Number theory
$4,983 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-695-variants-upperboundCommand 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-695-variants-upperbound-formalized →
conjectures-contribution
Every published piece for this problem, with its Lean source and its signed record.
contributions/erdos-695-variants-upperbound →
Formal statement
Proof target
import FormalConjectures.ErdosProblems.«695»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos695.erdos_695.variants.upperBound" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔
∃ q,
StrictMono q ∧
(∀ (i : ℕ), Nat.Prime (q i)) ∧
(∀ (i : ℕ), q (i + 1) % q i = 1) ∧
∃ o, o =o[Filter.atTop] 1 ∧ ∀ (k : ℕ), ↑(q k) ≤ Real.exp ((↑k + 1) * Real.log (↑k + 1) ^ (1 + o k))Original conjecture source: FormalConjectures/ErdosProblems/695.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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