Ternary arithmetic, factorization, and the class number one problem

Ordinary multiplication of natural numbers can be generalized to a ternary operation by considering discrete volumes lattice hexagons. With this operation, notion ‘3-primality’ -primality with respect multiplication- is defined, and it turns out that there are very few 3-primes. They correspond imaginary quadratic fields Q(√-n), n > 0, odd discriminant whose ring integers admits unique factorization. We also describe how determine representations as products related algorithms for usual primality testing integer