All open problems
Source labels openChecked July 26, 2026

Erdős ProblemsNumber theory

Erdős Problem 409: I

How many iterations of nϕ(n)+1n\mapsto\phi(n) + 1 are needed before a prime is reached?

Mathematical statement

How many iterations of nϕ(n)+1n\mapsto\phi(n) + 1 are needed before a prime is reached?

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.parts.i

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_409.parts.i (n : ) (hn : 0 < n) :    IsLeast { i | (φ · + 1)^[i] n |>.Prime } answer(sorry) := 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