Theorems · Theorem · number theory
Nat.exists_prime_lt_and_le_two_mul_eventually
∀ (n : ℕ), 512 ≤ n → ∃ p, Nat.Prime p ∧ n < p ∧ p ≤ 2 * n
Proves that Bertrand's postulate holds for all sufficiently large n.
- Defined in
- Mathlib.NumberTheory.Bertrand
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- le_reflproof · cited by 2,061
- Nat.Primestatement and proof · cited by 2,059
- mul_assocproof · cited by 1,667
- le_transproof · cited by 985
- le_imp_le_of_le_of_leproof · cited by 576
- lt_of_lt_of_leproof · cited by 438
- mul_le_mul'proof · cited by 274
- Nat.centralBinomproof · cited by 24
- Nat.four_pow_lt_mul_centralBinomproof · cited by 2
- centralBinom_le_of_no_bertrand_primeproof · cited by 1
- bertrand_main_inequalityproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Nat.exists_prime_lt_and_le_two_mulproof · cited by 1