Number theory
$5,056 bountynobody has started
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
Even one lemma helps. Whoever finishes this later shares the pool with everyone who got them there.
contrib new erdos-428Command line, then a pull request on GitHub.
Nothing has been published against this problem yet.
A first lemma is worth as much as a last one: whoever closes the problem shares the pool with everyone who got them there.
Formal statement
Proof target
import FormalConjectures.ErdosProblems.«428»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos428.erdos_428" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔
∃ A,
(∃ᶠ (n : ℕ) in Filter.atTop, ∀ a ∈ A, 0 < a → a < n → Nat.Prime (n - a)) ∧
Filter.liminf (fun n => Erdos428.primeDensityRatio A n) Filter.atTop > 0Original conjecture source: FormalConjectures/ErdosProblems/428.lean
References
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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