Search for prime Gaussian-Mersenne norms (and G-M-cofactors)

[Cruelty]

You guys are really fast I see. It's a pity though that there was no prime nor other PRP in the 2M-3.5M range :surprised

Since I cannot effectively compete with you, I cancel my 5M-6M reservation. Good luck!

[Citrix]

So I have sieved everything up to 55-bits. When I do the LLR testing it is using AVX-all complex FFTs.

Am I doing something wrong. Shouldn't the LLR be faster (and use smaller AVX length) as everything is done modulo 2^4P+1.

[Cruelty]

All technicalities aside, using LLR to search for Gaussian Mersenne Norms and Co-norms always took more time than standard k*b^n+c tests. On the other hand LLR still should be faster than PFGW in that area

[Batalov]

Originally Posted by Citrix

So I have sieved everything up to 55-bits. When I do the LLR testing it is using AVX-all complex FFTs.

Am I doing something wrong. Shouldn't the LLR be faster (and use smaller AVX length) as everything is done modulo 2^4P+1.

2^2P+1, actually.

1. 55-bits is too low (one should sieve until the removal rate is comparable to running real tests. ~58-59 bits is more like it - and that's for the low range).
2. (on an average bench machine) From 3.5 to 3.85M, iterations take 4.7ms; from 3.85M to >4.5M, iterations take 6.3ms, then higher still (I haven't benchmarked, you can do it yourself).
3. Take the values left in the sieve, and estimate the necessary time already. It is easy.

Originally Posted by Citrix

Am I doing something wrong.

Well, ...
You haven't still done the time estimate, for one thing. You haven't sieved well enough, for another. Your grasp exceeds your reach, but according to Browning, this is not necessarily wrong - or else, what's heaven for.

[Citrix]

My question was regarding the AVX all complex FFT? Is LLR choosing the right FFT type? Is there some setting I am getting wrong. Shouldn't mod 4^p+1 be faster than all-complex FFT?

In terms of the sieving question:- 55 bits is right depth for me. Given the number of 32 bit computer available and on my 64 bit computer it takes about 4 ms per iteration-- 55-56 bit seems the correct number for me. If some how we could get a GPU to sieve then maybe 62 bits would be the right number. I have tried sieving upto 60 bits for the 3.5-3.6M range.

There are 67499 numbers left. With 1 computer it will take ~2000 days. with 2 computers ~1000 days. I might be able to put more computers on this range (I am trying to get PRPnet to work). So definately less than 10 years. I might unreserve 4M-5M, if I am unable to put more computers, so everything will be done in 1 year. I will let you know.

Searching for primes is a hobby and not my profession. Batalov, I am not sure why you keep on pressurizing me to finish this range? There are plently of riesel k that members of riesel prime search have reserved and they are slowly making progress on them- even if it takes them more than a year to do a 0.25 M range. No one is pressurizing them. Do you rather want to do the whole range yourself than having me compute it? I don't understand your attitude towards me? Please let me know.

[Cruelty]

I've started my GM/GQ effort almost 8 years ago and from ~1M I have arrived almost @ 2M. Up until recently I was reserving 0.05M ranges and it took me some time to finish each of those on a single C2Q core. Right now all that changed in light of recent increase of interest and computing power dedicated to that effort, therefore I would suggest to limit reservation ranges. So how much should one reserve at a time? Since apparently only 3 of us are particularly interested in that subject, I think we can come to some decisions quite fast
I propose that one should not reserve more than one month worth of work, and for the sake of tracking progress, report status at least once a month in this thread.
Current status looks as follows:

till 600k - completed by Jean Penné (GQ-only effort)
600k - 700k - completed by Cruelty (GQ-only effort)
700k - GM36 - available (GQ-only effort)
GM36 - 1.95M - completed by Cruelty (2 GMs + 5 GQs found)
1.95M - 2M - reserved by Cruelty (currently @ 1.98M)
2M - 3.5M - completed by Batalov (1 GQ found)
3.5M - 5M - reserved by Citrix (prefactored to 55 bits)

I can also volunteer to set-up a results repository. Additionally together we can come up with an idea how to set up a PRPnet server to serve us all, and avoid all that reservation hassle altogether?
What do you think?

[Batalov]

Originally Posted by Cruelty

I propose that one should not reserve more than one month worth of work, and for the sake of tracking progress, report status at least once a month in this thread.

This is consistent with what most other projects are doing and sounds just right to me.

[Citrix]

I have already divided the ranges from 3.5-3.85M among the 2 computers. I will unreserve 3.85M-5M. I will update results once a month.

Is anyone else interested in finishing the 700k - GM36 - available (GQ-only effort) range?

[Batalov]

I'll run the start of the slow range 3.85M-4.00M.

[Thomas11]

Originally Posted by Citrix

Is anyone else interested in finishing the 700k - GM36 - available (GQ-only effort) range?

I just had a look into the "gmfcandidates.txt" file posted by Cruelty back in 2007. The range from 700k to GM36 accounts for 19197 tests. Quite a lot...

Is there a newer version of this file (perhaps containing less candidates)?

And what would be the right procedure and proper switches for LLR to tests those numbers? You mentioned "TestGQ=1" and "FactorOverride", but I may be missing some crucial information. And does one need the 32bit version of LLR?

[Thomas11]

Originally Posted by Thomas11

And what would be the right procedure and proper switches for LLR to tests those numbers? You mentioned "TestGQ=1" and "FactorOverride", but I may be missing some crucial information. And does one need the 32bit version of LLR?

Meanwhile I did some factoring tests using the 32 bit version of LLR. Using just "FacTo=45" already eliminates almost half of the candidates. And I learned it the hard way that I need to turn of GM testing using "TestGM=0", otherwise LLR reports and eliminates only those candidates which have factors on both sides.

I will continue factoring and do some initial primality tests and decide later whether I can cope with the whole range 700k-GM36 in reasonable time. If not, I will take at least a small section...