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Lax242665.OddPrimeBetween

An odd prime between n and 2n

concepts/Lax242665/OddPrimeBetween.lean · lax-242665

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    Theorem

    For every natural number n≥2n \geq 2 there is an odd prime number pp with n<p≤2nn < p \leq 2n.

    Lean source view on GitHub

    1import Mathlib.Algebra.Ring.Parity
    2import Lax242665.Primes
    3
    4/-!
    5---
    6title: An odd prime between n and 2n
    7type: theorem
    8---
    9For every natural number n≥2n \geq 2 there is an odd prime number pp with
    10n<p≤2nn < p \leq 2n.
    11-/
    12
    13namespace Lax242665.OddPrimeBetween
    14
    15/-- For every `n ≥ 2` there is an odd prime `p` with `n < p ≤ 2n`. -/
    16axiom exists_odd_prime_between :
    17 ∀ n : ℕ, 2 ≤ n → ∃ p : ℕ, Primes.Prime p ∧ Odd p ∧ n < p ∧ p ≤ 2 * n
    18
    19end Lax242665.OddPrimeBetween
    20
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