Source labels openChecked July 26, 2026

Erdős Problem 287: Prime Conjecture

For all large $N$ , there exists a prime $p \in [N, 2N]$ such that $\frac{p+1}{2}$ is also prime.

Mathematical statement

For all large $N$ , there exists a prime $p \in [N, 2N]$ such that $\frac{p+1}{2}$ is also prime.

This is an open conjecture. If true, it would imply erdos_287 for all but at most finitely many exceptions (see erdos_287.variants.prime_conjecture_implies).

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_287.variants.prime_conjecture

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_287.variants.prime_conjecture : answer(sorry) ↔    ∃ N₀ : ℕ, ∀ N : ℕ, N₀ ≤ N →      ∃ p : ℕ, Nat.Prime p ∧ N ≤ p ∧ p ≤ 2 * N ∧ Nat.Prime ((p + 1) / 2) := 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/287background