Details of the proof that
(14*10^6343-41)/99 is prime
may be found in

http://groups.yahoo.com/group/primeform/files/KP/hd6342kp.txt

Thanks to Jim Fougeron for showing the way,
with his BLS verification of the primality of
(17*10^4885-71)/99
first proven by Hans Rosenthal and Marcel Martin,
using the ECPP implementation Primo.

Also thanks to OpenPfgw and Marcel Martin for their
contributions to steps 1 and 2 of the present proof.
Step 3 was the use of the Konyagin-Pomerance cubic
given in Theorem 4.1.6 of the Crandall-Pomerance book,
"Prime Numbers: A Computational Perspective".

David Broadhurst