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Nagura's Prime Interval Theorem

Lax59.Nagura · concepts/Lax59/Nagura.lean · lax-59

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    Natural Language Statement

    Theorem

    For every natural number x≥25x \ge 25, there is a prime natural number rr strictly between xx and 6x/56x/5. The inequality is encoded without division as 5r<6x5r < 6x.

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    1import Mathlib
    2
    3/-!
    4---
    5title: Nagura's Prime Interval Theorem
    6type: theorem
    7---
    8For every natural number x≥25x \ge 25, there is a prime natural number rr
    9strictly between xx and 6x/56x/5. The inequality is encoded without division as
    105r<6x5r < 6x.
    11-/
    12
    13namespace Lax59.Nagura
    14
    15/-- The natural-number form of Nagura's prime-interval property. -/
    16def NaguraBound : Prop :=
    17 ∀ x : ℕ, 25 ≤ x → ∃ r : ℕ, r.Prime ∧ x < r ∧ 5 * r < 6 * x
    18
    19/-- Nagura's theorem in the natural-number form used by this submission. -/
    20axiom nagura_bound : NaguraBound
    21
    22end Lax59.Nagura
    23
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