Let be the Cube Root of unity . Then the Eisenstein primes are

- 1. Ordinary Primes Congruent to 2 (mod 3),
- 2. is prime in ,
- 3. Any ordinary Prime Congruent to 1 (mod 3) factors as , where each of and are primes in and and are not ``associates'' of each other (where associates are equivalent modulo multiplication by an Eisenstein Unit).

**References**

Cox, D. A. §4A in *Primes of the Form : Fermat, Class Field Theory and Complex Multiplication.*
New York: Wiley, 1989.

Guy, R. K. ``Gaussian Primes. Eisenstein-Jacobi Primes.'' §A16 in
*Unsolved Problems in Number Theory, 2nd ed.* New York: Springer-Verlag, pp. 33-36, 1994.

Wagon, S. ``Eisenstein Primes.'' *Mathematica in Action.* New York: W. H. Freeman, pp. 278-279, 1991.

© 1996-9

1999-05-25