Selfridge's conjectures

formal-conjectures · wikipedia · ams-11

**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.

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://en.wikipedia.org/wiki/John_Selfridge#Selfridge
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Wikipedia/Selfridge.lean
Local target: Corpus.WikipediaSelfridge.selfridge_conjecture
Source SHA-256: 4493c20da5530a9880d8530110ac96b2cbf304075e096ae8e7c5e60e97fc4915
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record