FormalConjectures.ErdosProblems.«234»

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import FormalConjecturesUtil

Erdős Problem 234

Reference: erdosproblems.com/234


open Real Set

open scoped NNReal


namespace Erdos234

Is it true that for all 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?

@[category research open, AMS 11]
theorem declaration uses 'sorry'erdos_234 : answer(sorry) ↔ ∃ f : ℝ≥0 → ℝ, Continuous f ∧
    ∀ c : ℝ≥0, HasDensity {n : ℕ | primeGap n / log n < c} (f c) := by⊢ True ↔ ∃ f, Continuous f ∧ ∀ (c : ℝ≥0), {n | ↑(primeGap n) / log ↑n < ↑c}.HasDensity (f c)
  sorryAll goals completed! 🐙


end Erdos234