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 gd_barnes 2007-12-14 19:45

With this effort, we aim to prove many of the Riesel and Sierpinski conjectures for bases <= 1030 that are not currently being worked on by other projects or efforts.

Project definition:
For every base (b) for the forms k*b^n+1 and k*b^n-1, there exists a k-value for each form that has been conjectured to be the lowest 'Sierpinski value' (+1 form) or 'Riesel value' (-1 form) that is composite for all values of n >= 1. k's that have a trivial factor (one factor the same) for all n-values as well as k's that make Generalized Fermat #'s are not considered. See more specifics for exclusions at the bottom of this post.

Sub-project #1:
Assist in proving the [URL="http://www.rieselprime.de/Related/LiskovetsGallot.htm"]Liskovets-Gallot conjectures[/URL] for the forms k*2^n+1 and k*2^n-1 where n is always odd -and- where n is always even.

Sub-project #2:
Assist in proving the Sierp base 2 2nd conjecture for the form k*2^n+1. The 1st conjectured k where all n are proven composite is k=78557 and is extensively tested by the PrimeGrid [URL="http://www.primegrid.com/forum_thread.php?id=1647"]Seventeen or Bust[/URL] project. The 2nd conjectured k where all n are proven composite is k=271129. The range of 78557<k<271129 has been extensively tested by the PrimeGrid [URL="http://www.primegrid.com/forum_thread.php?id=972"]Prime Sierpinski Problem[/URL] and [URL="http://www.primegrid.com/forum_thread.php?id=1750"]Extended Sierpinski Problem[/URL] projects. All of these projects have omitted even k's from testing. For the 1st conjecture there are no even k's remaining. For the 2nd conjecture some even k's remain. Therefore CRUS is testing even k's for the Sierp base 2 2nd conjecture.

Sub-project #3:
Assist in proving the Riesel base 2 1st conjecture and prove the Riesel base 2 2nd conjecture for the form k*2^n-1. The 1st conjectured k where all n are proven composite is k=509203 and is extensively tested by the PrimeGrid [URL="http://www.primegrid.com/forum_thread.php?id=1731"]Riesel Problem[/URL] project. The 2nd conjectured k where all n are proven composite is k=762701. The 1st conjecture project has omitted even k's from testing and some even k's remain. The 2nd conjecture has not previously been tested. Therefore CRUS is testing even k's for the Riesel base 2 1st conjecture and all k's for the Riesel base 2 2nd conjecture.

Goal:
Prove the conjectures by finding at least one prime for all lower values of k. Many of the conjectures have already been proven but much more work is needed to prove additional bases. Proving them all is not possible but we aim to prove many of them.

Here is what is different about this effort than others previously started outside of bases 2 and 5:

1. All known info. from all threads here and many other places on the web have been brought together and have been extended to base 1030. There are currently several web pages that contain all of the info. and others pages solely dedicated to reservation info. about all of the bases. Links to them are below. They will be updated daily or as needed.

2. There will be separate threads for important k to search, reservations, and sieving efforts. If you are new to the conjectures, you'll see a portion of the more important forms that we need primes found for. The reservations page will guarantee that there is no duplication of effort and the 'last status' date will keep the effort moving along.

3. We have well-sieved files for searching at all n-ranges. See links in the reservations web pages below.

4. There is a wide variety of k's for people of all tolerances. We have k's that can be started anywhere from n>=1M down to n=2500. There are also some bases that can be started from scratch where you can find 1000's of very small primes. (Not for the faint of heart!) :smile:

5. There are many conjectures where only ONE k needs a prime (and many more that need only two). If you find it, you could be the one to prove a conjecture! This is a big deal to us here.

6. Algebraic factors have been found for many k's, which prove them composite for all n, allowing them to be removed from searches. For me, there's nothing worse then searching a k for a long time that later is proven to have no primes. :cry:

7. For those who prefer to search the conjectures using BOINC, there is a BOINC effort called SRBase for the project. See [URL="https://srbase.my-firewall.org/sr5/"]SRBase[/URL].

[URL="http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm"]Riesel conjectures[/URL]
[URL="http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm"]Riesel conjectures powers of 2[/URL]
[URL="http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm"]Sierpinski conjectures[/URL]
[URL="http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm"][COLOR=#800080]Sierpinski conjectures powers of 2[/COLOR][/URL]

Reservation pages:
[URL="http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm"]Riesel conjecture reservations[/URL]
[URL="http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm"]Sierpinski conjecture reservations[/URL]

Summarized statistics and
general short summary pages:
[URL="http://www.noprimeleftbehind.net/crus/tab/CRUS_tab.htm"]Condensed table of all conjectures[/URL]
[URL="http://www.noprimeleftbehind.net/crus/vstats_new/crus-stats.htm"]Overall progress[/URL]
[URL="http://www.noprimeleftbehind.net/crus/vstats_new/crus-top20.htm"]Top 20 lists[/URL]
[URL="http://www.noprimeleftbehind.net/crus/vstats_new/crus-unproven.htm"][COLOR=#000080]Unproven conjectures[/COLOR][/URL]
[URL="http://www.noprimeleftbehind.net/crus/vstats_new/crus-proven.htm"]Proven conjectures[/URL]

BOINC effort (SRBase):
[URL="https://srbase.my-firewall.org/sr5/"]SRBase[/URL]

The Liskovets-Gallot conjectures are shown as 'base 2 even-n' and 'base 2 odd-n'.

Detailed notes about exclusions in the conjectures:
[code]
1. k-values with at least one of the following conditions
are excluded from the conjectures:
a. All n-values have a single trivial factor.
b. Make a full covering set with all or partial algebraic factors.
c. Make generalized Fermat numbers (GFn's), that is:
q^m*b^n+1 where b is the base, m>=0, and q is a root of the base.

2. k-values that are a multiple of base (b) and where k-1 (Riesel) or
k+1 (Sierp) are composite are included in the conjectures but excluded
from testing. Such k-values will have the same prime as k / b.
[/code]For reference, here is a link to generalized Fermat number primes for bases <= 1030 up to n=2^22:
[URL="http://www.noprimeleftbehind.net/crus/GFN-primes.htm"]GFN primes[/URL]

Thanks and come join us for the fun at..."Conjectures 'R Us". :smile:

Gary

 michaf 2007-12-15 00:04

Is there a program available to 'start' a search easily?
i.e. get a program to search each number upto say n=1000, and let it report (and abort that k) whenever a prime is found.
(and also get an output file containing remaining k's of course)

I tried to make myself a ubasic program, but is seems waaaay slow, and it leaves about 1 in 10 numbers when I search only upto 100 in base 24, which would be too much to handle still :>

 gd_barnes 2007-12-15 03:54

starting a new base...

[quote=michaf;120724]Is there a program available to 'start' a search easily?
i.e. get a program to search each number upto say n=1000, and let it report (and abort that k) whenever a prime is found.
(and also get an output file containing remaining k's of course)

I tried to make myself a ubasic program, but is seems waaaay slow, and it leaves about 1 in 10 numbers when I search only upto 100 in base 24, which would be too much to handle still :>[/quote]

For starting a new entire base, I suggest PFGW. But you're talking about starting a single k on a new base. I don't recommend that because it would be highly inefficient and would take weeks just to search a few 1000 k. For instance on base 24 Riesel, it would require 32,335 separate searches (minus a small percentage with trivial factors).

For me personally, I would use PFGW to search all 32,335 k's at once up to n=3000. This would take it anywhere from 2-4 hours on one 3-Ghz P4 machine depending on how many k's it was eliminating in the early going. What's cool about PFGW is that it will stop searching a k after it finds a prime for it if you tell it to. The set up and recognition of the output wouldn't be too hard either because for base 24, there are few k's with trivial factors. (1 out of every 23 k's has a trivial factor of 23).

I think Robert did a good thing when he split up the base 16 Sierp effort into 4-5 pieces because that conjecture is k=66741. So that would be an option also. If you went with Robert's option, you might want to take the first 5000-7500 k's on base 24 to 'get your feet wet' on using PFGW and recognizing the remaining k's.

If you still want to bite off part of a new base like this, let me know and I'll send you a PM that will have detailed instructions on downloading PFGW and setting up the parameters properly. But if messing with proving many new primes, reporting k's remaining to me for others to search, etc., isn't to your liking, I have a suggestion just for you personally: You tested the remaining candidates on Base 23 up to n=34.5K. I've searched the Riesel side for them up to n=45K now. I have sieved files that go all the way up to n=100K that I can send you and you could start testing from there. As you may remember, there are 2 candidates remaining for both the Riesel and Sierpinski conjectures. (Top-5000 status is reached at ~n=74K for base 23.) If that's too long of a search per candidate for your tastes, there are many k's searched to much lower ranges such as for base 28 where there are a total of 23 k's remaining that have been searched to just n=5K.

If you're familiar with running LLR, that is what I recommend for all of the prime searches past about n=5K here after they have been sieved. Mine for base 23 have been sieved to P=600G, which is plenty sufficent, even for the longer running times of higher-n higher-base searches.

I will post what software to use including PFGW for all of the various searches and detailed instructions about their set up and how to use them in the next couple of hours but I won't go into how to start a new base like this, which would require way too many different instructions for the different situations on the many bases.

I know this doesn't answer your question completely but now that you know the above, if you can let me know how you want to proceed, I can taylor the answers more to what you want to do.

Gary

 Citrix 2007-12-15 06:11

[QUOTE=michaf;120724]Is there a program available to 'start' a search easily?
i.e. get a program to search each number upto say n=1000, and let it report (and abort that k) whenever a prime is found.
(and also get an output file containing remaining k's of course)

I tried to make myself a ubasic program, but is seems waaaay slow, and it leaves about 1 in 10 numbers when I search only upto 100 in base 24, which would be too much to handle still :>[/QUOTE]

You can write a script in pfgw. There is some documentation of this feature in the package.

gd_barnes, if some previous threads could be locked/deleted if no one is using them, let me know. This will help organize the open projects section.

Thanks!

 gd_barnes 2007-12-15 07:20

[quote=Citrix;120741]You can write a script in pfgw. There is some documentation of this feature in the package.

gd_barnes, if some previous threads could be locked/deleted if no one is using them, let me know. This will help organize the open projects section.

Thanks![/quote]

That was brought up to me before in a PM so it is a good idea. First I'd like to post a message in each of them, which I'll do in the next couple of days. The ones that I'd like to see locked are the conjectures for bases 10, 22, 23, and 6 thru 18. Rogue is still searching base 10 and Simelink is still searching base 22 per statuses in those threads in the last month. I have reservations shown for them on the web pages for this effort. What I'll do is ask that they coordinate their searches and reservations here; wait a few days for a response and then suggest that the threads be locked.

Initially I thought that base 4 Sierp could be locked and coordinated here but I noticed that it is an official prime search project as defined on the top-5000 site. So I'll leave that one alone and keep it on my list of sites and threads to observe from time to time to keep the pages up to date, similar to Riesel Sieve, Seventeen-or-bust, and base 5.

Detailed instructions on using software for this effort are coming up shortly, including the proper parameters and scripts to use for PFGW for a new effort. I had to download all of the latest versions of everything first! :rolleyes:

Gary

 Citrix 2007-12-15 08:20

It would be nice if each project could just have one thread, this would make coordinating things easier. (is it possible to do this?). If you want to have several threads, a separate category might be helpful.:smile:

 gd_barnes 2007-12-15 09:03

[quote=Citrix;120749]It would be nice if each project could just have one thread, this would make coordinating things easier. (is it possible to do this?). If you want to have several threads, a separate category might be helpful.:smile:[/quote]

I've asked xyzzy for moderator duties but I needed to get something started first. I think he implied that this could be moved over to the prime search projects forum and if the reaction to the effort was good, I may be able to be a moderator.

IMHO, separate threads are very much needed. If you look at the base 6-18 thread, there was a dukes mixture of reservations, k's remaining, k's being searched, statuses, you name it. People were getting mixed up.

That said...I think we do need to have the separate threads under a SINGLE project. Since this is 'Open projects', it does look a bit messy mixed in with threads from many other things. But if we had a stand-along project with just these 4 threads, I think it would look more like a well-structured directory structure on a computer. :smile:

Perhaps that's what you were implying that we needed a separate project for these several threads. I'm all for that. Citrix, do you have moderator priviledges for this forum? I kind of got that impression when you suggested having the other conjecture-threads locked. Just curious.

Software instructions now posted but 'how to's for this effort still to go. Fortunately those will be much quicker...Long night here. :yawn: :smile:

Gary

 Citrix 2007-12-15 16:29

[QUOTE=gd_barnes;120752]

Perhaps that's what you were implying that we needed a separate project for these several threads. I'm all for that. Citrix, do you have moderator priviledges for this forum? I kind of got that impression when you suggested having the other conjecture-threads locked. Just curious.

Gary[/QUOTE]

Yes I do. Let me know if I can help with anything.:smile:

 mdettweiler 2007-12-15 17:37

[quote=gd_barnes;120752]Citrix, do you have moderator priviledges for this forum? I kind of got that impression when you suggested having the other conjecture-threads locked. Just curious.
...
Gary[/quote]
Hint: On the left, right next to where a post is in a thread, where it shows the username and other relevant information, there's a hint: The username is in blue if the user is just a regular user, green if they're a mod, and red if they're a forum administrator (sort of a super-mod, I think). The only exception (as far as I know) is Xyzzy, who shows up as a regular user but obviously has super-super-mod privileges. :smile:

 michaf 2007-12-15 18:58

I was under the impression that Xyzzy was only a device used by the gerbils. Actually one gerbil and a spirit of one I believe.

 gd_barnes 2007-12-19 05:56