Number theory
c ≥ 0, the density f c of integers for which
(p (n + 1) - p n) / log n < c exists and is a continuous function of c?
$5,124 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-234Command 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.«234»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos234.erdos_234" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔ ∃ f, Continuous f ∧ ∀ (c : NNReal), {n | ↑(primeGap n) / Real.log ↑n < ↑c}.HasDensity (f c)Original conjecture source: FormalConjectures/ErdosProblems/234.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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