Source labels openChecked July 26, 2026

Erdős Problem 535: First Open Case

The first open case of Erdős Problem 535 is $r = 3$ : there should exist $c > 0$ such that $f_3(N) \leq N^{c/\log\log N}$ for all sufficiently large $N$ .

Combinatorics AMS 5 AMS 11

Mathematical statement

The first open case of Erdős Problem 535 is $r = 3$ : there should exist $c > 0$ such that $f_3(N) \leq N^{c/\log\log N}$ for all sufficiently large $N$ .

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_535.variants.first_open_case

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_535.variants.first_open_case : ∃ c > (0 : ℝ),    ∀ᶠ (N : ℕ) in atTop,      (f 3 N : ℝ) ≤ (N : ℝ) ^ (c / log (log (N : ℝ))) := 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

Pinned Formal Conjectures sourceformalization erdosproblems.com/535background