Very Prime Riesel and Sierpinski k

[robert44444uk]

Originally Posted by Thomas11

Sorry, it was limited to E<268.

Please try the attached version. It should work up to E=466 (if ever needed).

I'm still only getting 10000 results for E268 and E292.

Can you remind me what the program does, in terms of how many factors it tries to remove?

[robert44444uk]

Getting there slowly. Now up to 229074:

190 229069
191? 255530
192? 294807
193? 318934
194? 334623
195? 334645
196? 363020
197? 376732
198? 403709
199? 414907
200? 449150
201? 472040
202? 479697
203? 496187

[Thomas11]

Originally Posted by robert44444uk

I'm still only getting 10000 results for E268 and E292.

Can you remind me what the program does, in terms of how many factors it tries to remove?

Oh, now I see. This is "by design"!
The default Nash sieve uses an exponent limit of 256.
If the E level is larger than this limit, no eliminations will be found up to this limit.

So, for the larger E levels one would need a modified Nash weight by using a higher exponent limit. But then the weights are no longer comparable...

Regarding the algorithm: Please have a look into the source code (see the attached file) - it's relatively simple. It follows the code used in Jack Brennen's Proth weight Java applet.

BTW.: There is a different kind of weight (also called "Nash weight") computed within Robert Gerbicz's Payam program.
Here are a few examples from the Sierpinski side:

S 989877837408365 316 10.860427
S 42356974817175081 292 10.825832
S 215381047310089587 292 10.823601
S 229441208260289053 268 10.795702
S 140164672130719673 226 10.781194
S 317035114487308151 210 10.701962
S 371766949523237405 210 10.568048

[Thomas11]

And still another prime before n=500,000:

204? 498496

The range n=250,001-500,000 is now fully tested. No other primes to be expected...

[robert44444uk]

I am almost at the end of the range 200000 to 250000. There is another to report:

191? 245288
192? 255530
193? 294807
194? 318934
195? 334623
196? 334645
197? 363020
198? 376732
199? 403709
200? 414907
201? 449150
202? 472040
203? 479697
204? 496187
205? 498496

Testing gaps at the time of writing are 237464-238500; 239927-240000 and 245311-250000. I should be through my Thursday.

[robert44444uk]

There were no more primes up to 250K so the question marks can be taken off:

191 245288
192 255530
193 294807
194 318934
195 334623
196 334645
197 363020
198 376732
199 403709
200 414907
201 449150
202 472040
203 479697
204 496187
205 498496

[f1pokerspeed]

Just a bit of blue-sky thinking, but I wonder if this search could be BOINCified? It would be interesting to see how powerful this search could become if such a thing were to come to fruition.

I guess a framework for the server would be something like...

1. Finding Payam k-values at various E levels
2. Low-level primality test ranges
3. High-level primality test singles

How much effort would be required to set such a system up?

[robert44444uk]

Originally Posted by f1pokerspeed

Just a bit of blue-sky thinking, but I wonder if this search could be BOINCified? It would be interesting to see how powerful this search could become if such a thing were to come to fruition.

I guess a framework for the server would be something like...

1. Finding Payam k-values at various E levels
2. Low-level primality test ranges
3. High-level primality test singles

How much effort would be required to set such a system up?

I would have liked to have seen this done, but I think there is limited interest because it is really hard to get top 5000 primes. The prime testing takes three times longer than for small k.

RPS volunteers are taking the one recent candidate up, but we are falling behind! We cant process the n fast enough to keep up with the 5000th prime cut.

But in principle there is no technical reason that the three exercises you mention could not be successfully done on a distributed basis. I for one don't know how to do this.

[f1pokerspeed]

I think that 1) wouldn't be that difficult. When the project is set up, people that connect will download Payam2, the in.txt, progress.txt and results.txt file.

The files are customized to cover, say, 1 hour's work per core (so however many iterations, more for larger E values), then when the WU is done the results.txt file is sent back and the Ks found get put in to a database.

2) is slightly more tricky, just downloading PFGW and a sieve file (may require a Perl script to split the files or something?) Maybe this is best left to manual testing. 3), on the other hand, is perfect - it's basically equivalent to PrimeGrid, just on a smaller scale.

I think that 2) and 3) would be made even simpler by perhaps creating a PRPnet server or something, which would save a lot of backend issues and time. 1) is still feasible on BOINC, it is just a case of building the apps and setting up a server - non-trivial but could be easier depending on how it would work out here.

I may start work on at least BOINCifying Payam2 (if possible) and maybe thinking about a VM for the server.

http://www.spy-hill.com/~myers/help/...e_Project.html

[robert44444uk]

Originally Posted by f1pokerspeed

I think that 1) wouldn't be that difficult. When the project is set up, people that connect will download Payam2, the in.txt, progress.txt and results.txt file.

The files are customized to cover, say, 1 hour's work per core (so however many iterations, more for larger E values), then when the WU is done the results.txt file is sent back and the Ks found get put in to a database.

2) is slightly more tricky, just downloading PFGW and a sieve file (may require a Perl script to split the files or something?) Maybe this is best left to manual testing. 3), on the other hand, is perfect - it's basically equivalent to PrimeGrid, just on a smaller scale.

I think that 2) and 3) would be made even simpler by perhaps creating a PRPnet server or something, which would save a lot of backend issues and time. 1) is still feasible on BOINC, it is just a case of building the apps and setting up a server - non-trivial but could be easier depending on how it would work out here.

I may start work on at least BOINCifying Payam2 (if possible) and maybe thinking about a VM for the server.

http://www.spy-hill.com/~myers/help/...e_Project.html

2) and 3) is where the resources would be most wanted and as you say, would require the minimum adjustment to BOINC - the format would be familiar for most participants. There are 20,000 or so VPS discovered, and the majority of them need to be taken from n=10000.

[f1pokerspeed]

Ugh... this is going to be so much more difficult than I imagined...

1) I need a static IP - I can do that but it'll be a little difficult to manage
2) PRPNet server binaries don't really sem to exist...
3) BOINC projects are annoying to start with w.r.t setting up on Ubuntu - maybe I can test on a VM.

I'd say maybe a day at the least to get the static IP and the VM set up. Do you think Ubuntu/variants or Debian would be better for me to use? I believe the best way to do it might just be to get the VM running on my home server and then push it to Amazon EC2, but I don't have the funds for that.