twin prime, but sieving n instead of k. Possible?

[jasong]

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.

[Citrix]

Yes newpgen and srsieve can do it.

[mdettweiler]

Originally Posted by Citrix

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).

[kar_bon]

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).

[Citrix]

Originally Posted by Anonymous

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

[axn]

Originally Posted by jasong

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.

[Citrix]

Originally Posted by axn1

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.

[mdettweiler]

Originally Posted by Citrix

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!

[mdettweiler]

Originally Posted by axn1

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.

[axn]

Originally Posted by Citrix

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.

[axn]

Originally Posted by Anonymous

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?