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Source labels openChecked July 26, 2026

Erdős ProblemsNumber theory

Erdős Problem 32: Log Bound

Can the bound O(logN)O(\log N) be achieved for an additive complement to the primes? [Guy04] writes that Erdős offered $50 for the solution.

Mathematical statement

Can the bound O(logN)O(\log N) 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

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_32.variants.log_bound : answer(sorry)   A : Set ,    IsAdditiveComplementToPrimes A     (fun N => (((Finset.Icc 1 N).filter (·  A)).card : )) =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