Gaussian Integers (A057429)

[Hans Havermann]

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