Schinzel.lean`

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

1 declarations, 1 contain sorry, 0 declared as axioms

Hypothesis H

Reference: Wikipedia

Imports (1)

FormalConjecturesUtil

Imported by 1 file

FormalConjectures/ErdosProblems/252.lean

theorem Schinzel.schinzel_conjecture Schinzel conjecture (H hypothesis) If a finite set of polynomials sorry line 37 source
Source documentation
Schinzel conjecture (H hypothesis) If a finite set of polynomials $f_i$ satisfies both Schinzel and Bunyakovsky conditions, there exist infinitely many natural numbers $n$ such that $f_i(n)$ are primes for all $i$.

depends on sorry what this means
Statement uses: Finset, Polynomial, Int, Membership.mem, BunyakovskyCondition, SchinzelCondition, 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
13 instances, coercions and auxiliary constants left out.

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