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

[roger]

Great results Robert! Can you post the excel spreadsheet you used for reference?

Is there a way to sieve and test individual n values using the batch files that were posted here? For example, if I sieved and tested n-values to k=50M, and still had some left over, could I plug in the n-values I need into the batch files for it to sieve for 50M<k<100M?

Thanks!

[robert44444uk]

Originally Posted by roger

Great results Robert! Can you post the excel spreadsheet you used for reference?

Is there a way to sieve and test individual n values using the batch files that were posted here? For example, if I sieved and tested n-values to k=50M, and still had some left over, could I plug in the n-values I need into the batch files for it to sieve for 50M<k<100M?

Thanks!

My Excel spreadsheet is huge, with 19 graphs - this is the most instructive.
To recreate:

Download the data posted in this thread, paste into an excel sheet, use "data" "text to columns" to separate info into columns, using "space" as the separator. Construct formula using =median() over 50 values, construct another column next to it using the formula cell*2^cell.

Create a graph using chart wizard, with the choice "xy scatter", set the font size to 2 point and you should be able to construct the graph easily

I then screenprinted the graph and created a .jpg in Irfan jpg viewer before posting here

[gd_barnes]

Originally Posted by MooooMoo

Could you give us a quick guide on how to use NewPGen's increment counter? I'll see what a good sieve depth is after trying out some values.

Sure thing:
1. On the main 'page', do everything like you would normally with a couple of exceptions:
(a) The n-value will be the beginning of your n-range.
(b) The output file name will be simply ".txt". (explanation as to why below)

2. Go to 'options' 'Sieve until' and do the following:
(a) Select your 'Sieve up to p=' limit like you would normally. (Needs to be determined ahead of time.)
(b) Go to the part that says 'When complete, automatically increment...', check the box on the left, and change the box on the right to 1.
(c) On the next line for the stop point, simply tell it what n-value you want to stop at.

You'll want to determine LLR times for the highest k in your range ahead of time to determine the optimal removal rate needed. When there is a jump in fftlen is when you'll want to increase your sieve depth. In other words, set 2(c) above to the highest n-value right before an fftlen change.

One note: Because it is sieving a much smaller range of n, you will get to optimal depth at a much lower P-value because it is only removing candidates from that single-n value at a time. It can still only sieve one n at a time but this allows the process to be automated. This means that you will have to do more LLR tests than for a comparible single-n search BUT those LLR tests will be so much faster that you'll still be saving a lot of testing time overall. k=10G-100G takes a very long time to LLR, far longer than k=1M-3M.

On the file names, Newpgen will create one file per n-value. It will give you a pop up that tells you what it will call them. NewPGen's default file name is: (n-value)_(the name you put in the output file name).

So...by putting ".txt" in the output file name for a range starting at n=50K, you'll get file names of 50000_.txt, 50001_.txt, 50002_.txt, etc.

I personally sieve 1000n at a time for my 'all twin prime search' here. I then go to the DOS prompt and copy all of the files into one big 1000n file. DOS is good about copying them into one big file in the correct numerical order as long as you allow Newpgen to name them numerically as specified above. Also, LLR ignores multiple instances of the header in the file. The first one is all that it pays attention to.

That's all there is to it. It's extremely easy after you've done it once.

Originally Posted by robert44444uk

I strongly advise a test at lower than 200000 to check if this approach is worthwhile. The test should be at greater than the range Gary is currently checking, say n range 40000-41000, testing up to k=670000, to see if this produces at least one twin. The alternative test could be at nrange=67000-68000. which would be archivable, testing to 1860000. I really advise this approach (baby steps and modest target). A candidate in the 450000 range takes that much longer to test, and the chance of a twin is only 55% of that at the 333333 level. And the chance of a twin at the 333333 level is 36% of one at the 200000 level.

I have sieved the 'all twin prime search' up to n=51K for k=3-1M. The LLR testing is currently paused at n=36200. If anyone wants any 1000n range sieved file from n=37K-51K to test, let me know and I'll send it to you. I'd only ask that you test the entire 1000n-range (~1 CPU week at n=37K) and return the results to me.

Also, I would greatly appreciate being the one to start testing above n=66K for a top-20 twin for k<1M. My goal with this effort is to find all of the twins up to the top-20 table and then continue on up to n=100K. Or if someone wants to coordinate with me on such an effort, that would be fine too and we could share any twin found. k>1M is fair game. I have no intention of testing any k's > 1M for twins other than what I already did with my n=100K twin.


Gary

[roger]

Here's a .xls chart of the data on Gary's website.

I notice of interest the swung s shape on the gap chart, and the sudden jumps in smallest twin k-values n-values of multiples of 1000. Perhaps there are smaller twins in some of these areas as a smooth curve makes a bit more sense to me than these jumps. (These are more evident when the graph is not in logarithmic mode)

Is there a way to use the batch files posted earlier here for specific n-values, instead of a range?

Thanks!

[kar_bon]

Originally Posted by roger

(...)
Is there a way to use the batch files posted earlier here for specific n-values, instead of a range?

yes, it is.
call the second batch (called 'do_one.bat') with the k you want to test, for example
do_one 20000 to find the first twin for k=20000.
make sure to set the kmax and pmax you need in this batch first.

[MooMoo2]

Originally Posted by gd_barnes

One note: Because it is sieving a much smaller range of n, you will get to optimal depth at a much lower P-value because it is only removing candidates from that single-n value at a time. It can still only sieve one n at a time but this allows the process to be automated. This means that you will have to do more LLR tests than for a comparible single-n search BUT those LLR tests will be so much faster that you'll still be saving a lot of testing time overall. k=10G-100G takes a very long time to LLR, far longer than k=1M-3M.

Well, I got the increment counter to work, and I did some sieving to see what the optimal sieve depth was.

After we find a twin for n=333,333, a proposed n-range for finding our next twin is from n=450,001 to n=524,288. The k-range is from k=3 to k=2.8M, and there is a > 90% chance that a twin will be found in this range.

Anyway, I found that the optimal sieve depth was about 3T. However, we won't sieve that high because 3T * 74,287 n-values = 222,861T to sieve, which is way too much. As a comparison, we've only sieved a total of 4772T for n=333,333.

A more realistic sieve depth for that k and n range is 0.1T. That means that there will be a total of 7429T to sieve, which is reasonable compared with the previous sieve effort of 4772T.

[roger]

call the second batch (called 'do_one.bat') with the k you want to test, for example
do_one 20000 to find the first twin for k=20000.
make sure to set the kmax and pmax you need in this batch first.

Yes, I have that one, but is there a way to sieve and test a series of n-values that are not a specific range? Eg. could I use the batch files to sieve and test n=9000,9029,9052,9123,9211 without having to change the n-value every time? Also, it would be very handy to have the batch files test one n-value after another, so I can leave it to work and not waste time with it idle.

Thanks!

EDIT: I think by k=20000 you mean n=20000.

[kar_bon]

(yes: k<->n, i mixed them up)

to make specific values of k you can do this:
create a file named 'do.bat' and put the following lines in:

call do_one 9000
call do_one 9029
call do_one 9052
call do_one 9123
call do_one 9211

then you can execute this batch and all these k's will tested.

[robert44444uk]

Originally Posted by roger

Here's a .xls chart of the data on Gary's website.

I notice of interest the swung s shape on the gap chart, and the sudden jumps in smallest twin k-values n-values of multiples of 1000. Perhaps there are smaller twins in some of these areas as a smooth curve makes a bit more sense to me than these jumps. (These are more evident when the graph is not in logarithmic mode)

Is there a way to use the batch files posted earlier here for specific n-values, instead of a range?

Thanks!

There is something wrong with the first 1000 values of the Excel spreadsheet, it says k in order of n and then starts 3,15,447,345,267... whereas the data is 3,1,9,15,81,3

This is because the Gary's website grid has been incorrectly transposed, best instead to the take the first 1000 values that I posted in this thread.

The jumpy pattern of the first 1,000 n then disappears

I will be posting the 5,000 - 6,000 probably tomorrow.

Then I will plan to do the test at 30-31000 n, ignoring the first 1,000,000 k - will keep timings

[roger]

to make specific values of k you can do this:
create a file named 'do.bat' and put the following lines in:

call do_one 9000
call do_one 9029
call do_one 9052
call do_one 9123
call do_one 9211

then you can execute this batch and all these k's will tested

Do you mean these n's will be tested?
I'm looking to test specific n-values, not k-values in k*2^n+-1

[kar_bon]

Originally Posted by roger

Do you mean these n's will be tested?
I'm looking to test specific n-values, not k-values in k*2^n+-1

sorry again.... i should'nt write so late...

of course these n-values will be tested!