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Dickson's conjecture

Conjecture · dickson_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.

Formal statement · Lean 4.lean
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

Proof. sorry

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