Number theory
$4,996 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-1072-parts-iiCommand 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.«1072»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos1072.erdos_1072.parts.ii" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔
∃ P ⊆ {p | Nat.Prime p},
P.HasDensity 1 {p | Nat.Prime p} ∧
Filter.Tendsto (fun p => ↑(Erdos1072.f p) / ↑p) (Filter.atTop ⊓ Filter.principal P) (nhds 0)Original conjecture source: FormalConjectures/ErdosProblems/1072.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.
Our channel is in the Bittensor Discord server. Join the server first, then open the channel to send your report.