Constant n-Search for k*2^n-1

[kar_bon]

while including more primes from Top5000 with a link in our summary pages i see more often special n by many people, most of them not related with RPS but i think there's no data available for such searches.
i want to make a new page with constant n-searched ranges and found primes in k and perhaps information for Sophie-Germain/Cunningham Chains and twins for the specific n.
also the max k or range for k is a data to collect.
to imagine what i mean i did some searches for n=9990 to 9993 and k upto 1M (a quick shot). i also tested SG/CC (for n-1 and n+1) and twins (but none found). see the attachment.
so please everybody who has information of constant n searched ranges post your infos here.

[gd_barnes]

Originally Posted by kar_bon

while including more primes from Top5000 with a link in our summary pages i see more often special n by many people, most of them not related with RPS but i think there's no data available for such searches.
i want to make a new page with constant n-searched ranges and found primes in k and perhaps information for Sophie-Germain/Cunningham Chains and twins for the specific n.
also the max k or range for k is a data to collect.
to imagine what i mean i did some searches for n=9990 to 9993 and k upto 1M (a quick shot). i also tested SG/CC (for n-1 and n+1) and twins (but none found). see the attachment.
so please everybody who has information of constant n searched ranges post your infos here.

Karsten,

A most interesting effort that I agree is needed. It'd be great to post as an additional page on 15k.org.

Quite sometime back, I did a search on constant n for all n<=100 for all k<=100K. What I was looking for is some 'bias' in the # of primes on specific n's by first calculating the expected # of primes in the given range of k for each n vs. actual primes found. Alas, I found none that were statistically significantly different than the norm.

I'm attaching a spreadsheet of the list. Although I only searched n<=100, it is set up for 0<=n<=600, which includes n=0. Obviously for n=0, the k's shown are just one greater than actual single prime #'s. I did it to prove that my formula for prediction was correct. I got the main crux of the formula from the top-5000 site.

The graph in the spreadsheet is the % difference from the expected # of primes for each n. It's interesting but ultimately probably not very useful since there were no 'biased' n's found.

With the spreadsheet set up to go to n<=600, I'll be glad to expand the effort up to n=600 if you think it would be worth it. For that matter, with my sieving laptop about to be freed up after tonight, I can go quite a bit higher. Let me know.

Late note...I can't attach it. It is 900K zipped. I can't access my Email from work so I'll send it to you sometime after I get home tonight.


Gary

[Kosmaj]

Collecting data is all right, but please resist the temptation and don't post such primes as a part of the RPS project. This is something else, and sieving is much easier.

Here is a piece of info for your collection:
n=505000
Tested: k=3 to 100000 (100k), only odd k's
Found prime for k=395 (!)

[kar_bon]

that's my intention: collecting information of riesel-primes and make it for everyone easier to avoid double work especially for 'newcomers' like i was some time ago. i had to find the information around the net by myself and want to make this search simplier for everyone.
no, this is not a new workarea for our RPS-team but only collecting of data.
thanks for the data, Kosmaj. hope others follows to make 15k.org the best data source for k*2^n-1 primes in the net!

[gd_barnes]

Originally Posted by Kosmaj

Collecting data is all right, but please resist the temptation and don't post such primes as a part of the RPS project. This is something else, and sieving is much easier.

Here is a piece of info for your collection:
n=505000
Tested: k=3 to 100000 (100k), only odd k's
Found prime for k=395 (!)

I can understand that since it is outside of the scope of RPS. One thing I might mention...I've given credit to RPS for my twin and quad primes on top-5000 even though they were fixed-n searches and weren't in the criteria for the RPS project. I did this because it was as a result of this forum and the 15k.org site that got me interested in searching for them and I thought it would be a nice thing to do for the project.

I've somewhat resisted the temptation to do fixed n searches at higher ranges because they leave 'holes' in the k's. If I do much of this, it probably wouldn't be reportable primes.

A couple of questions: When you say "don't post such primes as a part of the RPS project", are you saying that it should be on his own web pages only? Should we show RPS in the prover code if we find a top-5000 prime from this?


Thanks,
Gary

[Flatlander]

One of the disadvantages of searching for k*2^n+/-1 with fixed n is that, as n grows, LLR gets slower as it works its way up the FFT sizes. But not always. If n is allowed to be even as well as odd then occasionally a lower FFT size will be chosen by LLR because, for example, (65536*5)*2^500000-1 is the same as 5*2^500016-1. We can use this to our advantage if we are prepared to keep the k comparatively low.

Let's say we want to do some fixed n searching from 500000 upwards. We will use k from 2001 to 65535. ('2001' because lots of searching has been/is being done below that.)
By creating a file and getting NewPGen to continue sieving it (actually NewPGen will be sieving from scratch) we can sieve 16 ns at the same time. (Using 256MB of memory. It is important to increase the maximum memory usage in the NewPGen 'Options' menu or it uses a very slow sieving algorithm.)

The created file would look like this (without the comments):

1:M:0:2:16386 \A suitable header.
2001 500000
2003 500000
2005 500000
\... until
65535 500000
\ Then k is doubled and we start again
4002 500000 \ actually 2001 500001
4006 500000 \ actually 2003 500001
4010 500000 \ actually 2005 500001
\... until
13170 500000 \ actually 65535 500001
\ Then k is doubled and we start again 14 more times.

To NewPGen it appears as a single n with large gaps over a huge range, but LLR will use FFT size(s) for a k <16 bits. (ie. quicker than testing n = 500000 with k from 2001 to (16 x 65535))

If you choose a maximum k of 32767 (15 bits) then you could have 17 ranges using 256MB. Or you could use a maximum k of 131071 (17 bits) and have 15 ranges etc., etc.

I have been using this technique for over a year and have a simple DOS program written in FreeBasic to create the files for NewPGen to sieve. You enter r,p or t for Riesel, Proth or Twin. This decides the header. Then you enter the (minimum) n. Then the minimum and maximum k (both should be odd) and number of ranges (16 in the example above). Also the k step (usually 2), and the range step (1 for consecutive ns, 2 for just odds or evens etc.).

I also have another program to convert the file outputted from NewPGen so each candidate is in its simplest form. (Easier to read any primes found.)

Using this technique has given me quite a bit of data to look for any biases. After quite a bit of searching with fairly low n I was convinced that it was more productive (ie. a greater primes/candidates )to choose just odd n when searching. However, there does not seem to be any bias with higher n.

Another apparent bias I found with low n but not higher, was to run NewPGen sieving for twins but change the header so that LLR outputs any Riesel primes. I was finding 30% more primes than when I just sieved for Riesels with similar ranges/candidates.

I suspect both these 'biases' to be just random fluctuations.

[Kosmaj]

A couple of questions: When you say "don't post such primes as a part of the RPS project", are you saying that it should be on his own web pages only? Should we show RPS in the prover code if we find a top-5000 prime from this?

Gary, if you find a reportable prime from the fixed-n search, please use or create a prover's code which contains no reference to RPS. Thanks.

[gd_barnes]

Originally Posted by Kosmaj

Gary, if you find a reportable prime from the fixed-n search, please use or create a prover's code which contains no reference to RPS. Thanks.

OK, will do.

[em99010pepe]

Just to remind:

The "Riesel Prime Search" project is searching for Riesel primes k*2^n-1, k>1. We have three subprojects as follows.
(1) k's that can produce many primes in the given range of exponent n,
(2) low-weight k's that produce a very small number of primes [opposite to (1) above],
(3) small k < 300 (with exception of those k's already reserved by other projects).

[Cruelty]

Given the lack of definition of the word "many" for no 1, I guess we can report just any riesel prime as part of RPS

[em99010pepe]

I have a question...RPS is a one person project or a community one?