Re: [primeform] 32476090*binomial(1531785651*2^10110+18,23)-1
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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:
They were proved prime with Marcel Martin's Primo by Luigi Morelli,
V. M. Ulyanov and Pierre Cami. The 3 verified certificates are in
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:
This was a PrimeForm e-group project:
Jens Kruse Andersen