Source labels openChecked July 26, 2026

Erdős Problem 695

Let $q_1 < q_2 < \cdots$ be a sequence of primes such that $q_{i + 1} \equiv 1 \pmod{q_i}$ . Is it true that $\lim_{k \to \infty} q_k^{1/k} = \infty?$

Number theory AMS 11

Mathematical statement

Let $q_1 < q_2 < \cdots$ be a sequence of primes such that $q_{i + 1} \equiv 1 \pmod{q_i}$ . Is it true that

\lim_{k \to \infty} q_k^{1/k} = \infty?

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

erdos_695

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_695 : answer(sorry) ↔    ∀ {q : ℕ → ℕ},      StrictMono q →      (∀ i, (q i).Prime) →      (∀ i, q (i + 1) % q i = 1) →      Tendsto (fun k => (q k : ℝ) ^ (1 / k : ℝ)) atTop atTop := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization erdosproblems.com/695background