Announcement to be linked from the e-group bio.

32476090*C(1531785651*2^10110+18,23)-1 is prime.
C(x,y) = x!/((x-y)!*y!) is the binomial function.

In 2001 Michael Angel, Dirk Augustin, Paul Jobling's NewPGen,
Paul Jobling, Yves Gallot's Proth.exe found this CC3 of the 2nd kind:
p = 1531785651*2^10107+1, 2p-1, 4p-3
Let N = 8*(p-1) = 1531785651*2^10110.
The CC3 gives all factors of N, N+2, N+4, N+8.

Jens Kruse Andersen used GMP-ECM to find 3 further complete
factorizations with these prp's:
(N-4)/(2^2*5*7*31237*286235451569*11609891459483469679)
(N+5)/(47*2087*240631)
(N+15)/(3*6343*1655652931*1809537707*376766311088897*7992061535285413)

They were proved prime with Marcel Martin's Primo by Luigi Morelli,
V. M. Ulyanov and Pierre Cami. The 3 verified certificates are in
http://hjem.get2net.dk/carlkruse/certif/kc23.zip

Andersen sieved k*C(N+18,23)-1 to 5*10^11.
Andersen, Morelli, Ulyanov, Cami and Décio Luiz Gazzoni Filho made
Fermat prp tests with PrimeForm/GW. Cami found a prp with k=32476090.

There is a little more than 30% factorization of C(N+18,23).
This is insufficient for a BLS primality proof by PrimeForm.
David Broadhurst made a Konyagin-Pomerance proof:
http://physics.open.ac.uk/~dbroadhu/cert/kc23c.zip

This was a PrimeForm e-group project:
http://primes.utm.edu/bios/page.php?id=339

--
Jens Kruse Andersen