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Old 2010-04-14, 13:31   #1
rogue
 
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Default Sierp base 63 - team drive #5

I have been running some tests to estimate the effort involved for S63. I would like to get it to n=10000. Based upon my tests I estimate that close to 70% of the k (of 237,036) have primes for n < 10000. Based upon my tests I also estimate that testing 10000 k to n=10000 will take about 2 months on a single core of a C2D at 2.4 GHz.

I used srsieve to sieve to a depth of 1e10. I then took the ABC file that srsieve output (using the -w switch) and modified the first line to read as follows:

ABC $a*63^$b$c // {number_primes,$a,1}

I then ran the file (sr_63.pfgw) through PFGW without any additional switches. In my test I only did 100 k, so my test results are an extrapolation. You can certainly use sr2sieve, but you would have to break up the one file into multiple files. It might save some time sieving, but takes more time to manage.

I have created 23 files, each with 10,000 k (I've already taken the last file with 7036 k). To join in this effort, please select a file from one of the following links and state your reservation into this thread. When you have completed processing the file, please zip up the primes you have found and attach them to a post in this thread. Based upon the success of this thread I might do a second drive in the future.

Group 1 (complete by Mathew Steine; 2444 k's remaining)
Group 2 (complete by Lennart; 2381 k's remaining)
Group 3 (complete by Lennart; 2419 k's remaining)
Group 4 (complete by Lennart; 2343 k's remaining)
Group 5 (complete by Lennart; 2365 k's remaining)
Group 6 (complete by Lennart; 2360 k's remaining)
Group 7 (complete by rogue; 2456 k's remaining)
Group 8 (complete by Xentar; 2322 k's remaining)
Group 9 (complete by Lennart; 2384 k's remaining)
Group 10 (complete by rogue; 2393 k's remaining)
Group 11 (complete by appeldorff; 2368 k's remaining)
Group 12 (complete by Mini-Geek; 2437 k's remaining)
Group 13 (complete by rogue; 2394 k's remaining)
Group 14 (complete by rogue; 2462 k's remaining)
Group 15 (complete by kar_bon; 2369 k's remaining)
Group 16 (complete by Lennart; 2359 k's remaining)
Group 17 (complete by rogue; 2327 k's remaining)
Group 18 (complete by rogue; 2389 k's remaining)
Group 19 (complete by rogue; 2348 k's remaining)
Group 20 (complete by rogue; 2379 k's remaining)
Group 21 (complete by rogue; 2427 k's remaining)
Group 22 (complete by rogue; 2344 k's remaining)
Group 23 (complete by rogue; 2380 k's remaining)
Group 24 (complete by rogue; 1698 k's remaining)

Any comments or suggestions are welcome.

The drive is now complete! 180488 primes were found. 56548 k's remain at n=10K. 76.14% of all k's were eliminated for n=1K-10K!

Last fiddled with by gd_barnes on 2011-02-22 at 21:12 Reason: status update
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Old 2010-04-14, 14:13   #2
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I was playing around with group 1, (not reserving it) and I have a very useful (though maybe obvious) tip for anybody planning on doing this: when starting out the sieve, make srsieve quiet by setting -m to the same as -P. Otherwise, when srsieve hits -m's value (default 100K), it slows down tremendously trying to print every one of the millions of factors found.

Also, sr2sieve is impractical for very large k's (e.g. everything except group 1) and large groups of k's (e.g. any of these groups unless you split them up). Even in group 1, you'd definitely want to only spend the half hour to generate the Legendre tables once (run "sr2sieve -c -i sr_63.abcd" once, it'll save it to sr2cache.bin where all other sr2sieve runnings will automatically look). Even with the first 1000 k's, it took 120 MB of RAM to run, so it might not be practical, depending on how it behaves with all 10000 k's and your RAM limits. I'm not sure how good sr2sieve -x (no Legendre lookup) would be.

Last fiddled with by Mini-Geek on 2010-04-14 at 14:20
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Old 2010-04-14, 14:29   #3
mdettweiler
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Cool idea! However, to avoid confusion with the "real" Drive #1 (S16), I suggest that we rename this to either:
"Sierpinski base 63 - team drive #4"
"Sierpinski base 63 - mini-drive 1"
per our established naming conventions for team efforts. Since this effort, at my rough approximation, will take about 4 CPU-years, I'm not sure it exactly fits in the category of a mini-drive, and am thinking that designating it team drive #4 would be more appropriate. Gary, what do you think?
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Old 2010-04-14, 14:33   #4
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I take Group 2

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Old 2010-04-14, 15:05   #5
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Quote:
Originally Posted by mdettweiler View Post
Cool idea! However, to avoid confusion with the "real" Drive #1 (S16), I suggest that we rename this to either:
"Sierpinski base 63 - team drive #4"
"Sierpinski base 63 - mini-drive 1"
per our established naming conventions for team efforts. Since this effort, at my rough approximation, will take about 4 CPU-years, I'm not sure it exactly fits in the category of a mini-drive, and am thinking that designating it team drive #4 would be more appropriate. Gary, what do you think?
Yeah, it probably needs to be something besides team drive 1.

The mini-drive designation applies to only the base itself and would be appropriate if we were doing only a portion of the k's with this drive like we did for base 3. But since we're doing all of them, then this wouldn't be considered a mini-drive.

Once complete to n=10K, then this drive could be simply extended to n=15K or 25K like we've done for base 16. Otherwise if we made it another team drive for n>10K, we'd have to have another thread and would ultimately innundate ourselves with threads and drives. We've kind of done that already, especially for base 3, which is why I unstickied all of those long ago. :-)

Therefore I think team drive #4 is the way to go.

Thoughts from anyone else on it?


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Old 2010-04-14, 15:11   #6
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Quote:
Originally Posted by Mini-Geek View Post
I was playing around with group 1, (not reserving it) and I have a very useful (though maybe obvious) tip for anybody planning on doing this: when starting out the sieve, make srsieve quiet by setting -m to the same as -P. Otherwise, when srsieve hits -m's value (default 100K), it slows down tremendously trying to print every one of the millions of factors found.

Also, sr2sieve is impractical for very large k's (e.g. everything except group 1) and large groups of k's (e.g. any of these groups unless you split them up). Even in group 1, you'd definitely want to only spend the half hour to generate the Legendre tables once (run "sr2sieve -c -i sr_63.abcd" once, it'll save it to sr2cache.bin where all other sr2sieve runnings will automatically look). Even with the first 1000 k's, it took 120 MB of RAM to run, so it might not be practical, depending on how it behaves with all 10000 k's and your RAM limits. I'm not sure how good sr2sieve -x (no Legendre lookup) would be.
Agreed on every front here. If doing 10,000 k's at once for k's of this size, you have to use srsieve or sr2sieve without the symbols, i.e. with the -x switch. I believe that sr2sieve has an inherent limitation itself on memory allocation, although I could be wrong. I seem to recall butting up against a memalloc error even when my machine had far more memory than when the error occurred. Regardless, even the first 10,000 k's would likely eat 5-10 GB of memory or more and take days or even weeks to create the symbols. For such a low n-range, it isn't worth it.

If anyone would care to post their timings on srsieve vs. sr2sieve with the -x option, that would be helpful.


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Old 2010-04-14, 15:17   #7
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Quote:
Originally Posted by gd_barnes View Post
Yeah, it probably needs to be something besides team drive 1.

The mini-drive designation applies to only the base itself and would be appropriate if we were doing only a portion of the k's with this drive like we did for base 3. But since we're doing all of them, then this wouldn't be considered a mini-drive.

Once complete to n=10K, then this drive could be simply extended to n=15K or 25K like we've done for base 16. Otherwise if we made it another team drive for n>10K, we'd have to have another thread and would ultimately innundate ourselves with threads and drives. We've kind of done that already, especially for base 3, which is why I unstickied all of those long ago. :-)

Therefore I think team drive #4 is the way to go.

Thoughts from anyone else on it?
Gary, since you have admin access, feel free to change the name of the thread to the consensus.
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Old 2010-04-14, 15:46   #8
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I take
Group 3
Group 4
Group 5
Group 6


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Old 2010-04-14, 16:04   #9
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I have done some testing and can state that for the range I'm doing that srsieve is faster than sr2sieve.

Using srsieve with -P and -m, I am getting about 40000 p/s (1500 k's in the file).

Using sr2sieve with -P, -q, and -x, I am getting about 25000 p/s on the same file.

1e10 is not be the optimal sieve depth. It is a ballpark number. In reality it could be more or less dependent upon the number of k's in the input file. In my original test I had 100 k's (the lowest 100), but I also used sr2sieve. 1e10 was slightly deeper than necessary, but not by much.
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Old 2010-04-14, 20:27   #10
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OK, I've changed it to team drive #5. I've also showed Lennart's reservations in the 1st post.

Does anyone want group 1?
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Old 2010-04-15, 13:31   #11
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Since larger k take longer to test, so my estimate of two months is most likely incorrect. I have split group 24 (not shown in this thread) across 4 CPUs (2 of which are 'borrowed" for a few days) and will be able to provide a better estimate in a few weeks.
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