Eisenstein prime

Given the complex cubic root of unityMathworldPlanetmath ω=e2iπ3, an Eisenstein integerMathworldPlanetmath aω+b (where a and b are natural integers) is said to be an Eisenstein primeMathworldPlanetmath if its only divisorsMathworldPlanetmathPlanetmath are 1, ω, 1+ω and itself.

Eisenstein primes of the form 0ω+b are ordinary natural primes p2mod3. Therefore no Mersenne primeMathworldPlanetmath is also an Eisenstein prime.

Title Eisenstein prime
Canonical name EisensteinPrime
Date of creation 2013-03-22 16:10:10
Last modified on 2013-03-22 16:10:10
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 6
Author PrimeFan (13766)
Entry type Definition
Classification msc 11R04
Related topic EisensteinIntegers