Theorems · Theorem · number theory
Nat.prime_def
∀ {p : ℕ}, Nat.Prime p ↔ 2 ≤ p ∧ ∀ (m : ℕ), m ∣ p → m = 1 ∨ m = pNat.Prime p means that p is a prime number, that is, a natural number
at least 2 whose only divisors are p and 1.
The theorem Nat.prime_def witnesses this description of a prime number.
- Defined in
- Mathlib.Data.Nat.Prime.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- Nat.Primestatement and proof · cited by 2,059
- LT.lt.ne'proof · cited by 1,417
- LT.lt.trans_leproof · cited by 678
- dvd_mul_rightproof · cited by 89
- mul_right_inj'proof · cited by 56
- Nat.Prime.two_leproof · cited by 53
- Nat.Prime.eq_one_or_self_of_dvdproof · cited by 11
- Nat.isUnit_iffproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- Nat.prime_def_ltproof · cited by 3
- CharP.char_is_prime_of_two_leproof · cited by 1
- Nat.prime_of_pow_sub_one_primeproof · cited by 1