## Eisenstein Prime

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.