( ∃ a ) a p − 1 2 ≡ − 1 ( mod p ) ⇒ p is prime
( ∀ p ∈ ℤ + ) ( ∃ a , k , n ) p = k ⋅ 2 n + 1 ∧ k ∤ 2 ∧ k < 2 n ∧ a k 2 n − 1 ≡ − 1 ( mod p ) ⇒ p is prime
Proth's theorem
primality test for Proth numbers
mathematischer Satz