- From: Jens Franke (Tuesday, December 11, 2012 4:58 AM)

We have confirmed the primality of the Leyland numbers 3110^63+63^3110

(5596 digits) and 8656^2929+2929^8656 (30008 digits) by an implementation of a version of Mihailescu's CIDE. The certificates may be found at

http://www.math.uni-bonn.de:people/franke/ptest/x3110y63.cert.tar.bz2

and

http://www.math.uni-bonn.de:people/franke/ptest/x8656y2929.cert.tar.bz2 ,

a description of their format together with proofs of the underlying mathematical statements is at

http://www.math.uni-bonn.de:people/franke/ptest/fmt-0.1.pdf .

Tables of powers of Gauss sums used by the certificates are at

http://www.math.uni-bonn.de:people/franke/Gspk.tar.bz2 .

Calculations were carried out using resources at the Hausdorff Center for Mathematics (http://www.hausdorff-center.uni-bonn.de), the Institute for Numerical Simulation (http://www.ins.uni-bonn.de/institut/), and LACAL (http://lacal.epfl.ch )

J. Franke, T. Kleinjung, A. Decker, J. Ecknig, A. Großwendt - --- On Wed, 12/12/12, djbroadhurst wrote:
> --- In primenumbers@yahoogroups.com "thefatphil" <thefatphil@...> wrote:

Thanks to my NMBRTHRY posting, I've ended up in a delightful off-list chat with Preda himself, in which he has leaked the info that his CycloProv did indeed have the earliest seeds of CIDE within it, amongst other little nuggets.

> > > Here is Preda's method for cyclotomic numbers:

> > > http://arxiv.org/pdf/0709.4113v1.pdf

> >

> > How does that relate to:

> > Dual Elliptic Primes and Cyclotomy Primality Proving

> > Preda Mihailescu and Francois Morain

> > Which I downloaded as 10.1.1.29.6756.pdf from goodness-knows-where

>

> That 1999 conference report may be obtained from

>

> http://130.203.133.150/viewdoc/download?doi=10.1.1.29.6756&rep=rep1&type=pdf

>

> As Phil has noted, the single-author paper of 2007

> makes no reference to it, which seems a little odd.

There's definitely an interesting future for this algorithm...

Phil

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