Riesel/Sierp #'s for bases 3, 7, and 15

[michaf]

Originally Posted by rogue

I was thinking that a fixed n sieve would probably be faster, but I don't know the removal rate. For example if you test to n=100, what percentage of k still do not have a prime? What about n=1000? n=10000?

I've done the following:

testing upto 25k, 2M per day, 2M k's leaving 10 candidates
testing upto 10k, 0.3M per hour 1.5M k's left 30
testing upto 1k, 1M per hour, 10M k's left 2150 remaining
testing upto 100, 86564 per 5 minutes, 367 remaining

so:

25k: 1M takes 12 hours, leaving 5 candidates. The whole range will approx leave: 315k candidates +- 90 CPU years
10k: 1M takes 3 hours, leaving 20 candidates. The whole range will approx leave: 1.3M candidates +- 22 CPU years
1k: 1M takes 1 hour, leaving 2150 candidates. The whole range will approx leave: 140M candidates +- 8 CPU years
100: 1M takes 57 minutes??, leaving 4404 candidates. The whole range will approx leave: 286M candidates +- 8 CPU years

Thoughts:
* Testing to 25k certainly looks ineffecient,
* Testing to 1k looks a tad bit too little to me
* 2150 candidates left are still quite a bunch to process, so I think 10k (5k?) is the way to go
* 1.3M candidates left sounds manageable to me, especially if a sieve can handle say 100k at a time
* testing to 100 is a waste of space :)

[KEP]

@Michaf: Well with the new changes, this is freaking awesome. I will take it to n=1,000 and try to run a batch of 100M. Thanks for your mighty work, really glad that the reductiong has been so great, and that you has coocked up such a program, now I even dare to guess that within 10 years this base 3 will be broken at least for Riesel, but hey it should be weird if reductions want come to the sierpinski .

Kenneth!

Ps. I'll try to get back to you with some timings But I think for now, that I'll take the entire range tested to n<=25,000 simply to have as few candidates to test as possible.

It appears that taking 1M towards 25,000 will take about 1 hour, which means 96M k's a day on my Quad gr8

[michaf]

Originally Posted by KEP

It appears that taking 1M towards 25,000 will take about 1 hour, which means 96M k's a day on my Quad gr8

What? :) is your quad 12 times faster then my laptop!!??!!
I'm very amazed...
That would mean, if you'd take it on your own to 10k, you'd 'only' need about 22/12/4=half a year of dedication on your machine!

[michaf]

Can anyone come up with a sensible name for the script?
Using just sierp3, or riesel3 sounds so boring :)

[KEP]

Originally Posted by michaf

What? :) is your quad 12 times faster then my laptop!!??!!
I'm very amazed...
That would mean, if you'd take it on your own to 10k, you'd 'only' need about 22/12/4=half a year of dedication on your machine!

It might actually be 12 times faster, but I think you might have checked or tested on a lower range, where the primes were differently n'ed. At a closer look, I could see that from n=100M to n=100.25M almost all primes were below n=100. So maybe when I starts working really hard on my Dual core in about 5-7 days, we can get a more accurate timing, and then I will run an entire range of 10M, and note the starting time, and then when it finishes, I'll be able to finally know exactly how long this will take. Realisticly, I think that we are talking around endings of 2009 then all k's remaining will have been taken to 25,000. I'm considering to test to n=<2,500 since this will leave around 40 k's per million or maybe 400 (I don't remember), but times saved on using srsieve and then switch to WinPFGW once sieving is at optimal depth is just grand, compared to bringing it up to 25,000 n.

Actually just think I'll do a test run of a 1 million range. It should either way be able to finish tomorrow :)

Kenneth!

Ps. Suggestion for name: Very desctructive counter conjecture script or plain k_killer... I dunno, but someone may come up with a really great name eventually mine is after all also a bit lame!

Second edit: It appears that going to n<=5,000 for each k will leave around 20 candidates per million. This however can be reduced, when dividing the candidate k's with 3 (k mod 3 = 0 then del), either way 100 of thousands is left at n<=5,000 for the entire range, but maybe this can be used for testing the sievelimit for srsieve

[gd_barnes]

Wow, I got so lost in all of this. If anyone has anything specific to a status, that is k-range and n-range that has been tested and what k's are remaining, I'll list them on the web pages.

As for k's remaining, to list them all, I'd have to ask that they be searched to at least n=5K and even better n=10K first. I don't want to get into listing 1000's or 10000's of k's and then removing multitudes of them as we go higher...too much maintenance is required.

I would be OK with just stating the NUMBER of k's remaining at a given search limit for a specific k-range, even if the search limit is small such as n=1000. When calculating the number of k's remaining, please make sure and remove any k's that are divisible by 3^q (where q>=1) if k / 3^q yields a k-value that is also remaining.


Thanks,
Gary

[KEP]

Originally Posted by gd_barnes

Wow, I got so lost in all of this. If anyone has anything specific to a status, that is k-range and n-range that has been tested and what k's are remaining, I'll list them on the web pages.

As for k's remaining, to list them all, I'd have to ask that they be searched to at least n=5K and even better n=10K first. I don't want to get into listing 1000's or 10000's of k's and then removing multitudes of them as we go higher...too much maintenance is required.

I would be OK with just stating the NUMBER of k's remaining at a given search limit for a specific k-range, even if the search limit is small such as n=1000. When calculating the number of k's remaining, please make sure and remove any k's that are divisible by 3^q (where q>=1) if k / 3^q yields a k-value that is also remaining.


Thanks,
Gary

Well I'm going to search all k's to n<=25,000. This should ultimately have us end up with ~315,000 k's remaining (before div 3) if the conjecture is not even more reduced. I'm considering to run a lot of ranges of k's up to n<=5000, propably 50 or so, since that will leave 2000 candidates, that I'll then sieve. Maybe I'll go even further k's and sieve a lot more k's from n<=5,000 to n<=25,000.

About maintenance, there may still be a lot, but at least I think we will be able to progress pretty fast once I get this conjecture to n<=25,000. I just has to run around 6300 ranges (of 10M k's), so really not a big deal anymore to do work on this k.

Hope it all made sence.

Regards

Kenneth!

[gd_barnes]

Originally Posted by KEP

Well I'm going to search all k's to n<=25,000. This should ultimately have us end up with ~315,000 k's remaining (before div 3) if the conjecture is not even more reduced. I'm considering to run a lot of ranges of k's up to n<=5000, propably 50 or so, since that will leave 2000 candidates, that I'll then sieve. Maybe I'll go even further k's and sieve a lot more k's from n<=5,000 to n<=25,000.

About maintenance, there may still be a lot, but at least I think we will be able to progress pretty fast once I get this conjecture to n<=25,000. I just has to run around 6300 ranges (of 10M k's), so really not a big deal anymore to do work on this k.

Hope it all made sence.

Regards

Kenneth!

OK, fire away. Right now, I'm assuming that your last status stands. That is that you have tested up to k=2M and n=25K with 6 k's remaining and of course that you'll be searching ALL k-values. If you see anything that you'd like me to update on the web pages, let me know.

Micha, I am taking it by your conversation with Kenneth that you are OK letting him do the entire Riesel base 3. With automated scripts in hand on a high-speed machine, it will be interesting to see what he can do since the conjecture is now at a manageable level.

Kenneth, one warning from experience: It can get VERY boring finding hundred of thousands and millions of small primes for months at a time. You may find that you want to do like Micha and I are going to do on the Sierp side. That is search for small primes to k=50M, sieving all the k's remaining, test up to k=50M for higher primes while searching k=50M-100M for small primes, etc. My eyes are about to glaze over from the Sierp k<30M effort that I'm finally about done with. lol

One thing that I find that people underestimate on prime searching in general: The boredom factor surrounding searching for extremely huge primes (takes so long to search one) or searching for huge numbers of very small primes (takes so long to finally get up to the interesting primes). Both make it much more difficult to continue with any one effort so you have to have a good mix of different efforts in order to stay with them all.


Gary

[KEP]

@Gary:

OK I'll fireaway. About boredom, this is actually why, I will run my own project for the next 3-26 weeks, mostly because this keeps me from dying out of boredom and also it gives me time to prepare the thousands of script files needed and the total of 4-6 batch files needed, to spread the conjecture over all 6 cores. I know that everything can get boring, but thinking about the fact that I'm going to find thousands of primes maybe even millions, actually also gives a great chance to test out srsieve and its limits, so actually something new can come out of it

You can by the way, aswell as other can, follow the progress with the Riesel Base 3 Conjecture on my website, which will be updated once every week or every second week (promise). Maybe you can post a link to my website on your Riesel site, Gary?

Actually I think that Michafs script and the command-line version of WinPFGW, should offer us some great opportunities for having PrimeGrid help us tackle the Sierpinskis, but who knows they are also building up more and more work with only a very little flow of people coming to their aid

Take care everyone.

Kenneth!

[R. Gerbicz]

I've found by my program this new record Sierpinski value for base=3:
1694420352676*3^n+1 is composite for all n values. The covering set is
5,7,13,19,37,41,73,757,6481

new record Sierpinski value for base=7:
1112646039348*7^n+1 is composite for all n values. The covering set is
5,13,19,37,43,73,181,193,1201

[michaf]

Originally Posted by R. Gerbicz

I've found by my program this new record Sierpinski value for base=3:
1694420352676*3^n+1 is composite for all n values. The covering set is
5,7,13,19,37,41,73,757,6481

new record Sierpinski value for base=7:
1112646039348*7^n+1 is composite for all n values. The covering set is
5,13,19,37,43,73,181,193,1201

Congrats and thanks :)

That's quite a difference from the last conjecture base 3, a 3000 times reduction 'only' 26 times the effort for riesel 3, but surely manageable!

base 7 is a magnitude harder still, due to the larger base, but also, doable within a few thousand cpu-years (I'll give it a go to test how much will be left for base 7)