Hello,
Updating the database of factors of 10^n +/- 1 located in the files
area of the Primefactors group reminded me that the palindrome
N=3D(34*10^15768-43)/9 still hasn't been proven prime. Even though it's
no longer even close to a record for the largest palindromic prime
with prime digits, I think it's worthwhile doing for completeness.
Since 10^15768-1 is 27% factored, this is now possible with the new
CHG code of John Renze and David Broadhurst. I proceeded as follows:
1. I extracted all of the PRP factors of 10^15768-1 from the
database, added the factors of 34 and removed 9 of course, and proved
all but one of them prime using VFYPR.
2. I performed the BLS tests using PFGW using these prime factors in
a helper file.
3. I created a CHG input file and started the code running. I had to
adjust the precision a couple of times to avoid errors, and it appears
\p9000 worked. The search for factors congruent to 1 completed
overnight on my Opteron. Since F=1 in this case, the search for
factors congruent to n is unnecessary, so a certificate was output. I
think there is a bug in the code, however, since at this point it
began a search for factors congruent to n. It also claimed to have
run David's verifier on the certificate, but since I don't have the
verifier, it could not have.
So, at this point, there is one missing bit. The primality of the
2454-digit PRP
Phi(7884,10)/(3951358309*43519681*11668781326071061*50594869824289387600141*
698321409620914728282889*10226827901261393154083521*2768214255974519676483980192126941)
remains to be proven. This is where I need help. Primo would make
easy, if time consuming, work of this, but since I'm in the US, the
Primo license prohibits me from using it. Could someone outside of
the US, Canada, and Japan prove the primality of this number?
It would also be nice for someone (David?) to independently verify the
CHG certificate. It can be downloaded from
http://www.pa.uky.edu/~childers/certs/P15769.zip
Thanks,
Greg