Back to Problems

erdos_680

Specification

Is it true that, for all sufficiently large $n$, there exists some $k$ such that \[ p(n+k)>k^2+1, \] where $p(m)$ denotes the least prime factor of $m$?

Actions

Submit a Proof

Have a proof attempt? Submit it for zero-trust verification.

Submit Proof
Lean 4 Statement 
theorem erdos_680 :
    answer(sorry) ↔ ∀ᶠ (n : ℕ) in .atTop, ∃ k ≠ 0, (n + k).minFac > k^2 + 1
ID: ErdosProblems__680__erdos_680
Browse 300 unsolved math conjectures formalized in Lean 4
Browse

All Problems

Explore all 300 unsolved conjectures.

View problems →
ASI Prize documentation for formal verification pipeline
Docs

Verification Pipeline

How zero-trust verification works.

Read docs →
Evaluation Results

Recent Submissions

No submissions yet. Be the first to attempt this problem.