Erdős Problem 32: Log Bound
Can the bound be achieved for an additive complement to the primes? [Guy04] writes that Erdős offered $50 for the solution.
Mathematical statement
Can the bound be achieved for an additive complement to the primes? [Guy04] writes that Erdős offered $50 for the solution.
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_32.variants.log_bound
theorem erdos_32.variants.log_bound : answer(sorry) ↔ ∃ A : Set ℕ, IsAdditiveComplementToPrimes A ∧ (fun N => (((Finset.Icc 1 N).filter (· ∈ A)).card : ℝ)) =O[atTop] fun N => Real.log 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