Representations with prime conditions

formal-conjectures · oeis · ams-11

Any integer $n > 1$ can be written as $x + y$ with $x, y > 0$ such that both $x + ny$ and
$x^2 + ny^2$ are prime.

Zhi-Wei Sun has offered a \$200 prize for the first proof.

**Zhi-Wei Sun's Conjecture (A232174)**: Any integer $n > 1$ can be written as $x + y$ with
$x, y > 0$ such that both $x + ny$ and $x^2 + ny^2$ are prime.

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/A232174
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://arxiv.org/abs/1211.1588
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/232174.lean
Local target: Corpus.OEIS232174.conjecture
Source SHA-256: 1a3c284d5632dbbd61831671ec7731689119ac9681297a9a9d3161b20b6bc51b
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