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Old 2007-11-23, 20:58   #1
jasong
 
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Default twin prime, but sieving n instead of k. Possible?

I have someone who I trust that says that a certain k should be dense with primes based on his Number Theory research(he's working on a paper). I was wondering if there's a program to sieve twin primes, but sieve n instead of k, which is what I think newpgen does.

Last fiddled with by jasong on 2007-11-23 at 20:59
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Old 2007-11-23, 21:45   #2
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Yes newpgen and srsieve can do it.
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Old 2007-11-23, 21:47   #3
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Originally Posted by Citrix View Post
Yes newpgen and srsieve can do it.
Really? I always thought srsieve couldn't do fixed-n sieving; otherwise, I think the TPS project would be using it instead of NewPGen (since from what I hear, srsieve is supposed to be a LOT faster).
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Old 2007-11-23, 21:47   #4
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that's right, newpgen does:
choose as type "Twin" and fill base, n, kmin and kmax (you can check "include even values of k" too to search more candidates and more chance to find a twin).
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Old 2007-11-23, 21:54   #5
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Really? I always thought srsieve couldn't do fixed-n sieving; otherwise, I think the TPS project would be using it instead of NewPGen (since from what I hear, srsieve is supposed to be a LOT faster).
Read jasong's post carefully
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Old 2007-11-23, 22:20   #6
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Quote:
Originally Posted by jasong View Post
I have someone who I trust that says that a certain k should be dense with primes based on his Number Theory research(he's working on a paper). I was wondering if there's a program to sieve twin primes, but sieve n instead of k, which is what I think newpgen does.
There are no software that I know of that can do this on its own. However, with a bit of manual intervention, you can coax NewPGen into doing it. Essentially, you'll have to sieve the + side first, followed by - side, while carefully messing with the header so that you sieve both properly. You can also try with srsieve, since it can sieve + and - sequences together (together but separate -- not like proper "twin sieving"), but here also, you'll have to do some trial & error to figure out how best to do it (there might be some trouble if the same k appears both for + and -)

Or, you could just ask geoff to code something up specifically for twins -- shouldn't be /that/ much of a big deal.

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Old 2007-11-23, 22:45   #7
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Quote:
Originally Posted by axn1 View Post
There are no software that I know of that can do this on its own. However, with a bit of manual intervention, you can coax NewPGen into doing it. Essentially, you'll have to sieve the + side first, followed by - side, while carefully messing with the header so that you sieve both properly. You can also try with srsieve, since it can sieve + and - sequences together (together but separate -- not like proper "twin sieving"), but here also, you'll have to do some trial & error to figure out how best to do it (there might be some trouble if the same k appears both for + and -)

Or, you could just ask geoff to code something up specifically for twins -- shouldn't be /that/ much of a big deal.
You could use k'=k*k and base =4 instead of 2, search on the -1 side.
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Old 2007-11-23, 22:55   #8
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Quote:
Originally Posted by Citrix View Post
Read jasong's post carefully
Oh, I see now. I thought he was asking about a fixed-n sieve, whereas he was really asking about a fixed-k sieve. Whoopsie!
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Old 2007-11-23, 22:57   #9
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Quote:
Originally Posted by axn1 View Post
There are no software that I know of that can do this on its own. However, with a bit of manual intervention, you can coax NewPGen into doing it. Essentially, you'll have to sieve the + side first, followed by - side, while carefully messing with the header so that you sieve both properly. You can also try with srsieve, since it can sieve + and - sequences together (together but separate -- not like proper "twin sieving"), but here also, you'll have to do some trial & error to figure out how best to do it (there might be some trouble if the same k appears both for + and -)

Or, you could just ask geoff to code something up specifically for twins -- shouldn't be /that/ much of a big deal.
Why not just simply sieve the -1 side, then edit the header so that LLR will realize you're searching for twins; LLR will then test all the -1 candidates, and if it finds a prime, it will test the +1 too. (Please note that it doesn't go the other way around, as far as I know.) I think that's usually the way twin prime searches are done.
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Old 2007-11-23, 23:49   #10
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Quote:
Originally Posted by Citrix View Post
You could use k'=k*k and base =4 instead of 2, search on the -1 side.
That's one of those ideas where you go "D'oh, why didn't I think of that!". This should work well with NewPGen. Srsieve has a limitation of k < 2^64, so you'll be limited to 32 bit k's only.
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Old 2007-11-23, 23:50   #11
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Quote:
Originally Posted by Anonymous View Post
Why not just simply sieve the -1 side, then edit the header so that LLR will realize you're searching for twins; LLR will then test all the -1 candidates, and if it finds a prime, it will test the +1 too. (Please note that it doesn't go the other way around, as far as I know.) I think that's usually the way twin prime searches are done.
Yes, but sieving on the + side will take out even more candidates and you'll get a much smaller list. Why test the - side when you know the + side has a small factor and therefore can't be a twin?
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