20081013, 00:52  #1 
Apprentice Crank
Mar 2006
2·227 Posts 
Sophie Germains, multiple nranges, 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 triplesieving a range of 10G to p=1T. Continuing to p=1000T with a twinsieve would leave 320,000 candidates remaining, while continuing to p=1000T with a triplesieve 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. Another suggested idea came up in this rather long thread: http://www.mersenneforum.org/showthread.php?t=8479 It was suggested that TPS search for a range of n with a smaller k range instead of searching a large krange with a fixed n. The advantage is that the low kcandidates in a variable nrange 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 krange for triple sieving n=500K. For those who want to try triplesieving 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: http://www.sendspace.com/file/261wdk 
20081014, 14:40  #2  
A Sunny Moo
Aug 2007
USA (GMT5)
2×5^{5} Posts 
Quote:
(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'. ) 

20081029, 17:17  #3 
Dec 2006
Anchorage, Alaska
2×3×13 Posts 
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? 
20081029, 20:35  #4 
I quite division it
"Chris"
Feb 2005
England
31×67 Posts 
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 top5000 level. Last fiddled with by Flatlander on 20081029 at 20:38 
20081029, 21:10  #5  
Apprentice Crank
Mar 2006
2×227 Posts 
Quote:
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 3040 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. Last fiddled with by MooooMoo on 20081029 at 21:12 

20081030, 00:02  #6 
Dec 2006
Anchorage, Alaska
2×3×13 Posts 
Alright. I'll download that as soon as I get home and play with it. Thanks!

20081105, 08:37  #7 
Jan 2007
Germany
625_{10} Posts 

20081105, 12:17  #8  
Jan 2007
Germany
5^{4} Posts 
Quote:
The first prime "987975*2^1970021 is prime!" Last fiddled with by Cybertronic on 20081105 at 12:18 

20081105, 15:03  #9 
Jan 2007
Germany
5^{4} Posts 
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*2^2000651 is prime! Time : 86.763 sec." I wonder how easy it is to find so large primes :) 
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