Smallest prime formed by concatenation $n, n-1, \dots, n-k$

formal-conjectures · oeis · ams-11

$a(n)$ is the smallest prime which has the form of the concatenation
$n, n-1, n-2, \dots, n-k$ for some $k < n$, or $0$ if no such prime exists.

Conjecture: There are infinitely many composite numbers $n$ such that $a(n)$ is nonzero.

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/A087571
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/87571.lean
Local target: Corpus.OEIS87571.conjecture
Source SHA-256: 10af71953107cb47fe8462dc72416f4821cf10c593fcffc504b90f770228d004
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