Prime Tuples Conjecture

formal-conjectures · paper · ams-11

For any k ≥ 2, let a₁,...,aₖ and b₁,...,bₖ be integers with aᵢ > 0. Suppose that for
every prime p there exists an integer n such that p ∤ ∏ i, (aᵢ n + bᵢ). Then there exist
infinitely many n such that aᵢ n + bᵢ is prime for all i.

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
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Paper/PrimeTuples.lean
Local target: Corpus.PaperPrimeTuples.prime_tuples_conjecture
Source SHA-256: f3fdbaeddf49cdabe5b67a69f48f8af9176a33ebb2b90261b365a3e554bb199f
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