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WikipediaNumber theory

Dickson's conjecture

Dickson's conjecture* If a finite set of linear integer forms fi(n)=ain+bif_i(n) = a_i n+b_i satisfies Schinzel condition, there exist infinitely many natural numbers mm such that fi(m)f_i(m) are primes for all ii.

Number theoryAMS 11

Mathematical statement

Dickson's conjecture* If a finite set of linear integer forms fi(n)=ain+bif_i(n) = a_i n+b_i satisfies Schinzel condition, there exist infinitely many natural numbers mm such that fi(m)f_i(m) are primes for all ii.

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

dickson_conjecture

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem dickson_conjecture (fs : Finset ℤ[X]) (hfs : ∀ f ∈ fs, f.degree = 1 ∧ BunyakovskyCondition f)    (hfs' : SchinzelCondition fs) : Infinite {n : ℕ | ∀ f ∈ fs, (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 sourceformalizationWikipediabackgroundPrimePages glossarybackgroundOEIS Wikibackground