Theorems · Theorem · number theory
isPrimePow_nat_iff_bounded_log
∀ (n : ℕ), IsPrimePow n ↔ ∃ k ≤ Nat.log 2 n, 0 < k ∧ ∃ p ≤ n, n = p ^ k ∧ Nat.Prime p
- Defined in
- Mathlib.Algebra.IsPrimePow
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.Primestatement and proof · cited by 2,059
- Nat.logstatement and proof · cited by 101
- IsPrimePowstatement · cited by 77
- Nat.Prime.two_leproof · cited by 53
- isPrimePow_nat_iffproof · cited by 9
- Nat.AtLeastTwo.propproof · cited by 9
- Nat.log_powproof · cited by 4
- Nat.log_monoproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- isPrimePow_nat_iff_bounded_log_minFacproof · cited by 2