page_title: Eisenstein prime
hierarchical_section_title: Eisenstein prime
context_page_description: In mathematics, an Eisenstein prime is an Eisenstein integer
  that is irreducible in the ring-theoretic sense: its only Eisenstein divisors are the units {±1, ±ω, ±ω²}, a + bω itself and its associates.
  The associates and the complex conjugate of any Eisenstein prime are also prime.
context_section_description: In mathematics, an Eisenstein prime is an Eisenstein integer
  that is irreducible (or equivalently prime) in the ring-theoretic sense: its only Eisenstein divisors are the units {±1, ±ω, ±ω²}, a + bω itself and its associates.
  The associates (unit multiples) and the complex conjugate of any Eisenstein prime are also prime.
caption: Small Eisenstein primes. Those on the green axes are associate to a natural prime of the form 3n − 1. All others have an absolute value squared equal to a natural prime.