Lax Lean Archive

The twin prime conjecture

Lax242665.TwinPrimes · concepts/Lax242665/TwinPrimes.lean · lax-242665

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    Natural Language Statement

    Conjecture

    For every natural number nn there is a prime number p>np > n such that p+2p + 2 is prime as well.

    Concept map
    2 concepts
    100%
    Open claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

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    In the paper

    • page 2 of this submission's paper

    Lean source view on GitHub

    1import Lax242665.Primes
    2
    3/-!
    4---
    5title: The twin prime conjecture
    6type: conjecture
    7---
    8For every natural number nn there is a prime number p>np > n such that
    9p+2p + 2 is prime as well.
    10-/
    11
    12namespace Lax242665.TwinPrimes
    13
    14/-- Beyond every natural number `n` lies a prime `p` with `p + 2` prime as
    15well. -/
    16axiom exists_twin_prime_gt :
    17 ∀ n : ℕ, ∃ p : ℕ, Primes.Prime p ∧ Primes.Prime (p + 2) ∧ n < p
    18
    19end Lax242665.TwinPrimes
    20
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