Problem NT-003 — the twin prime conjecture

Conjectura.Problems.NT003.Statement

/-
Copyright (c) 2026 The Conjectura Authors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: The Conjectura Authors
-/
import Conjectura.Defs.Mathematics.NumberTheory.TwinPrimePair

/-! # Problem NT-003 — the twin prime conjecture

LOCKED: solvers cannot modify this file.
-/

namespace Conjectura.NT003

/-- Are there infinitely many pairs of primes differing by two? -/
def goal : Prop :=
  ∀ N : ℕ, ∃ p : ℕ, N < p ∧ Conjectura.NumberTheory.IsTwinPrimePair p (p + 2)

end Conjectura.NT003