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Lax242665.InfinitelyManyPrimes

There are infinitely many primes

concepts/Lax242665/InfinitelyManyPrimes.lean · lax-242665

proven

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    Theorem

    For every natural number nn there is a prime number p>np > n.

    Lean source view on GitHub

    1import Lax242665.Primes
    2
    3/-!
    4---
    5title: There are infinitely many primes
    6type: theorem
    7---
    8For every natural number nn there is a prime number p>np > n.
    9-/
    10
    11namespace Lax242665.InfinitelyManyPrimes
    12
    13/-- Beyond every natural number `n` lies a prime `p`. -/
    14axiom exists_prime_gt : ∀ n : ℕ, ∃ p : ℕ, Primes.Prime p ∧ n < p
    15
    16end Lax242665.InfinitelyManyPrimes
    17
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