An Eisenstein prime is an Eisenstein integer aω + b that has only two Eisenstein divisors, the complex cube root of unity and aω + b itself. In mathematics, Eisenstein integers are complex numbers of the form aω + b where ω is a complex cube root of unity, and a and b are rational integers. ...

Cox and Wagon proved that besides 1 - ω, there are only three kinds of Eisenstein primes:

1. aω + b such that a² − ab + b² is a natural prime number of the form 3n + 1.

1. aω² + b such that a² − ab + b² is a natural prime number of the form 3n + 1.

1. aω + b where a = 0 (and thus there is no imaginary part) and b is a natural prime number of the form 3n − 1.

Therefore, this last kind of Eisenstein prime is also a kind of natural prime. The first few Eisenstein primes of this form are: In mathematics, a prime number (or prime) is a natural number greater than one whose only positive divisors are one and itself. ...

2, 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101 For the Austin Powers character, see Number 2(Austin Powers 2 (two) is a number, numeral, and glyph. ... 5 (five) is the natural number following 4 and preceding 6. ... 11 (number) - Wikipedia, the free encyclopedia /**/ @import /skins-1. ... 17 (seventeen) is the natural number following 16 and preceding 18. ... 23 (twenty-three) is the natural number following 22 and preceding 24. ... 29 (twenty-nine) is the natural number following 28 and preceding 30. ... 41 is the natural number following 40 and preceding 42. ... 47 is the natural number following 46 and followed by 48. ... 53 is the natural number following 52 and preceding 54. ... 59 is the natural number following 58 and preceding 60. ... 71 is the natural number following 70 and preceding 72. ... 83 is the natural number following 82 and preceding 84. ... 89 is the natural number following 88 and preceding 90. ... 101 (one hundred [and] one) is the natural number following 100 and preceding 102. ...

which are listed in Sloane's A003627.