Erdős Problem 889

formal-conjectures · erdos-problems · ams-11

Let $v(n,k)$ count the prime factors of $n+k$ which
do not divide $n+i$ for $0\leq i < k$. Is it true that
$v_0(n)=\max_{k\geq 0}v(n,k)\to \infty$ as $n\to \infty$?

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://www.erdosproblems.com/889
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/ErdosProblems/889.lean
Local target: Corpus.Erdos889.erdos_889
Source SHA-256: 868092ba74cc6adda7dfa309fbb56fdffcf0e6025a6e59327f263db12a8665a0
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