Source labels openChecked July 26, 2026

Selfridge's conjectures

PSW conjecture* (Selfridge's test) Let $p$ be an odd number, with $p \equiv \pm 2 \pmod{5}$ , $2^{p-1} \equiv 1 \pmod{p}$ and $F_{p+1} \equiv 0 \pmod{p}$ , then $p$ is a prime number.

Number theory AMS 11

Mathematical statement

PSW conjecture* (Selfridge's test) Let $p$ be an odd number, with $p \equiv \pm 2 \pmod{5}$ , $2^{p-1} \equiv 1 \pmod{p}$ and $F_{p+1} \equiv 0 \pmod{p}$ , then $p$ is a 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

selfridge_conjecture

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem selfridge_conjecture (p : ℕ) (hp : IsSelfridge p) : p.Prime := 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