From mihailes@inf.ethz.ch Wed Jan 28 15:29:26 1998
Date: Wed, 28 Jan 1998 08:56:14 -0500
From: Preda Mihailescu <mihailes@inf.ethz.ch>
To: NMBRTHRY@LISTSERV.NODAK.EDU
Subject: New Wagstaff prime proved

I have the pleasure to announce the completion of the primality proof
for the Wagstaff prime N=(2^11279+1)/3. The proof was performed using
cyclotomy.  This is an example of "good cooperation" between Jacobi -
Sum and Lucas - Lehmer tests: about 600 digits of factors of N+/-1
could be collected from Cunningham tables and additional Cunningham
factorizations performed by myself. This ammounted to about 40% of the
required factored part, the rest being provided, as usual, by Jacobi -
Sums.

The factoring (ecm, LiDIA) took roughly two days and revealed
following new Cunningham factorization:

2,1253+
[(32579,1)(12479881,1)(4480918457,1)(4059601388172111433,1)(63642650836610
8334471074209986972008436874291945998377361825843169581006681193485334938756
7397046206419273268435035021893288365929329769323908169149982883100332056432
2788509598079553928417442558321884657690102185988492660333818386898831258604
4638709585024638281660169598101448280761,1)]

The proof process itself was often interrupted or delayed due to
intense work on our institute's machine. It eventually completed
yesterday, adding up to 157 hours of CPU time ( 6 1/2 days).

The proof for N=(2^14479+1)/3 will follow according to machine
disponibilites.


Preda Mihailescu