Source labels openChecked July 26, 2026

Erdős Problem 244

Let $C > 1$ . Does the set of integers of the form $p + \lfloor C^k \rfloor$ , for some prime $p$ and $k\geq 0$ , have density $>0$ ?

Number theory AMS 11

Mathematical statement

Let $C > 1$ . Does the set of integers of the form $p + \lfloor C^k \rfloor$ , for some prime $p$ and $k\geq 0$ , have density $>0$ ?

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_244

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_244 : answer(sorry) ↔    ∀ C > (1 : ℝ), 0 < { p + ⌊C ^ k⌋₊ | (p) (k) (_ : p.Prime) }.lowerDensity := 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/244background