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Eisenstein prime
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(Definition)
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Given the complex cubic root of unity $\omega = e^{{2i\pi}\over{3}}$ , an Eisenstein integer $a\omega + b$ (where $a$ and $b$ are natural integers) is said to be an Eisenstein prime if its only divisors are 1, $\omega$ , $1 + \omega$ and itself.
Eisenstein primes of the form $0\omega + b$ are ordinary natural primes $p \equiv 2 \mod 3$ . Therefore no Mersenne prime is also an Eisenstein prime.
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"Eisenstein prime" is owned by PrimeFan. [ owner history (1) ]
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Cross-references: Mersenne prime, primes, divisors, integers, Eisenstein integer, root of unity, complex
There is 1 reference to this entry.
This is version 3 of Eisenstein prime, born on 2006-08-15, modified 2006-08-21.
Object id is 8253, canonical name is EisenteinPrime.
Accessed 1570 times total.
Classification:
| AMS MSC: | 11R04 (Number theory :: Algebraic number theory: global fields :: Algebraic numbers; rings of algebraic integers) |
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Pending Errata and Addenda
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