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.

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