Number theory
$4,994 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-269-variants-irrationalCommand 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.
conjectures-tasks
The pinned statement, the Lean challenge file and the exact bundle you build against.
pool/tier-1/erdos-269-variants-irrational-formalized →
conjectures-contribution
Every published piece for this problem, with its Lean source and its signed record.
contributions/erdos-269-variants-irrational →
Formal statement
Proof target
import FormalConjectures.ErdosProblems.«269»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos269.erdos_269.variants.irrational" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔ ∀ (P : Finset ℕ), (∀ p ∈ P, Nat.Prime p) → P.card ≥ 2 → Irrational (Erdos269.series ↑P)Original conjecture source: FormalConjectures/ErdosProblems/269.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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