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 conorms (PRPs)  highweight "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^n1") 
I think we can indeed extend the list of subprojects to include Gaussian Mersenne Norms and conorms and SophieGermain primes when p=k*2^n1 (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 sideprojects 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 Top5000 :sad: As for 4*3^n1 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^n1 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^n1 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^n1 tested till n=4M 
k=2 and k=4 @ base=3 tested till n=1.15M
127*128^n1 tested till n=4.05M 
[QUOTE=Cruelty;320163]k=2 and k=4 @ base=3 tested till n=1.15M
127*128^n1 tested till [COLOR="Red"][B]n=4.05M[/B][/COLOR][/QUOTE] My mistake: should be 127*128^n1 tested till [B]n=580k[/B] :smile: 
status report
k=2 and k=4 @ base=3 tested till n=1.17M
127*128^n1 tested till n=620k 
status report
k=2 and k=4 @ base=3 tested till n=1.17M
127*128^n1 tested till n=640k 
status report
k=2 and k=4 @ base=3 tested till n=1.18M
127*128^n1 tested till n=660k 
k=2 and k=4 @ base=3 tested till n=1.18M (I really need some non base 2 sieve software for GPU :smile: )
127*128^n1 tested till n=700k 
k=2 and k=4 @ base=3 tested till n=1.19M
127*128^n1 tested till n=715k 
status report
k=2 and k=4 @ base=3 tested till n=1.19M
127*128^n1 tested till n=725k 
k=2 and k=4 @ base=3 tested till n=1.2M
127*128^n1 tested till n=760k 
status report
k=2 and k=4 @ base=3 tested till n=1.21M
127*128^n1 tested till n=770k 
k=2 and k=4 @ base=3 tested till n=1.22M
127*128^n1 tested till n=780k 
I know it is little of topic but it looks like nobody search 2*7^n1 :)
It looks interesting :) 
k=2 and k=4 @ base=3 tested till n=1.24M
127*128^n1 tested till n=820k 
I've decided to move the discussion concerning GMs and GQs [URL="http://www.mersenneforum.org/showthread.php?t=19235"]here[/URL] :smile:
Meanwhile status of my other searches: k=2 and k=4 @ base=3 tested till n=1.24M 127*128^n1 tested till n=830k 
k=2 and k=4 @ base=3 tested till n=1.25M
127*128^n1 tested till n=850k 
status report
k=2 and k=4 @ base=3 tested till n=1.26M
127*128^n1 tested till n=880k 
status report
k=2 and k=4 @ base=3 tested till n=1.27M
127*128^n1 tested till n=890k 
status report
k=2 and k=4 @ base=3 tested till n=1.29M
127*128^n1 tested till n=920k 
status report
k=2 and k=4 @ base=3 tested till n=1.3M
127*128^n1 tested till n=930k 
status report
k=2 and k=4 @ base=3 tested till n=1.32M
127*128^n1 tested till n=950k 
I have some new cores for LLR use, and am again testing 127 actively. May I have a 56M file for 127 with your tests removed?
I had hoped to catch up to you by 6M, but I don't foresee pressing above 6M for quite some time and you are now well above 6M. 
[QUOTE=VBCurtis;391536]I have some new cores for LLR use, and am again testing 127 actively. May I have a 56M file for 127 with your tests removed?
I had hoped to catch up to you by 6M, but I don't foresee pressing above 6M for quite some time and you are now well above 6M.[/QUOTE] You've got mail :smile: 
Thank you!

status report
k=2 and k=4 @ base=3 tested till n=1.33M
127*128^n1 tested till n=970k 
k=2 and k=4 @ base=3 tested till n=1.34M
127*128^n1 tested till n=980k 
status report
k=2 and k=4 @ base=3 tested till n=1.35M
127*128^n1 tested till n=990k 
k=2 and k=4 @ base=3 tested till n=1.35M
127*128^n1 tested till n=1M 
status report
k=2 and k=4 @ base=3 tested till n=1.35M
127*128^n1 tested till n=1.01M 
status report
k=2 and k=4 @ base=3 tested till n=1.39M
127*128^n1 tested till n=1.05M 
k=2 and k=4 @ base=3 tested till n=1.42M
127*128^n1 tested till n=1.06M 
status report
k=2 and k=4 @ base=3 tested till n=1.43M
127*128^n1 tested till n=1.12M 
status report
k=2 and k=4 @ base=3 tested till n=1.45M
127*128^n1 tested till n=1.18M 
status report
k=2 and k=4 @ base=3 tested till n=1.47M
127*128^n1 tested till n=1.21M 
status report
k=2 and k=4 @ base=3 tested till n=1.48M
127*128^n1 tested till n=1.25M 
status report
k=2 and k=4 @ base=3 tested till n=1.49M
127*128^n1 tested till n=1.29M 
status report
k=2 and k=4 @ base=3 tested till n=1.51M
127*128^n1 tested till n=1.32M 
status report
k=2 and k=4 @ base=3 tested till n=1.53M
127*128^n1 tested till n=1.34M 
status report
k=2 and k=4 @ base=3 tested till n=1.54M
127*128^n1 tested till n=1.37M 
status report
k=2 and k=4 @ base=3 tested till n=1.55M
127*128^n1 tested till n=1.42M 
k=2 and k=4 @ base=3 tested till n=1.55M  doublechecking several ranges
127*128^n1 tested till n=1.46M 
status report
k=2 and k=4 @ base=3 tested till n=1.55M  doublechecking several ranges
127*128^n1 tested till n=1.5M 
status report
k=2 and k=4 @ base=3 tested till n=1.55M  doublechecking several ranges
127*128^n1 tested till n=1.51M 
1 Attachment(s)
To Cruelty:
You are tested for (b1)*b^n1, which is the Riesel problem for the special case, k=b1. According to the website [URL]http://harvey563.tripod.com/wills.txt[/URL], there are some large primes found: (up to base b=500, exponent > 1000) (381)*38^1362111 (this website wrongly writes the exponent as 136221) (831)*83^214951 (981)*98^49831 (1131)*113^2866431 (1251)*125^87391 (1881)*188^135071 (2281)*228^36951 (3471)*347^44611 (3571)*357^13191 (4011)*401^1036691 (4171)*417^210021 (4431)*443^16911 (4581)*458^468991 (4941)*494^215791 etc. The first few bases without known prime are 128, 233, 268, 293, 383, 478, 488, ..., I known that you only test base 128 because it is the first such base, but how about larger bases? How about (b1)*b^n+1, the Sierpinski problem for the same case, k=b1? Recently, I searched this form for bases b up to 500, but found no prime for b = 122, 123, 180, 202, 249, 251, 257, 269, 272, 297, 298, 326, 328, 342, 347, 362, 363, 419, 422, 438, 452, 455, 479, 487, 497, 498. Some terms are given by the CRUS project: [URL]http://www.noprimeleftbehind.net/crus/Sierpconjectures.htm[/URL]. Besides, how about (b+1)*b^n1 and (b+1)*b^n+1 (the Sierpinski/Riesel problem for k=b+1)? You only tests the case b=3. (Of course, for the case (b+1)*b^n+1, b should not = 1 (mod 3), or all the numbers of this form are divisible by 3 and cannot be prime) 
Indeed I am searching for those so called Williams Primes, already found some at base = 3 and one at base = 113. Currently I am focusing on base 128 and 3. I will consider next base after finding prime for b=128, so you're free to reserve any other base :smile: Just let know Steven Harvey about it.
I don't know whether someone is searching for similar primes on the "+" side however. 
Why you don't search (b1)*b^n+1? In [URL]http://oeis.org/A087139[/URL], someone is searching it for prime b, just as in [URL]http://oeis.org/A122396[/URL], someone is searching (b1)*b^n1 for prime b.
According to [URL]http://oeis.org/A087139[/URL], the b=251 case for (b1)*b^n+1 is searched to n=73000, no prime was found. However, there is also no known prime for bases b=122, 123, 180, 202, ..., why you don't search (b1)*b^n+1 for b=122? I searched (b1)*b^n+1 for all bases 2<=b<=500, but only tested n<=1024. (except of the primes (881)*88^3022+1 and (1581)*158^1620+1) Besides, you said "k=2 and k=4 @ base=3 tested ...", are you searching all of the four families? (31)*3^n1, (31)*3^n+1, (3+1)*3^n1, and (3+1)*3^n+1? 
status report
k=2 and k=4 @ base=3 tested till n=1.56M
127*128^n1 tested till n=1.53M Concerning my b=3 effort, I am posting this status in Riesel Prime Search, so I mean that I am working only on 2*3^n1 and 4*3^n1 :smile: 
status report
k=2 and k=4 @ base=3 tested till n=1.57M
127*128^n1 tested till n=1.57M 
status report
k=2 and k=4 @ base=3 tested till n=1.6M
127*128^n1 tested till n=1.59M 
status report
k=2 and k=4 @ base=3 tested till n=1.61M
127*128^n1 tested till n=1.6M 
I am almost to 6M on 127*2^n1. Might you prepare a 6M7M file for me with the tests you've run removed? If that's inconvenient, I'll settle for a results file of your tests from 6M to 7M.

[QUOTE=VBCurtis;458080]I am almost to 6M on 127*2^n1. Might you prepare a 6M7M file for me with the tests you've run removed? If that's inconvenient, I'll settle for a results file of your tests from 6M to 7M.[/QUOTE]
Even before reaching 6M, by knowing that Borys already searched for these 127*2^(7*n)1 (reaching at least 7*n <= 11,200,000), you could simply remove all n :: 7n from your candidate list. 
status report
k=2 and k=4 @ base=3 tested till n=1.63M
127*128^n1 tested till n=1.66M 
status report
k=2 and k=4 @ base=3 tested till n=1.66M
127*128^n1 tested till n=1.71M (sieving) 
status report
k=2 and k=4 @ base=3 tested till n=1.67M
127*128^n1 tested till n=1.72M 
status report
k=2 and k=4 @ base=3 tested till n=1.68M
127*128^n1 tested till n=1.73M 
Please see the project [URL="http://mersenneforum.org/showthread.php?t=21818&page=6"]http://mersenneforum.org/showthread.php?t=21818&page=6[/URL] for the primes of the form (b+1)*b^n+1 and (probable) primes of the form b^n+(b+1). (b^n+(b+1) is the dual of (b+1)*b^n+1) I have searched these forms for all bases 2<=b<=1024.

status report
k=2 and k=4 @ base=3 tested till n=1.69M
127*128^n1 tested till n=1.74M 
[QUOTE=Cruelty;479098]k=2 and k=4 @ base=3 tested till n=1.69M
127*128^n1 tested till n=1.74M[/QUOTE] You can update the primes of the form (b+1)*b^n+1 and the test limits in the page [URL="http://www.mersennewiki.org/index.php/Williams_prime"]http://www.mersennewiki.org/index.php/Williams_prime[/URL]. 
[QUOTE=Batalov;458092]Even before reaching 6M, by knowing that Borys already searched for these 127*2^(7*n)1 (reaching at least 7*n <= 11,200,000), you could simply remove all n :: 7n from your candidate list.[/QUOTE]
I'm ready to search 78M, and may as well learn how to remove such candidates myself. How would I go about removing such n in a nonmanual fashion? 
status report
k=2 and k=4 @ base=3 tested till n=1.72M
127*128^n1 tested till n=1.8M 
status report
k=2 and k=4 @ base=3 tested till n=1.76M
127*128^n1 tested till n=1.86M 
status report
k=2 and k=4 @ base=3 tested till n=1.78M
127*128^n1 tested till n=1.88M 
status report
k=2 and k=4 @ base=3 tested till n=1.8M
127*128^n1 tested till n=1.88M 
status report
k=2 and k=4 @ base=3 tested till n=1.81M
127*128^n1 tested till n=1.93M 
status report
k=2 and k=4 @ base=3 tested till n=1.84M
127*128^n1 tested till n=1.95M 
Made pages for [url='https://www.rieselprime.de/ziki/Williams_prime_MM_3']2*3^n1[/url] and [url='https://www.rieselprime.de/ziki/Williams_prime_PM_3']4*3^n1[/url] in the PrimeWiki, S.Harvey is aware of these, too.
For k=4 I've not included n=0 as in the OEISentry. 
status report
k=2 and k=4 @ base=3 tested till n=1.93M
127*128^n1 tested till n=2.07M 
status report
k=2 and k=4 @ base=3 tested till n=1.94M
127*128^n1 tested till n=2.08M 
status report
k=2 and k=4 @ base=3 tested till n=2M (sieving)
127*128^n1 tested till n=2.15M 
status report
k=2 and k=4 @ base=3 tested till n=2M (sieving)
127*128^n1 tested till n=2.22M 
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