Is it true that for all large $n$ there exists $k$ such that $n + k$ is composite and $p (n + k) > k^{2},$ where $p (m)$ is the least prime factor of $m$ ?

Worked, still open.

number theory · open · formalized (Lean) · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

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unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

In fact, your exact question appears as **Erdős Problem #681** and is listed as **OPEN**:

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

AMS 11 · open (literature)

theorem erdos_681 : answer(sorry) ↔
    ∀ᶠ n in .atTop, ∃ k > 0, (n + k).Composite ∧ ∀ p, IsLPF p (n + k) → p > k ^ 2

open