Bases 251-500 reservations/statuses/primes

[KEP]

Originally Posted by gd_barnes

KEP reported in an Email that he has completed Sierp base 252 k=27 to n=25K. No primes were found and he is unreserving it.

KEP, the only reservations I now have you down for are Sierp base 255 up to n=2500 and Riesel base 3 up to k=500M and n=25K.


Gary

That checks out. All dependent on the verification and testing speed, I hope to have it all to you on friday

[KEP]

I'm going to begin to make conjectures for all b<=1024. I'll begin conjecturing base 1024 and then move my way down, since I've no idea which bases>31 (besides those mentioned on the website) that is actually conjectured I'll start working on the Sierpinski bases and then (unless someone reaches it before me) start conjecturing the Riesel bases.

Why bases<=1024 selected? Well it makes no sence to get to work on too high bases with current technology, and also there will be plenty of work for us to work on proving all bases <= 2^10 (1024)...

Is by the way going to use following exponents:

4, 6, 8, 12, 16, 24, 36, 48, 60, 72, 96, 120, and 144

when using conjecture.exe program.

Regards

KEP

Ps. Is sieving Sierpinski base 252 k=27 for n<=100K. After sieving completes, I'll begin LLR the range.

[gd_barnes]

Riesel base 256 all k's at n=40K; continuing.

Two primes already reported for n=35K-40K.

[gd_barnes]

Originally Posted by KEP

I'm going to begin to make conjectures for all b<=1024. I'll begin conjecturing base 1024 and then move my way down, since I've no idea which bases>31 (besides those mentioned on the website) that is actually conjectured I'll start working on the Sierpinski bases and then (unless someone reaches it before me) start conjecturing the Riesel bases.

Why bases<=1024 selected? Well it makes no sence to get to work on too high bases with current technology, and also there will be plenty of work for us to work on proving all bases <= 2^10 (1024)...

Is by the way going to use following exponents:

4, 6, 8, 12, 16, 24, 36, 48, 60, 72, 96, 120, and 144

when using conjecture.exe program.

Regards

KEP

Ps. Is sieving Sierpinski base 252 k=27 for n<=100K. After sieving completes, I'll begin LLR the range.

Prof. Caldwell at the top-5000 site provided me with a list of the Sierp conjectures for bases <= 100 in an unpublished math paper shortly after I started the project. His university also did searches on all of them to a shallow depth; n=~10K-40K it appears. They did not work on the Riesel side.

I could have shown those had I so chosen on the web pages but the scope of this effort is already huge. I doubt that I'll post many more conjectures on the web pages in the near future; let alone 900-1000 of them. So you can leave us with the info. if you like but don't expect to see it 'up in lights' so to speak. Perhaps you'll want to create your own web pages with them on there.

On the exponent, although I found that to be part of the issue with the covering set, you also had to reduce the maximum factor. New suggestion; try this:
Exponents of 4, 12, 48, and 144
Max factors of 100, 300, 1000, and 10000.

Even the above is unlikely to give the covering set with the fewest factors in some instances. For that reason, you have to experiment with each base at Alperton's site, which can take up to 15-20 mins. to get it correct. You have to carefully analyze which factors are eliminating which modulos of n.

Doing 900-1000 exponents correctly is a huge task. Combine that with k=27 on base 252 to n=100K (~2-3 CPU months!) and Riesel base 3 to k=500M & n=25K and I see where this is leading...

KEP, you're taking on too much work again and I see you getting bored with it before it's finished! Let's take it easy; please! Please think through your reservations before posting here.

Why don't you try it with 100 bases, see how comfortable figuring out what the correct covering sets are, and then see if you want to continue?

I have an alternative suggestion: Consider doing some searches on our LLRnet server port 6 for Sierp base 6. Well sieved files are ready to test. We'd really like to have some work done on that. There are also manual reservations with sieved files available for both Riesel and Sierp base 16, well into the top-5000 range. Bases that are powers of 2 test far faster than bases that are not. What I'm getting at is that there is plenty of work without making more.


Thank you,
Gary

[KEP]

Originally Posted by gd_barnes

Prof. Caldwell at the top-5000 site provided me with a list of the Sierp conjectures for bases <= 100 in an unpublished math paper shortly after I started the project. His university also did searches on all of them to a shallow depth; n=~10K-40K it appears. They did not work on the Riesel side.

I could have shown those had I so chosen on the web pages but the scope of this effort is already huge. I doubt that I'll post many more conjectures on the web pages in the near future; let alone 900-1000 of them. So you can leave us with the info. if you like but don't expect to see it 'up in lights' so to speak. Perhaps you'll want to create your own web pages with them on there.

On the exponent, although I found that to be part of the issue with the covering set, you also had to reduce the maximum factor. New suggestion; try this:
Exponents of 4, 12, 48, and 144
Max factors of 100, 300, 1000, and 10000.

Even the above is unlikely to give the covering set with the fewest factors in some instances. For that reason, you have to experiment with each base at Alperton's site, which can take up to 15-20 mins. to get it correct. You have to carefully analyze which factors are eliminating which modulos of n.

Doing 900-1000 exponents correctly is a huge task. Combine that with k=27 on base 252 to n=100K (~2-3 CPU months!) and Riesel base 3 to k=500M & n=25K and I see where this is leading...

KEP, you're taking on too much work again and I see you getting bored with it before it's finished! Let's take it easy; please! Please think through your reservations before posting here.

Why don't you try it with 100 bases, see how comfortable figuring out what the correct covering sets are, and then see if you want to continue?

I have an alternative suggestion: Consider doing some searches on our LLRnet server port 6 for Sierp base 6. Well sieved files are ready to test. We'd really like to have some work done on that. There are also manual reservations with sieved files available for both Riesel and Sierp base 16, well into the top-5000 range. Bases that are powers of 2 test far faster than bases that are not. What I'm getting at is that there is plenty of work without making more.


Thank you,
Gary

Well again I may have not expressed myself clear enough ... I was not reserving the conjectures for working on all the conjectures for b<=1024 down to anyone else not worked on for both Riesel and Sierpinski. I was only thinking about finding the conjectured value for each bases.

So here is what I have left to do:

1. Sierpinski base 252 for k=27: Take it to n<=100K (currently at n=42287, ~600 sec. per k/n pair)
2. Finish Riesel base 3 for all k<=500M... ETA between 2 or most likely 4 weeks

Well if you can send me a PM or an e-mail containing the files that I need to launch and run LLRNet, I would really like to see if I can get the LLRNet working. A lonely/abandoned base is never a good thing to have ... please notice that I can't guarantee that any work will actually be done

So now I'll sit back and wait patiently... and see if the LLRNet system is the same as for Riesel and Sierp Base 5

Regards

KEP

[gd_barnes]

Originally Posted by KEP

Well again I may have not expressed myself clear enough ... I was not reserving the conjectures for working on all the conjectures for b<=1024 down to anyone else not worked on for both Riesel and Sierpinski. I was only thinking about finding the conjectured value for each bases.

So here is what I have left to do:

1. Sierpinski base 252 for k=27: Take it to n<=100K (currently at n=42287, ~600 sec. per k/n pair)
2. Finish Riesel base 3 for all k<=500M... ETA between 2 or most likely 4 weeks

Well if you can send me a PM or an e-mail containing the files that I need to launch and run LLRNet, I would really like to see if I can get the LLRNet working. A lonely/abandoned base is never a good thing to have ... please notice that I can't guarantee that any work will actually be done

So now I'll sit back and wait patiently... and see if the LLRNet system is the same as for Riesel and Sierp Base 5

Regards

KEP

Here is the thread about a general discussion about setting up and running LLRnet servers. It is virtually the same as Riesel and Sierp base 5.

Here is the thread that contains the server and port for Sierp base 6.

Everything is explained somewhere in these threads. Any questions...just ask.

On coming up with the conjectures for all bases <=1024, you communicated correctly. What I'm saying is this:
When coming up with the conjectures, correct covering sets are also needed. Otherwise it is of only small help to us.

In order to come up with the conjectures, you can run covering.exe in several batch processes and accomplish it quickly: perhaps < 1 CPU day if the parameters are set up correctly.

Coming up with the correct covering sets takes far longer. I know of no software yet developed that gives the correct smallest covering set so it must be done manually. I explained how I do it previously. Perhaps Willem has an idea on how he does it.

If you want to provide us with all of the conjectured values only, that's fine. We will keep them for future use but it is of only a small amount of help and is generally outside the scope of the current project.

How many tests remain for Sierp base 252 at n=42287? Some info. for you: A test at n=2*42287=84574 will take you 600 secs * 4 = 2400 secs. (40 mins.) so hopefully you will find a prime before that.


Gary

[em99010pepe]

I would stick to manual LLRing and not use llrnet, the latter is slower, default 10 % but can go as high as 20 % upon the n size of the number.

[KEP]

Originally Posted by gd_barnes

Here is the thread about a general discussion about setting up and running LLRnet servers. It is virtually the same as Riesel and Sierp base 5.

Here is the thread that contains the server and port for Sierp base 6.

Everything is explained somewhere in these threads. Any questions...just ask.

On coming up with the conjectures for all bases <=1024, you communicated correctly. What I'm saying is this:
When coming up with the conjectures, correct covering sets are also needed. Otherwise it is of only small help to us.

In order to come up with the conjectures, you can run covering.exe in several batch processes and accomplish it quickly: perhaps < 1 CPU day if the parameters are set up correctly.

Coming up with the correct covering sets takes far longer. I know of no software yet developed that gives the correct smallest covering set so it must be done manually. I explained how I do it previously. Perhaps Willem has an idea on how he does it.

If you want to provide us with all of the conjectured values only, that's fine. We will keep them for future use but it is of only a small amount of help and is generally outside the scope of the current project.

How many tests remain for Sierp base 252 at n=42287? Some info. for you: A test at n=2*42287=84574 will take you 600 secs * 4 = 2400 secs. (40 mins.) so hopefully you will find a prime before that.


Gary

2597 tests remain at that level for Sierp base 252 for k=27. I'll take a look at the LLRNet if I decide to run it, at a later scale. Since you have a way to find the conjectured values automatically and I've to do it manually, I'll not continue that effort. So for now only Base 252 Sierp is remaining and hopefully in 2 weeks the first batches of k's remaining can be delivered to you for Riesel base 3 k<=500M

Take care

Kenneth!

[gd_barnes]

Originally Posted by KEP

2597 tests remain at that level for Sierp base 252 for k=27. I'll take a look at the LLRNet if I decide to run it, at a later scale. Since you have a way to find the conjectured values automatically and I've to do it manually, I'll not continue that effort. So for now only Base 252 Sierp is remaining and hopefully in 2 weeks the first batches of k's remaining can be delivered to you for Riesel base 3 k<=500M

Take care

Kenneth!

Based on the provided info. that you gave me, it will take you ~54 CPU days to take Sierp base 252 from n=42287 to n=100K. Not bad.


Gary

[gd_barnes]

Originally Posted by em99010pepe

I would stick to manual LLRing and not use llrnet, the latter is slower, default 10 % but can go as high as 20 % upon the n size of the number.

People make way too big of a deal about a 10-20% boost in speed. Anon and I had a PM exchange about this. My motto:

Slow and steady wins the race.

In the long run, if your machines are always running, you will outpace most searchers whose computers spend at least 10-20% of their time idle because of reserving manual ranges or deciding what to do next. I suspect that for many people, it is longer than that because they are trying to decide what to do.

It's why I keep finding primes day-in and day-out at NPLB with almost no effort since I moved 5+ quads to drive 1. Those babies never stop! I'm out of town right now and I can't do anything with my machines. They just crunch away and suck my electricity while I'm gone. lol

So my opinion: Ignore the speed boost and put over half of your machines on LLRnet from some project. For less than half that you can always quickly add manual files to: Use those for manual reservations.

The best of both worlds...


Gary

[Siemelink]

Originally Posted by gd_barnes

Coming up with the correct covering sets takes far longer. I know of no software yet developed that gives the correct smallest covering set so it must be done manually. I explained how I do it previously. Perhaps Willem has an idea on how he does it.

Gary

I wrote a program that generates covering sets and then it calculates the lowest conjecture. I am optimizing it this weekend, after that I can make it available.
By hand it is easy to do with pfgw.

Willem.