It is well known that for any prime number p the integers {2,3,4,...p-2} group into pairs (called "inverse pairs" or "modular inverses") for which the product of each pair is ≡ +1 (mod p). In a similarly way they also form pairs (we call "anti-inverses") such that the product is ≡ −1 (mod p). Further, we find that for all primes that are ≡ +1 (mod 4) there are two and only two integers a and b ∈ {2, 3, 4, ...p − 2} which are self-anti-inverse, i.e. a 2 ≡ b 2 ≡ −1 (mod p). These serve as self-anti-inverses uniquely to a single p. Deeper investigation of these primes and their self-anti-inverses reveals a triplet of integers (K ab , Ka, K b) from which p, a and b can be generated. Two prime-generating algorithms, one based on the self-anti-inverses, and one based on the triplet of K's, are described
