Questions›Does the Collatz process really always reach one, from every possible starting number?Open QuestionsDoes the Collatz process really always reach one, from every possible starting number?Citation FormatsGeneral ReferenceGeneral Reference Citation TextMathematics Atlas. "Does the Collatz process really always reach one, from every possible starting number?." Accessed August 30, 2026. https://mathematics.interactiveatlas.org/open-questions-index/collatz-conjecture-open-question.Copy General ReferenceAPA StyleAPA Style Citation TextMathematics Atlas. (n.d.). Does the Collatz process really always reach one, from every possible starting number?. Retrieved August 30, 2026, from https://mathematics.interactiveatlas.org/open-questions-index/collatz-conjecture-open-questionCopy APA StyleBibTeXBibTeX Citation Text@misc{mathematicsatlas-does-the-collatz-process-really-always-r, author = {Mathematics Atlas}, title = {Does the Collatz process really always reach one, from every possible starting number?}, year = {2026}, url = {https://mathematics.interactiveatlas.org/open-questions-index/collatz-conjecture-open-question}, note = {Accessed August 30, 2026} }Copy BibTeXOpen QuestionCross-Tradition ConnectionsSourcesComments (0)Reader Challenges (0 open reader challenges)Open QuestionEvery starting number ever tested by computer, into the astronomically large, reaches one, but no proof rules out either an unbounded starting number whose path never terminates or a hidden cycle other than the trivial one at 1-4-2; Paul Erdos himself is widely quoted as doubting mathematics currently has the tools to settle it.What would resolve this A general proof covering every positive starting integer, or the discovery of a starting number that provably never reaches one (an unbounded trajectory or a second cycle).OpenNumber theory / dynamical systemsWolfram MathWorldCross-Tradition ConnectionsQuestion OnCollatz Conjecture, Conjectures Well-attested Source Wolfram MathWorldtier 1SourcesWolfram MathWorldtier 1Wolfram Research, Inc.View 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