Gaussian Integers (A057429)
Franklin T. Adams-Watters
franktaw at netscape.net
Tue Feb 1 04:15:13 CET 2005
Hans Havermann <pxp at rogers.com> wrote:
>sven-h.simon:
>
>> I found another interesting article about 'Mersenne Primes In Imaginary
>> Quadratic Number Fields' with Google. There are numbers (1+i)**n-1,
>> which are
>> Gaussian primes. n has to be prime. The sequence in OEIS is A057429,
>> found by
>> Mike Oakes and others.
>
>> Sequence:
>> 2,3,5,7,11,19,29,47,73,79,113,151,157,163,167,239,241,283,...
>> Name: Gaussian-Mersenne primes: (1+i)^n - 1 times its conjugate
>> is prime.
>> Comments: Equivalently, (1+i)^n - 1 is a Gaussian prime.
>
>Does the comment, I wonder, require a small caveat because (1+i)^4 - 1
>is a Gaussian prime?
>
>PrimeQ[(1 + I)^4 - 1]
>True
Ah, but (1+i)^4 - 1 = -5, which is an *integer* prime, but *not* a Gaussian prime.
--
Franklin T. Adams-Watters
16 W. Michigan Ave.
Palatine, IL 60067
847-776-7645
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