Source labels openChecked July 26, 2026

Erdős Problem 1095: Upper Conjecture

Ecklund, Erdős, and Selfridge [EES74] conjectured $g(k)\leq \exp((1+o(1))k)$ .

Number theory AMS 11

Mathematical statement

Ecklund, Erdős, and Selfridge [EES74] conjectured $g(k)\leq \exp((1+o(1))k)$ .

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_1095.variants.upper_conjecture

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_1095.variants.upper_conjecture :    ∃ f : ℕ → ℝ, Tendsto f atTop (𝓝 0) ∧ ∀ᶠ k in atTop, g k ≤ exp (k * (1 + f k)) := 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/1095background