erdos_375.le_two

Specification

It is easy to see that for any `n ≥ 1` and `k ≤ 2`, if `n + 1, ..., n + k` are all composite, then there are distinct primes `p₁, ... pₖ` such that `pᵢ ∣ n + i` for all `1 ≤ i ≤ k`.

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Lean 4 Statement

theorem erdos_375.le_two : ∀ n ≥ 1, ∀ k ≤ 2, (∀ i < k, ¬ (n + i + 1).Prime) →
    ∃ p : Fin k → ℕ, p.Injective ∧ ∀ i, (p i).Prime ∧ p i ∣ n + i + 1

ID: ErdosProblems__375__erdos_375.le_two

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