Primitive roots of the form k² + 1

formal-conjectures · oeis · ams-11

Every prime $p$ has a primitive root $0 < g < p$ of the form $k^2 + 1$, where $k$ is an integer.

Zhi-Wei Sun has offered a prize of RMB 2,000 for the first proof.

**Zhi-Wei Sun's Conjecture (A239957)**: Every prime $p$ has a primitive root $0 < g < p$ of the
form $k^2 + 1$, where $k$ is an integer.

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://oeis.org/A239957
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/239957.lean
Local target: Corpus.OEIS239957.conjecture
Source SHA-256: cb321e564a1333ccd81cba2a70db3cf0c36362b1191c06601db8e92a88c0f6a4
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