Source labels openChecked July 26, 2026

Erdős Problem 1065: I

Are there infinitely many primes $p$ such that $p = 2^k * q + 1$ for some prime $q$ and $k ≥ 0$ ?

Number theory AMS 11

Mathematical statement

Are there infinitely many primes $p$ such that $p = 2^k * q + 1$ for some prime $q$ and $k ≥ 0$ ?

This is mentioned as B46 in Unsolved Problems in Number Theory by Richard K. Guy

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_1065.parts.i

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_1065.parts.i :    answer(sorry) ↔ Set.Infinite {p | ∃ q k, p.Prime ∧ q.Prime ∧ p = 2^k * q + 1} := 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 Unsolved Problems in Number Theorybackground erdosproblems.com/1065background