Bunyakovsky.lean`

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

1 declarations, 1 contain sorry, 0 declared as axioms

Bunyakovsky conjecture

Reference: Wikipedia

Imports (1)

FormalConjecturesUtil

theorem Bunyakovsky.bunyakovsky_conjecture Bunyakovsky conjecture If a polynomial sorry line 37 source
Source documentation
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.

depends on sorry what this means
Statement uses: Polynomial, Int, And, BunyakovskyCondition, SchinzelCondition, Singleton.singleton, Finset, Infinite, Nat, Set.ofPred, Nat.Prime, Int.natAbs, Polynomial.eval
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat
11 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem bunyakovsky_conjecture (f : ℤ[X]) :
    BunyakovskyCondition f ∧ SchinzelCondition {f} →
    Infinite {n : ℕ | (f.eval (n : ℤ)).natAbs.Prime} := by
…
```
Mentions: BunyakovskyCondition, SchinzelCondition