Number theory
q : ℕ → ℕ be a strictly increasing sequence of primes such that
q (n + 2) - q (n + 1) ≥ q (n + 1) - q n. Must lim q n / (n ^ 2) = ∞? $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-455Command 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.«455»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos455.erdos_455" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔
∀ (q : ℕ → ℕ),
StrictMono q →
(∀ (n : ℕ), Nat.Prime (q n) ∧ q (n + 2) - q (n + 1) ≥ q (n + 1) - q n) →
Filter.Tendsto (fun n => ↑(q n) / ↑n ^ 2) Filter.atTop Filter.atTopOriginal conjecture source: FormalConjectures/ErdosProblems/455.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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