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This is the Prime Pages'
interface to our BibTeX database. Rather than being an exhaustive database,
it just lists the references we cite on these pages. Please let me know of any errors you notice.References: [ Home  Author index  Key index  Search ]
 PH2002
 Perschell, Karaloine and Huff, Loran, "Mersenne primes in imaginary quadratic number fields," (2002) avaliable from http://www.utm.edu/staff/caldwell/preprints/kpp/Paper2.pdf.
Abstract:
We examine all primes of the form b^{n}1 in imaginary quadratic number fields, noting that besides a finite list of specific prime numbers, we find only three interesting classes of primes. Using the rational Mersenne primes (the first of the three cases) as a model, we follow Robert Spira and Mike Oakes in defining the Gaussian Mersenne primes to be the primes of the form (1±)^{p}1 and the Eisenstein Mersenne primes to be the primes of the form ((3± sqrt(3) /2)^{p}1. We show how to characterize these via their norms, list the known examples and speculate on their distributions.
