Quote:
Originally Posted by jshort
Fyi  I personally used the Pollardrho algorithm with the iterating function to weed out many composites
Alternatively, the p1 test could be used instead to weed out composites. I'm not sure which of the two would be more efficient tbh (if anyone knows the answer to this, that'd be awesome!).

In additional to what UTM's (and Mathworld's iirc has one) comprehensive pages says, quick note: Gaussian Mersenne norms share many similarities to Mersenne numbers. In particular,
* n needs to be prime  why? because otherwise there is an algebraic factorization. (And in the algebraic factorization you will find both + and  forms)
* Any factor (except 5 which is intrinsic) is of form
2 * k * p + 1, so trial factoring is simplified but is very similar to Mersenne project: you don't sieve databasewide  you prefactor each candidate. Furthermore, just like factors of Mersenne composites, these will not share the same factors (except the trivial case when one divides the other).
...that's just a few quick thoughts is a spare time during lunch break.
P.S. All primes of this form at this time are known  loosely speaking to the limit of p < 10,000,000. So searching below this limit will not bring too much joy to the searcher.