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Source labels openChecked July 26, 2026

Erdős ProblemsNumber theory

Erdős Problem 208: Log Bound

In [Er79] Erdős says perhaps sn+1snlogsns_{n+1} - s_n \ll \log s_n, but he is 'very doubtful'.

Mathematical statement

In [Er79] Erdős says perhaps sn+1snlogsns_{n+1} - s_n \ll \log s_n, but he is 'very doubtful'.

[Er79] Erdős, Paul, Some unconventional problems in number theory. Math. Mag. (1979), 67-70.

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_208.variants.log_bound

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_208.variants.log_bound :    (fun n  (s (n + 1) - s n : )) =O[atTop] fun n  log (s n) := 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