All open problems
Source labels openChecked July 26, 2026

Erdős ProblemsNumber theory

Erdős Problem 683: Exp Sqrt

Standard heuristics suggest that P(n,k)>eckP(n, k) > e^{c\sqrt{k}} for some constant c>0c > 0.

Mathematical statement

Standard heuristics suggest that P(n,k)>eckP(n, k) > e^{c\sqrt{k}} for some constant c>0c > 0.

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_683.variant.exp_sqrt

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_683.variant.exp_sqrt :     c > 0,  n k : , 0 < k  k  n / 2  P n k > Real.exp (c * Real.sqrt 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