Product of composite numbers in triangular intervals

formal-conjectures · oeis · ams-11

Product of all composite numbers between $n(n-1)/2+1$ and $n(n+1)/2$ (including boundaries),
where $n(n-1)/2 = \binom{n}{2}$ and $n(n+1)/2 = \binom{n+1}{2}$.

Conjecture: There are finitely many numbers such that $a(n)$ is not $\equiv 0 \pmod{a(n-1)}$.
(Also mentioned in A093455.)

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/A093456
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/93456.lean
Local target: Corpus.OEIS93456.conjecture
Source SHA-256: 1fd85ae690d237a5122757634549db75d53ab8a4c43b02e2d335af50e5d87f5a
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