Source labels openChecked July 26, 2026

Andrica's conjecture

Andrica's conjecture* The inequality $\sqrt{p_{n+1}}-\sqrt{p_n} < 1$ holds for all $n$ , where $p_n$ is the $n$ -th prime number.

Number theory AMS 11

Mathematical statement

Andrica's conjecture* The inequality $\sqrt{p_{n+1}}-\sqrt{p_n} < 1$ holds for all $n$ , where $p_n$ is the $n$ -th prime number.

Statement source: Wikipedia statement material

Statement terms: CC-BY-SA-4.0

Attributed source material. Reuse must follow the linked attribution and share-alike terms.

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

andrica_conjecture

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem andrica_conjecture (n : ℕ) :    Real.sqrt ((n+1).nth Nat.Prime) - Real.sqrt (n.nth Nat.Prime) < 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 Wikipediabackground Luan Alberto Ferreira, *Real exponential sums over primes and prime gaps*background