Bases 6-32 reservations/statuses/primes

[MyDogBuster]

Cool. You kind of like those PRPnet servers and the new PFGW, eh?

I'm doing my own testing but so far things look good. I also found out that the AMD quad I have that was basically useless, likes PRPNet and PFGW. Nice to see that machine doing something useful for a change.

[mdettweiler]

Originally Posted by MyDogBuster

I'm doing my own testing but so far things look good. I also found out that the AMD quad I have that was basically useless, likes PRPNet and PFGW. Nice to see that machine doing something useful for a change.

Useless in what way? PRP tests with PFGW do the same types of underlying calculations as LLR tests, so a machine that's good with them should be good with LLR as well.

[gd_barnes]

Sierp base 31 is at n=14K; 72 primes found for n=13K-14K. 1567 k's remain.

[henryzz]

reserving riesel base 15 2M-3M
i will use this to work out the best way to run base 3

BTW once i have run the sieve file through prpnet how will i get the list of remaining ks?
it might take me a little while to work out prpnet
it is based on ecmnet which i have used before so it shouldnt be too much of a problem

edit:
i am using the latest PFGW 3.2 on linux
i presume that is safe?

[rogue]

Originally Posted by henryzz

reserving riesel base 15 2M-3M
i will use this to work out the best way to run base 3

BTW once i have run the sieve file through prpnet how will i get the list of remaining ks?
it might take me a little while to work out prpnet
it is based on ecmnet which i have used before so it shouldnt be too much of a problem

edit:
i am using the latest PFGW 3.2 on linux
i presume that is safe?

You can get the list of remaining k's via server_status.html. If will also help if you set up e-mail for prime notification.

Yes, PFGW 3.2 is safe on linux.

[gd_barnes]

Originally Posted by henryzz

reserving riesel base 15 2M-3M
i will use this to work out the best way to run base 3

BTW once i have run the sieve file through prpnet how will i get the list of remaining ks?
it might take me a little while to work out prpnet
it is based on ecmnet which i have used before so it shouldnt be too much of a problem

edit:
i am using the latest PFGW 3.2 on linux
i presume that is safe?

This is NOT a straight-forward task! Besides learning to use PRPnet, you have to know the math involved about removing multiples of the base to come up with k's remaining. Here are some particulars:

(Obvious part)
Don't test the following that have trivial factors:
odd k's, i.e. k==(1 mod 2)
-or-
k's where k==(1 mod 7)

(Not so obvious part)
Regarding eliminating k's that are divisible by 15, you cannot automatically eliminate all of those. After a preliminary run to a low limit such as n=2500 or 5000, then you'll want to eliminate all k's where BOTH of the following conditions are true:
k==(0 mod 15)
-and-
k-1 is prime

Any questions, let me know. If you don't want to do the 2nd part of the above, I can take care of it if you send me all of the k's remaining. To determine what is remaining is not particularly easy. For a base with a huge # of k's you need to know what you started with. Many people do it in many different ways. I do it differently depending on how big the base is.

How high were you planning on testing it? I'd suggest n=10K to start with but if you get comfortable with it, you could go on to n=25K.


Gary

[gd_barnes]

Originally Posted by rogue

You can get the list of remaining k's via server_status.html. If will also help if you set up e-mail for prime notification.

Yes, PFGW 3.2 is safe on linux.

This is incorrect on two accounts:

NO!! Do NOT set up Email for prime notification. There will be hundreds of thousand of primes for this run!

Second, the list of remaining k's will include k's that are a multiple of the base but where k-1 is not prime, which it should not. This is not a bug in PRPnet or anything else because the k's are actually in the file but they need to be manually removed at some point (usually after testing to a nominal limit such as n=5000.) Leaving them in there would cause a large amount of duplication of CPU effort in the future. See the last post that I just made.

Mark, wouldn't PRPnet barf when testing hundred of thousand of k's and attempting to create a web page that shows them? At the end of Henry's run, there will not be a lot remaining but when it starts out, there will be many 100's of thousands of them. Can it handle this?

Guys, I've said this to everyone who has started to try a new base or who have attempted to extend the k-range on a huge base like 3, 7, or 15. You have to know EXACTLY what you are doing on the math. If you're not very familiar with factorization and algebra as it relates to eliminating some (but not all) of the k's that are multiples of the base as well as algebraic factors that combine with numeric factors to make a full covering set, it's much better to take existing k's and search them deeper.

Here's a good way to do it once you understand the way to remove k's that are a multiple of the base (MOB) and you know that PRPnet can handle 100's of thousand of k's: Since PRPnet will have an output web page that shows k's remaining, use that as a starting point and then use your knowledge to remove k's that are MOB. In theory, that should give you an accurate list but we'll still probably need to check any k's remaining that are perfect squares or cubes for algebraic factors that eliminate the k. (There may be none at such a high k-limit.)

I suggesting thinking through this greatly before using a PRPnet server at the outset of a test for so many k's. You may need to test it manually at first before loading what appropriately is remaining into the server.


Thanks,
Gary

[rogue]

I pretty much agree with Gary on this.

If there are that many bases, then yes, it would be a problem due to memory constraints. It would certainly slow down the server when generating webpages. It would make more sense to load a few thousand k at a time and add more (using prpadmin) as primes are found.

[henryzz]

Originally Posted by gd_barnes

This is NOT a straight-forward task! Besides learning to use PRPnet, you have to know the math involved about removing multiples of the base to come up with k's remaining. Here are some particulars:

(Obvious part)
Don't test the following that have trivial factors:
odd k's, i.e. k==(1 mod 2)
-or-
k's where k==(1 mod 7)

(Not so obvious part)
Regarding eliminating k's that are divisible by 15, you cannot automatically eliminate all of those. After a preliminary run to a low limit such as n=2500 or 5000, then you'll want to eliminate all k's where BOTH of the following conditions are true:
k==(0 mod 15)
-and-
k-1 is prime

Any questions, let me know. If you don't want to do the 2nd part of the above, I can take care of it if you send me all of the k's remaining. To determine what is remaining is not particularly easy. For a base with a huge # of k's you need to know what you started with. Many people do it in many different ways. I do it differently depending on how big the base is.

How high were you planning on testing it? I'd suggest n=10K to start with but if you get comfortable with it, you could go on to n=25K.


Gary

i would prefer if you did the second part
i tested it to n=1k with the pfgw script here
i did the obvious part with that
there are only 99 sequences remaining at n=1k so maybe it would be best to remove unnecessary ks now
i have attached the remaining ks at n=1k
i would guess i will test to n=25k like i did with 1M-2M

[gd_barnes]

David,

Attached is the file with appropriate k's that are MOB removed. 16 k's were divisible by 15 (i.e. were MOB). Removing those leaves 83 k's remaining. But of the 16 k's that were MOB, three were k's where k-1 is prime. Adding the 3 back gives 86 k's remaining. None of the k's were perfect squares or cubes so there is virtually no chance that there is algebraic factors to make a full covering set in any of them.

I apologize in advance if I seem a little harsh here but in all fareness I have to do the same with you and anyone else that I've done with KEP in the past. If you do not 100% understand how to do the removal of k's that are MOB as well as check for k's that contain partial algebraic factors to make a full covering set, you'll need to find someone to assist you in that regard or find an automated process such as what I think Karsten has set up if he still has it available. I offered to help here to get you started but that is all that I can offer at this point.

If future files of k's remaining do not look correct, I'll simply state such and it will be up to you to figure out why. Bases 3, 7, and 15 take an extreme amount of time to administer as it is (mainly base 3 that the project just went off on its own tangent for). Listing all of the k's remaining and primes on the web pages, saving off primes and results files from everyone verifying monsterous # of k's, updating and posting files for the drives, etc. Personally, I'd just as soon that the project ignore them completely as they have no chance of being close to solved in our lifetimes. For that reason, I will not be starting any more drives for base 3 and certainly not starting any for bases 7 or 15.

BTW, I saw that the post that you provided a link to contained a broken link within it. I've now fixed that.


Thank you,
Gary

[henryzz]

Gary,

I completely see where you are coming from. After that explanation i think i can remove the correct ks divisible by the base. Algebraic factors are a bit harder but hopefully i we be able to spot them.
I have been using base 15 as my test base for working out a good routine for starting a base with new programs, scripts, etc..
Once i have completed this i will attempt proving some bases.