Riesel Primes k*2^n-1, k<300 [Was "k=1"]

[wpolly]

<Edit>Links and info posted by Kosmaj on May 12, 2004. Updated Jan 23, 2007.

Originally Posted by Kosmaj

Form k*2^n-1

Software for primality testing:
LLR the latest version is 3.7.1

Software for sieving:
NewPGen the latest version is 2.82.

Other software:
Proth.exe
You may prefer to check small n's without a separate sieving phase using Proth.exe (composites with small factors will be sieved out on-the-filght). For example while sieving n's in the 50-500k range you can set another machine to run Proth.exe for 1<n<50k.

Status of our k<300 sub-project. Initially the plan was to check all k's (2<k<300) for 1<=n<=200000, now we work on larger exponents. The list was started by Joss, currently updated by Kosmaj.

A list of largest primes k*2^n-1 (k>1) reported to the Top-5000. As "Mathematical Description" enter "%*2^%-1" (without quotes) and optionally change the "Type" and the max number of primes to show.

Search for primes of form k*2^n+/1-1 in Top-5000. Only those currently within largest 5000 primes will be displayed, not all primes registered in the "Top-5000" data base.

List of primes k*2^n-1, k<300 compiled by Wilfrid Keller.

List of searched intervals by Keller.

When you find a new prime or complete a range please post the info here. When you complete a range of a considerable size (or, any size, if you don't plan to work on that k any more) please inform Wilfrid Keller so that he can update his lists. His address can be found at the bottom of this page

If there is anything else worth adding please let me know.

</Edit>

Orginal post by wpolly:

Have anyone considered about the most "basic" of the 15k's - 15?
I'm thinking about 15*2^n-1 primes (or other low k such as 75 165 225).

Those 15k's only completed to 10000 according to 15k stats page.
Anyone interested?

[jocelynl]

Thanks for the link wpolly.

I'll update the stats with the new stuff.
k=15 is not a prone prime sequence.
but if you wish, the stats would be helpfull.

Joss L15.

[robert44444uk]

Since the new LLR is 400% faster then looking at this series (15*2^n-1) makes an awful lot of sense. In fact I started my main machine sieving to 1 million immediately. After a week the sieve should be nice and lean. The reason for picking this low is because the speed up will work on SSE2 apparently.

I looked at this series as part of my primoproth search but gave up because it was so unprime up to n=100000, but if you are looking for big primes....

Robert Smith

[jocelynl]

Hi Robert,

I'm already working on it up to 150k for the complete sequence. So it's all yours from that point.

Joss

[robert44444uk]

Joss

Thank you for telling me this, saves half a day! The sieve is reducing my candidates still at an alarming rate, and there will be very few candidates left to use this blindingly fast software on!

Forecast between 100000 and 200000 ... 6, 200000..1000000 6 more. This is gut feel, no maths involved.

Regards

Robert Smith

[jocelynl]

Robert

I'm all done to 150k. It might be interesting to team test this one. How far are you at sieving?

Joss

[robert44444uk]

Joss

I had to go away for a few days, and I started testing the number. I found two between 150 and 212K. How many did you find between 100 and 150K? I would guess 4.

Disappointingly the LLR and the NewPgen sieve seem to compete for computer time in an inefficient manner. So the sieve is not as far advanced as I had hoped, only at 32 bn so far.

But of course, now I am testing the numbers! So I have stopped that, and will concentrate on sieving from 212000 to 1 million, until I only get one candidate sieved in approximately 4 minutes.

I think there are not enough people doing 15K to divert them from other tasks right now, especially as the other small numbers are begging to be worked on. But I am willing to share the sieve results if people are interested.

I can't be expected to do much for this group, as I am horribly busy in the real world at the moment. So someone else will have to organise it.

Regards

Robert Smith

[Kosmaj]

Hello Robert,
Congrats to you and Slash Dude on your new primes!

Can somobody post exe times/cpu info of the new LLR for various
exponents around n=200,000. Some exe times are given in the 3-2-1
forum but for much higher exponents and without cpu info, so they are
not so useful. Have been thinking to try one small k myself but don't know
which one...

[Thomas11]

Originally Posted by Kosmaj

Can somobody post exe times/cpu info of the new LLR for various
exponents around n=200,000. Some exe times are given in the 3-2-1
forum but for much higher exponents and without cpu info, so they are
not so useful. Have been thinking to try one small k myself but don't know
which one...

Seems that a few more people are testing small k's now, using the new LLR ...

For k=5 or k=7 my AthlonXP 2400+ (2 GHz) takes about 2 minutes for a test around n=200000. But I've found that only for the smallest values of k (e.g. 5, 7, 9 and may be 11) LLR behaves like for k=3. For somewhat larger k it seems that the new LLR switches much earlier to larger FFT-lengths, e.g. testing k=29 for a given n takes almost twice the time as testing the same n for k=3.

Last year I talked with Paul Underwood about extending the 321search project to k=5 and k=7, and I have already sieved k=5 and k=7 for n=191500-1000000 up to about p=300 billion. This is far from being complete, but at the moment I don't have the time and computer power to continue this work. So, I could send you the sieve files, if you're interested.

Just one last note:
Please inform Wilfried Keller http://www.prothsearch.net/riesel2.html about any ranges you have tested and the primes you have found (if any), to keep his list of primes for k<300 current and to avoid others from double and tripple testing empty ranges. It seems to me that quite a lot of k's have already been tested up to about n=400000 or 500000 by some Proth.exe users but without giving Wilfried Keller the information about the ranges they did.

-- Thomas.

[ET_]

Originally Posted by Thomas11

Just one last note:
Please inform Wilfried Keller http://www.prothsearch.net/riesel2.html about any ranges you have tested and the primes you have found (if any), to keep his list of primes for k<300 current and to avoid others from double and tripple testing empty ranges.

So I assume that Wilfried Keller has been contacted for 321 project.


Luigi

[SB2]

If it has not already been done or started I am preparing to sieve k=9 from 191500-1000000. or would it be better to continue the sieving of 5 and 7?