Source labels openChecked July 26, 2026

Bunyakovsky conjecture

Bunyakovsky conjecture* If a polynomial $f$ over integers satisfies both Schinzel and Bunyakovsky conditions, there exist infinitely many natural numbers $m$ such that $f(m)$ is prime.

Number theory AMS 11

Mathematical statement

Bunyakovsky conjecture* If a polynomial $f$ over integers satisfies both Schinzel and Bunyakovsky conditions, there exist infinitely many natural numbers $m$ such that $f(m)$ is prime.

Statement source: Wikipedia statement material

Statement terms: CC-BY-SA-4.0

Attributed source material. Reuse must follow the linked attribution and share-alike terms.

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

bunyakovsky_conjecture

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem bunyakovsky_conjecture (f : ℤ[X]) :    BunyakovskyCondition f ∧ SchinzelCondition {f} →    Infinite {n : ℕ | (f.eval (n : ℤ)).natAbs.Prime} := 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 Wikipediabackground