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-   -   Sophie Germains, multiple n-ranges, future of TPS (https://www.mersenneforum.org/showthread.php?t=10775)

 MooooMoo 2008-10-13 00:52

Sophie Germains, multiple n-ranges, future of TPS

This thread is for discussing a possible search for Sophies and searching a range of both n and k for twins.

Recently, a couple of people have asked me about doing a search for both sophies and twins for n=500K. Doing so means that there's a greater chance of finding either a sophie or a twin, but one problem is that the chance of finding a twin in a range decreases the higher you sieve. As a guide, there are about 500,000 candidates left after triple-sieving a range of 10G to p=1T. Continuing to p=1000T with a twin-sieve would leave 320,000 candidates remaining, while continuing to p=1000T with a triple-sieve would leave only 256,000 candidates remaining. Some of those candidates eliminated with a triple sieve but not eliminated with a twin sieve may have been twins.

It was suggested that TPS search for a range of n with a smaller k range instead of searching a large k-range with a fixed n. The advantage is that the low k-candidates in a variable n-range are faster to test than those with a fixed n, while a disadvantage is that sieving won't be as efficient.

If you want TPS to also look for sophies, I'd welcome suggestions for a suitable k-range for triple sieving n=500K. For those who want to try triple-sieving a test range to get the idea of how it works and how much time and RAM is required, download David Underbakke's Twingen software at:

[url]http://www.sendspace.com/file/261wdk[/url]

 mdettweiler 2008-10-14 14:40

[quote=MooooMoo;145219]This thread is for discussing a possible search for Sophies and searching a range of both n and k for twins.

Recently, a couple of people have asked me about doing a search for both sophies and twins for n=500K. Doing so means that there's a greater chance of finding either a sophie or a twin, but one problem is that the chance of finding a twin in a range decreases the higher you sieve. As a guide, there are about 500,000 candidates left after triple-sieving a range of 10G to p=1T. Continuing to p=1000T with a twin-sieve would leave 320,000 candidates remaining, while continuing to p=1000T with a triple-sieve would leave only 256,000 candidates remaining. Some of those candidates eliminated with a triple sieve but not eliminated with a twin sieve may have been twins.

It was suggested that TPS search for a range of n with a smaller k range instead of searching a large k-range with a fixed n. The advantage is that the low k-candidates in a variable n-range are faster to test than those with a fixed n, while a disadvantage is that sieving won't be as efficient.

If you want TPS to also look for sophies, I'd welcome suggestions for a suitable k-range for triple sieving n=500K. For those who want to try triple-sieving a test range to get the idea of how it works and how much time and RAM is required, download David Underbakke's Twingen software at:

[URL]http://www.sendspace.com/file/261wdk[/URL][/quote]I for one am highly in favor of the smaller k-range, variable n-range idea, and would be sure to find some CPU time to throw on it if TPS chooses to go that route. :smile:

(Anyway, just my \$0.02. I know I haven't really contributed much to this project besides a bunch of PrimeGrid TPS WU's a while back, so I guess my vote may not count as much as others'. :smile:)

 Skligmund 2008-10-29 17:17

I actually like the idea of doing multiple n small k range just above n=195000. I would like to see the feasablity of doing this. Can it be adapted to primegrid somehow? Assuming n=333333 stalls out or something, there might be interest in the possibility of a record with the smaller n's. I personally have lost any real interest in n=333333. I get htis feeling of 'going to take forever' to find the twin.

Again, I'd like to see a much larger prime, but with a lower n value, we could do a lot of work in less time to check feasablity for going higher.

Thoughts?

 Flatlander 2008-10-29 20:35

To save repitition of work, I have searched for twins from n=195,032 to 201,700(ish), k from 1003 to 124751. (I think I missed two ranges of n of size 8.)

I found about 150 Riesels but no twins. (Obviously!)
It took about 3 months of all 4 C2Q cores at 3.18GHz, including sieving.
I am no longer searching below top-5000 level.

 MooooMoo 2008-10-29 21:10

1 Attachment(s)
[QUOTE=Skligmund;147102]I actually like the idea of doing multiple n small k range just above n=195000. I would like to see the feasablity of doing this. Can it be adapted to primegrid somehow? Assuming n=333333 stalls out or something, there might be interest in the possibility of a record with the smaller n's. I personally have lost any real interest in n=333333. I get htis feeling of 'going to take forever' to find the twin.

Again, I'd like to see a much larger prime, but with a lower n value, we could do a lot of work in less time to check feasablity for going higher.

Thoughts?[/QUOTE]
I've posted a sieve file for you since you were interested in doing a multiple n, small k range. It tests n=197000-197009 from k=1-1M. It should be slightly faster to test than n=195000 because of the small k's.

The sieve file hasn't been sieved deeply (only to p=250G) because each n must be sieved separately and because the k range is so small. At p=250G, 1 k is eliminated every 30-40 seconds, while it takes slightly less than a minute to LLR them.

This search for twins a bit above n=195000 might be adapted to Primegrid, but I'll wait until n=333333 is done first.
Note: The file now excludes all k below 124,000 since Flatlander LLR'ed it already.

 Skligmund 2008-10-30 00:02

Alright. I'll download that as soon as I get home and play with it. Thanks!

 Cybertronic 2008-11-05 08:37

Hello,
is prping of 197000-197009.txt complete ? primes known ?

I will try to find fast any primes with my selection methode.

best[U][/U][URL="http://www.mersenneforum.org/attachment.php?attachmentid=2875&d=1225314621"]
[/URL]

 Cybertronic 2008-11-05 12:17

[quote=Cybertronic;147937]
I will try to find fast any primes with my selection methode.
[/quote]

Hm, it works fine .

The first prime "987975*2^197002-1 is prime!"

 Cybertronic 2008-11-05 15:03

No joke , I select n=200065 , sieved with Newpgen all k's from 125000 to 1M 3 minutes and start my 4 tasks. After 2 minutes I found
"830535*2^200065-1 is prime! Time : 86.763 sec."

I wonder how easy it is to find so large primes :-)

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