Source labels openChecked July 26, 2026

Infinitude of Wall–Sun–Sun primes

A prime $p$ is a Wall–Sun–Sun prime if and only if $L_p \equiv 1 \pmod{p^2}$ , where $L_p$ is the $p$ -th Lucas number. It is conjectured that there are infinitely many Wall-Sun-Sun primes.

Number theory AMS 11

Mathematical statement

A prime $p$ is a Wall–Sun–Sun prime if and only if $L_p \equiv 1 \pmod{p^2}$ , where $L_p$ is the $p$ -th Lucas number. It is conjectured that there are infinitely many Wall-Sun-Sun primes.

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

infinite_isWallSunSunPrime

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem infinite_isWallSunSunPrime : {p : ℕ | IsWallSunSunPrime p}.Infinite := 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