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Erdős problem 429

Is it true that, if A⊆NA\subseteq \mathbb{N} is sparse enough and does not cover all residue classes modulo pp for any prime pp, then there exists some nn such that n+an+a is prime for all a∈Aa\in A?

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/429.lean

Formal Conjectures

FormalConjectures/ErdosProblems/429.leanErdos429.erdos_4297 linesExact file
False ↔  ∃ f,    Filter.Tendsto f Filter.atTop Filter.atTop ∧      ∀ (A : Set ℕ),        A.Infinite →          (∀ (N : ℕ), (A ∩ Set.Icc 1 N).ncard ≤ f N) →            (∀ (p : ℕ), Nat.Prime p → ∃ b, ∀ a ∈ A, ↑a ≠ b) → ∃ n, ∀ a ∈ A, Nat.Prime (n + a)
SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.

Proof manifests naming this Problem

  • Jayyhk Erdős Leanjayyhk:erdos:429
  • PLBY Lean proofsErdosProblems.Erdos429

Reported activity

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

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