Let $2 = p_{1} < p_{2} < \dots$ be the primes and $k \geq 2$ . Is it true that, for all sufficiently large $n$ , there must exist an integer in $[n, n + p_{1} \dots p_{k})$ with $> k$ many prime factors?

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

It depends on what you mean by “(>k) prime factors”.

llm-hunter · gpt pro 5.2 · unverified

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

AMS 11 · open (literature)

theorem erdos_891 :
    answer(sorry) ↔
      ∀ k ≥ 2, ∀ᶠ n in atTop,
      ∃ m ∈ Ico n (n + ∏ i ∈ range k, i.nth Nat.Prime), k < ω m

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