List of most small twins of form k*2^n+/-1

[MooMoo2]

Originally Posted by gd_barnes

I am now sieving for twins in the range of 15K < n <= 20K and k < 1M.


Gary

Just out of curiosity, what software are you using to sieve that range?

[gd_barnes]

Originally Posted by MooooMoo

Just out of curiosity, what software are you using to sieve that range?

I'm using NewPGen with the increment counter turned on but it is anything but ideal. Unfortunately there is no real good software that I am aware of to sieve for twins across both multiple k's and n's. Proth works well at low n but is much too slow at the level of n that I'm now at. NewPGen overcomes some of the issue because it is very fast on a fixed n search but still not nearly as efficient as being able to sieve the entire range of k's and n's at once.

What I do is sieve each n to P=5G, which takes just over a minute on a high-speed machine, and then it automatically goes on to the next n. Unfortunately it creates one file per n so every 1000 n, I copy all 1000 files into one big sieve file and feed it to LLR. Fortunately LLR doesn't care if the T:0:2:3 line is embedded multiple times in the sieve. Thus the copy doesn't require any extra editing by me and the big file is only around 11-12 MB for 1000 n.

At P=5G for a range of k=1 to 1M for each n, it's removing candidates at about 0.8-0.9 sec. each. LLR at n=15K is taking about 0.4 secs. for each candidate so that's a little high to sieve but it will probably be pretty close as n approaches 20K. I also prefer to sieve a little too far instead of not far enough.

Since it's not sieving the entire range at once like you're able to do for a fixed n search on the n=333333 TPS project, this is certainly not a particularly efficient approach but is the best that I could come up with for the time being. I thought of sieving for Riesel's, using the output to sieve for Proth's, and then LLR what is left but the files got very big real quick for such a large range of k, causing extra effort to have to split them up. What I really need is a combination of Srsieve for a multi-k search and NewPGen's TPS algorithm.

If anyone can improve on my method here, I'm all ears!


Gary

[gd_barnes]

I had a request to post my latest on this effort. Attached is the Riesel-Proth twin prime search up to n=17K for all k < 1M. There were 16 twins for 15K < n <= 17K for k < 1M. Two of them were k < 100K.

With this effort, I also tested all Riesel primes for k < 1M shown on the RPS site, i.e. www.15k.org, for Proth primes. The continuous tested ranges of k shown on one of the listings take this into account. No additional twins were found above what I've already found.

I now have 2 high-speed cores LLRing up to n=20K. They should be done within a week and I'll post an updated list at that time.

I tested all 16 new twins for -5 and +5 triplets. None were found.


Gary

[XYYXF]

That reminded me...

http://tech.groups.yahoo.com/group/p...s/message/9836

[gd_barnes]

Originally Posted by XYYXF

That reminded me...

http://tech.groups.yahoo.com/group/p...s/message/9836

A very interesting list indeed. I spot-checked about 40-50 of this list where k < 100K vs. my own and found no problems.

If you know someone in the forum there, perhaps you could ask them to expand the list to include the first prime odd-k for each n up to n=10K. That would be interesting to see.

My LLR is up to n=20K for k < 1M now. See next post...

Thanks for sharing!


Gary

[gd_barnes]

Attached are Riesel-Proth twin prime search lists up to n=20K for all k < 1M. There were 40 twins for 15K<n<=20K. A surprising 9 of them were for k < 100K.

I have also started a web page to list all of these twins. It's in its initial stages of creation. Right now, it only includes k's < 1M that have twins for 10K<=n<=20K and ALL twins for k<100K that has a twin for n>=10K. Eventually I will have all twins currently in the attachments here on the page. Here it is... gbarnes017.googlepages.com/twinsk1-1Mn10K-20K.htm.

Sieving is now complete up to n=25K and LLR has just begun. I'll continue posting in n=5K pieces until n=30K and then drop back to n=10K pieces after that.


Gary

[gd_barnes]

The web page in the above message is no longer valid. I have now created two web pages that have all twins previously listed in the attachments in this thread. They are here:

http://www.noprimeleftbehind.net/gary/twins100K.htm
http://www.noprimeleftbehind.net/gary/twins1M.htm

A special thanks to Karsten Bonath (kar_bon) for helping out by writing a script to format the twins on the k<100K page.


Gary

[XYYXF]

Originally Posted by gd_barnes

A very interesting list indeed. I spot-checked about 40-50 of this list where k < 100K vs. my own and found no problems.

If you know someone in the forum there, perhaps you could ask them to expand the list to include the first prime odd-k for each n up to n=10K. That would be interesting to see.

It was me who posted this list on that forum. I'll try to find the data I used to generate it...

[jasong]

Originally Posted by gd_barnes

If you know someone in the forum there, perhaps you could ask them to expand the list to include the first prime odd-k for each n up to n=10K. That would be interesting to see.

Gary

[very masculine voice]
THIS SOUNDS LIKE A JOB FOR...PFGW!!!
[/very masculine voice]

Now, if I could just find my PFGW suit. It's got 'PFGW Man' written on the front, and it shows off my anatomy so well that I've been banned from wearing it in a few places.

[gd_barnes]

Originally Posted by jasong

[very masculine voice]
THIS SOUNDS LIKE A JOB FOR...PFGW!!!
[/very masculine voice]

Now, if I could just find my PFGW suit. It's got 'PFGW Man' written on the front, and it shows off my anatomy so well that I've been banned from wearing it in a few places.

Good one, Jasong! Had me rolling on the floor!

I agree, PFGW would be excellent for creating such a list.


Gary

[gd_barnes]

Originally Posted by XYYXF

It was me who posted this list on that forum. I'll try to find the data I used to generate it...

Excellent! My goal with all of this is to have the most complete and accurate list of Riesel-Proth twin primes anywhere on the web. The more information, the merrier!


Gary