$a(n) = (\text{smallest prime} > n^2) - n^2$

formal-conjectures · oeis · ams-11

The difference between the smallest prime strictly greater than $n^2$ and $n^2$.

Conjecture: $a(n) \le 1 + \phi(n)$ for $n > 0$. This improves on Oppermann's conjecture, which says
$a(n) < n$.
- Thomas Ordowski, Dec 17 2014

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/A053000
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/53000.lean
Local target: Corpus.OEIS53000.conjecture
Source SHA-256: c49c847965c1d720f99a29cdb96b7d0fe37562df05aa2d0a26427bffea3de342
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