Erdős Problem 409: Sigma Termination
If then the iteration necessarily reaches a prime. Note: this is open , it is not clear that the σ iteration always terminates, since it is non-decreasing (unlike the φ iteration which is strictly decreasing).
Mathematical statement
If then the iteration necessarily reaches a prime. Note: this is open , it is not clear that the σ iteration always terminates, since it is non-decreasing (unlike the φ iteration which is strictly decreasing).
Statement source: Erdős Problems statement material
Statement terms: Source-specific
Source-specific terms. Therefore does not assert reuse rights beyond attributed display.
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
erdos_409.variants.sigma_termination
theorem erdos_409.variants.sigma_termination (n : ℕ) (hn : n > 1) : ∃ i, (σ 1 · - 1)^[i] n |>.Prime := 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