FormalConjectures.Wikipedia.PrimeTriplets

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import FormalConjecturesUtil

Prime Triplet Conjecture

Reference: Prime Triplet Wikipedia Page


namespace PrimeTriplets

Are there infinitely many tuples of three consecutive primes $(p, q, r)$ such that $r - p = 6$?

@[category research open, AMS 11]
theorem declaration uses 'sorry'prime_triplets :
    answer(sorry) ↔ {p : ℕ | Prime p ∧ (Prime (p + 2) ∨ Prime (p + 4)) ∧ Prime (p + 6)}.Infinite := by⊢ True ↔ {p | Prime p ∧ (Prime (p + 2) ∨ Prime (p + 4)) ∧ Prime (p + 6)}.Infinite
  sorryAll goals completed! 🐙


end PrimeTriplets