Smallest composite $c$ such that $\textrm{primorial}(n) + c$ is prime

formal-conjectures · oeis · ams-11

Conjecture:
$\liminf_{n \to \infty} \frac{a(n)}{p_{n+1}^2} = 1 <$
$\limsup_{n \to \infty} \frac{a(n)}{p_{n+1}^2} = 2$.
- Charles R Greathouse IV and Thomas Ordowski, Apr 24 2015

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/A038771
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/38771.lean
Local target: Corpus.OEIS38771.conjecture1
Source SHA-256: 104af83255a4e4ff1206b76906434c8fa2e2bb3dfd300ac4511552eca9f864f3
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