Prime gaps

formal-conjectures · oeis · ams-11

Differences between consecutive primes: $a(n) = p_{n+1} - p_n$.

Any subsequence a(n .. n+m) with n > 2 (as to exclude the
untypical primes 2 and 3) should occur infinitely many times at other starting points k.

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/A001223
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/1223.lean
Local target: Corpus.OEIS1223.conjecture
Source SHA-256: ca8e0d6f33761af5a8d5ce754ff16e342362011d1a29f0d6975e20905b7378b0
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