New Subprojects
 

The real question as I would imagine is: can someone post primes that do not fit into one of the three subprojects defined on [URL="http://primes.utm.edu/bios/page.php?id=819"]RPS project page[/URL]?
Another, similar question: can we extend the list of subprojects?
Some candidates that come to my mind include:
- Gaussian Mersenne Norms and co-norms (PRPs)
- high-weight "k" proth primes (as suggested by Roger)
- some other ideas developed by participating individuals (e.g. I am working right now on primes of the form "4*3^n-1")

I think we can indeed extend the list of sub-projects to include Gaussian Mersenne Norms and co-norms and Sophie-Germain primes when p=k*2^n-1 (but excluding p=k*2^n+1) where p is the smaller prime of the Sophie Germain pair.

I'd like to suggest that we resist the temptation of adding high weight Proth primes, k*2^n+1, because one has to stop somewhere :smile: Of course everybody is free to pursue other side-projects unrelated to RPS. Specifically, for high weight Proth primes there is a project started by Robert and Phil Carmody where I took part for a while but currently it has no primes in the Top-5000 :sad:

As for 4*3^n-1 note that prof. Iskra (whom I think you already "met") developed his own method but I think it works only for 4*3^n+1 and he already reported tens of primes of that form.

Cruelty
 

I just created a new thread to discuss new subprojects.

If you agree I'd like to suggest that you lead the GM/GQ efforts.

Can you tell us for the beginning the status of the search, and what software is required to search for such primes/PRPs. I beleive LLR alone is enough but it has to be one of the latest versions. Is that right?

Info on some illustrative exe times will be appreciated as well.

status report
 

k=2 and k=4 @ base=3 tested till n=1.13M
112*113^n-1 tested till n=240k (looking for the first [URL="http://harvey563.tripod.com/wills.txt"]Williams prime[/URL] for this base)

k=2 and k=4 @ base=3 tested till n=1.14M
112*113^n-1 tested till n=280k

Status report
 

I release 112*113[SUP]n[/SUP]-1 @ n=290k.

status report
 

k=2 and k=4 @ base=3 tested till n=1.15M
127*128^n-1 tested till n=4M

k=2 and k=4 @ base=3 tested till n=1.15M
127*128^n-1 tested till n=4.05M

[QUOTE=Cruelty;320163]k=2 and k=4 @ base=3 tested till n=1.15M
127*128^n-1 tested till [COLOR="Red"][B]n=4.05M[/B][/COLOR][/QUOTE]

My mistake: should be 127*128^n-1 tested till [B]n=580k[/B] :smile:

status report
 

k=2 and k=4 @ base=3 tested till n=1.17M
127*128^n-1 tested till n=620k

status report
 

k=2 and k=4 @ base=3 tested till n=1.17M
127*128^n-1 tested till n=640k