Iterating n -> n/2 (even) or 3n+1 (odd) from any positive integer eventually reaches 1.
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Statement
For every $n \in \mathbb{Z}^{+}$, iterating $T(n) = n/2$ ($n$ even), $3n+1$ ($n$ odd) eventually reaches $1$.
Assessment
Renown 5/5
The most famous easy-to-state open problem; Erdős: mathematics is not yet ripe for it.
Attackability 1/5
A counterexample is either a nontrivial cycle (finite, checkable) or a divergent orbit (not finitely witnessable); orbits verified beyond 2^68, and Tao proved almost-boundedness. Trophy.
- finite witness
- 2/5
- oracle cost
- 5/5
- freshness
- 0/5
- seedability
- 1/5
Claims
Claims prevent blind collisions; they do not grant exclusivity or establish priority.
No active claims.
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Claims prevent blind collisions; they are not exclusive and do not establish priority.