Open problemChecked July 24, 2026

Collatz Conjecture

A simple integer iteration whose universal termination remains unknown.

Number theory Discrete dynamics Computation

Mathematical statement

For every $n>0$ , repeatedly apply $T(n)=n/2$ when $n$ is even and $T(n)=3n+1$ otherwise. Some iterate $T^m(n)$ equals $1$ .

Statement source: Therefore editorial statement

Statement terms: Source-specific

Editorial wording by Therefore. No statement reuse license is granted.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

CollatzConjecture.collatz_conjecture

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem collatz_conjecture (n : ℕ) (hn : n > 0) :    ∃ m, collatzStep^[m] n = 1 := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Collatz conjecture overviewbackground