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Lax242665.BertrandPostulate

Bertrand's postulate

concepts/Lax242665/BertrandPostulate.lean · lax-242665

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    Lemma

    For every natural number n≥1n \geq 1 there is a prime number pp with n<p≤2nn < p \leq 2n.

    Lean source view on GitHub

    1import Lax242665.Primes
    2
    3/-!
    4---
    5title: Bertrand's postulate
    6type: lemma
    7---
    8For every natural number n≥1n \geq 1 there is a prime number pp with
    9n<p≤2nn < p \leq 2n.
    10-/
    11
    12namespace Lax242665.BertrandPostulate
    13
    14/-- For every `n ≥ 1` there is a prime `p` with `n < p ≤ 2n`. -/
    15axiom exists_prime_between :
    16 ∀ n : ℕ, 1 ≤ n → ∃ p : ℕ, Primes.Prime p ∧ n < p ∧ p ≤ 2 * n
    17
    18end Lax242665.BertrandPostulate
    19

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