FormalConjectures.ErdosProblems.«203»

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import FormalConjecturesUtil

Erdős Problem 203

Reference: erdosproblems.com/203


namespace Erdos203

Is there an integer $m$ with $(m, 6) = 1$ such that none of $2^k \cdot 3^\ell \cdot m + 1$ are prime, for any $k, \ell \ge 0$?

@[category research open, AMS 5]
theorem declaration uses 'sorry'erdos_203 : answer(sorry) ↔ ∃ m, m.Coprime 6 ∧ ∀ k l, ¬ (2^k * 3^l * m + 1).Prime := by⊢ True ↔ ∃ m, m.Coprime 6 ∧ ∀ (k l : ℕ), ¬Nat.Prime (2 ^ k * 3 ^ l * m + 1)
  sorryAll goals completed! 🐙


-- TODO(rdivyanshu): add statements about covering system and odd integers `m` such that none of 2^k*m + 1 is prime

end Erdos203