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

OK, if we really want to start with GM and GQ search then we should convince Jean Penné to modify LLR to include "factoring-override" switch. IMO right now LLR spends too much time on factoring. Also when using pre-factored files LLR does not resume factoring at indicated depth (e.g. 56 bits) but starts from the beginning - this actually works but only if you continue factoring-only assignments.
Finally, as far as GQ search is concerned there is still a range below GM36 to be tested. Last time I was in contact with Jean he was doing 500k-600k range, and I have completed 600k-700k range, so 700k-GM36 range is still open for GQs - every GQ above 700k will enter TOP-10 on the [URL="http://www.primenumbers.net/prptop/prptop.php"]PRP record page[/URL] :tu:

Current status:
[code]till 600k - completed by Jean Penné (GQ-only effort)
600k - 700k - completed by Cruelty (GQ-only effort)
700k - GM36 - completed by Thomas11 (GQ-only effort, 1 GQ found)
GM36 - 2M - completed by Cruelty (2 GMs + 5 GQs found)
2M - 3.5M - completed by Batalov (1 GQ found)
3.5M - 3.85M - completed by Batalov (1 GM found)
3.85M - 4.3M - completed by Batalov
4.3M - 4.7M - completed by Batalov (1 GQ found)
4.7M - 5.1M - completed by Batalov (1 GM found)
5.1M - 7.5M - completed by Batalov+Propper (1 GQ found)
7.5M - 20M - reserved by Batalov+Propper (GM-only effort at this time, but 1 GQ found)
_________________________________________
5.1M - 21M - pre-factored to 63 bits by Batalov
3.85M - 5M - pre-factored till 55 bits by Citrix
GM37-40M - pre-factored till 48 bits by Cruelty[/code]
List of found primes and PRPs (since 2010):
[code]GM/GQ Decimal digits who when
2^15317227+2^7658614+1 4610945 Ryan Propper + Serge Batalov 07/2020
((2^6251862-1)^2+1)/10 3763995 Ryan Propper + Serge Batalov 07/2020
((2^2621670-1)^2+1)/10 1578402 Ryan Propper + Serge Batalov 06/2020
2^4792057-2^2396029+1 1442553 Serge Batalov 04/2014 Gaussian Mersenne 40?
((2^2266537+1)^2+1)/10 1364591 Serge Batalov 03/2014
2^3704053+2^1852027+1 1115032 Serge Batalov 09/2014 Gaussian Mersenne 39?
((2^1152891-1)^2+1)/10 694109 Serge Batalov 01/2014
((2^941394-1)^2+1)/10 566775 Borys Jaworski 11/2012
((2^834610-1)^2+1)/10 502485 Borys Jaworski 01/2011
2^1667321-2^833661+1 501914 Borys Jaworski 01/2011 Gaussian Mersenne 38?
((2^396031-1)^2+1)/10 238434 Thomas Ritschel 03/2014
[/code]

Software: head to this [URL="http://perso.orange.fr/jean.penne/index2.html"]page[/URL] and download latest LLR version.
In order to start search you have to download [URL="http://perso.wanadoo.fr/jean.penne/llr3/gmfcandidates.zip"]gmfcandidates.zip[/URL] file - it is prefactored till 32 bits.
Then, choose your range. Available ranges AFAIK are:
- 700000 till GM36 (991961) - some missing GQ might be found
- from 1203799 till ~40M (next GM and GQ)
Remember to add [code]TestGM=1
TestGQ=1[/code] to your [I]llr.ini[/I] - this will allow you looking for both GM and GQ.
As for the timings, testing single exponent @ 1.2M takes 2800-2900 seconds on a C2D @ 3GHz, however you should also take into account factoring which unfortunately takes a lot of time right now and you cannot limit it to given value (for current exponents, I would say that 50-51 bits is more than enough, unfortunately it goes till 59 bits AFAIR). The factoring depth really keeps me from continuing GM/GQ search right now.

I am prefactoring entire GM37-40M exponent range till 48 bits using GM=1 and GQ=1 switches.
I'm just hoping that Jean will enable his LLR software to resume factoring when doing primality / prp test + introduces factoring-depth switch that would override pre-defined factoring depth values :unsure:

how do you know what ranges are available.

I am assuming that ranges above GM37 are available for testing - I am not 100% sure though :no:
After I finish my factoring assignment (currently at 38.5M) I might do some ranges above GM37. Do you want to reserve some exponents grobie? I can also supply you with 48-bit prefactored ranges :smile:

[QUOTE=Cruelty;117845]I am assuming that ranges above GM37 are available for testing - I am not 100% sure though :no:
After I finish my factoring assignment (currently at 38.5M) I might do some ranges above GM37. Do you want to reserve some exponents grobie? I can also supply you with 48-bit prefactored ranges :smile:[/QUOTE]

Yes I would like to do some exponents.

I tested 6 exponents just to see how long they took:

2^749449-2^374725+1 is not prime. Proth RES64: 7DD5AC313F3329B5
(2^749449+2^374725+1)/5 is not prime. RES64: 71FE049240D82EDC Time: 4347.773 sec.
2^749453+2^374727+1 has a factor : 25766194141 and (2^749453-2^374727+1)/5 has a factor : 13208359673
2^749461+2^374731+1 is not prime. Proth RES64: 67F095B7D67C1D8A
(2^749461-2^374731+1)/5 is not prime. RES64: 7A443C6113C3912E Time: 4107.029 sec.
2^749467+2^374734+1 is not prime. Proth RES64: E060ADCEE0746E68
(2^749467-2^374734+1)/5 is not prime. RES64: A1A5C315C75F1E52 Time: 4067.686 sec.
2^749471-2^374736+1 is not prime. Proth RES64: A6FE3FBE4262FCA1
(2^749471+2^374736+1)/5 is not prime. RES64: 7AECD6ED6B5E5ECD Time: 4092.372 sec.
2^749543-2^374772+1 is not prime. Proth RES64: D5D342A9FB4F8824
(2^749543+2^374772+1)/5 is not prime. RES64: 2A9CF45A100CCDCE Time: 4085.882 sec.

Grobie, which range do you want to receive? Exponents are tested by me till 1203799. I can provide you with 295 exponents from 1203799 till 1210000. When you complete given range you can send the results to me.
You can also start with exponents between 700000 and GM36 hovewer you can only count on some PRPs in that range - besides, I haven't factored those.

[QUOTE=Cruelty;117911]Grobie, which range do you want to receive? Exponents are tested by me till 1203799. I can provide you with 295 exponents from 1203799 till 1210000. When you complete given range you can send the results to me.
You can also start with exponents between 700000 and GM36 hovewer you can only count on some PRPs in that range - besides, I haven't factored those.[/QUOTE]

send me the 295 exponents.
Thanks
Tony

I have finnished factoring entire GM37-40M exponent range till 48bits. Hopefully Jean reads it and will make the changes to LLR that I have already mentioned... :unsure:
Jean, if you want I can send you the 48-bit result file to replace your 32-bit file :rolleyes:

I am reserving 1.21M-1.22M range.

Update
 

I have just resumed range 1203799 till 1210000, 110 out of 295 exponents tested.

I am going for holidays so I am reserving 1.22-1.23M

OK, tests are completed till 1.23M, I am reserving 1.23M-1.24M range.

Cruelty
 

Can you refresh our memory (specially mine :smile:) what exactly are you seraching for? GM's and (PRP) GQ's, or only GQ's? What's an exe time per number on your best cpu? And have you got any response from Jean regarding your suggestions for more efficient search?

Thanks!

I am looking for both GM and GQ, exe time on 3.2 GHz C2D is ~2450 sec. per candidate. Jean has introduced a factor override switch in the latest release of LLR. I am using right now: [code]FactorOverride=51[/code]

1.23-1.24M range complete, reserving 1.24-1.25M

1.24-1.25M range complete, reserving 1.25-1.26M

1.25-1.26M range complete.

Taking 1.26-1.27M.

1.26-1.27M complete, reserving 1.27-1.28M

1.27-1.28M complete, reserving 1.28-1.29M

1.28-1.29M complete, reserving 1.29-1.3M

1.29-1.3M complete, reserving 1.3-1.31M

1.3-1.31M complete, reserving 1.31-1.32M
There was an FFT jump near 1.305M from 128k to 192k - iteration times increased ~52%. Currently it takes ~4220 sec. to test single candidate using 3GHz Core2 CPU.

1.31-1.32M complete, reserving 1.32-1.33M

1.32-1.33M complete, reserving 1.33-1.34M

1.33-1.34M complete, reserving 1.34-1.35M

(2^1347781-2^673891+1)/5 is 3-PRP! (12586.4712s+0.0013s)

I have verified it with PFGW @ base=3, and right now I am running additional tests at other bases :smile:

That's the new PRP record, isn't it??

You really had a happy night! A prime with almost 2M bits and the new PRP record :shock:

The new PRP record has 405722 digits :smile:
[quote](2^1347781-2^673891+1)/5 is 3-PRP, originally found using LLR ver.3.7.1 for Windows (no factor till 2^51).
This is a Fermat PRP at base 3, 5, 7, 11, 13, 17, 101, 137 - confirmed with PFGW ver.1.2.0 for Windows.
Additionally using the following command with PFGW:
pfgw -l -tc -a1 -q(2^1347781-2^673891+1)/5
I've received the following result:
Primality testing (2^1347781-2^673891+1)/5 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 2+sqrt(7)
Calling N-1 BLS with factored part 0.03% and helper 0.00% (0.08% proof)
(2^1347781-2^673891+1)/5 is Fermat and Lucas PRP! (104628.5231s+0.0022s)[/quote]

1.34-1.35M complete, reserving 1.35-1.36M

1.35-1.36M complete, reserving 1.36-1.37M

1.36-1.37M complete, reserving 1.37-1.38M

1.37-1.38M complete, reserving 1.38-1.39M

complete till 1.4M, reserving 1.4M-1.45M

complete till 1.45M, reserving 1.45M-1.5M

reserving 1.5M-1.51M

complete till n=1.51M, reserving 1.51M - 1.55M

Reserving 1.55 - 1.56M

complete till n=1.56M, reserving 1.56M - 1.6M

complete till n=1.6M, reserving 1.6M - 1.66M

complete till n=1.66M, reserving 1.66M - 1.7M

Well, here comes 6-th largest PRP @ 502485 digits ;-)

(2^1669219-2^834610+1)/5 is 5-PRP, originally found using LLR ver.3.8.4 for Windows (no factor till 2^54).
This is a Fermat PRP at base 3, 5, 7, 11, 13, 31, 101, 137 - confirmed with PFGW ver.3.4.4 for Windows (32-bit).

Additionally using the following command with PFGW:
pfgw -l -tc -q(2^1669219-2^834610+1)/5

I've received the following result:
[code]Primality testing (2^1669219-2^834610+1)/5 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 5
Running N-1 test using base 7
Running N-1 test using base 11
Running N-1 test using base 19
Running N-1 test using base 29
Running N+1 test using discriminant 37, base 2+sqrt(37)
Calling N-1 BLS with factored part 0.02% and helper 0.00% (0.07% proof)
(2^1669219-2^834610+1)/5 is Fermat and Lucas PRP! (229144.7431s+0.0642s)[/code]

complete till n=1.7M, reserving 1.7M - 1.77M

complete till n=1.77M, reserving 1.77M - 1.8M

Status report
 

complete till n=1.8M, reserving 1.8M - 1.85M

Status report
 

complete till n=1.85M, reserving 1.85M - 1.9M

Here comes the biggest (so far) PRP of 2012 (7-th overall according to [url]http://www.primenumbers.net/prptop/prptop.php[/url]).

[quote](2^1882787-2^941394+1)/5 is 5-PRP, originally found using LLR ver.3.8.9 for Windows (no factor till 2^54).
This is a Fermat PRP at base 3, 5, 7, 11, 13, 31, 101, 137 - confirmed with PFGW Version 3.6.6.64BIT.20120917.Win_Dev [GWNUM 27.8].

Additionally using the following command with PFGW:
-a2 -tp -q(2^1882787-2^941394+1)/5

I ve received the following result:
Running N+1 test using discriminant 2, base 2+sqrt(2)
Generic modular reduction using generic reduction AVX FFT length 224K, Pass1=896, Pass2=256 on A 1882787-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^1882787-2^941394+1)/5 is Lucas PRP! (346901.5912s+0.0100s)[/quote]

Hi Cruelty,

Congrats on a nice find! :smile:

Thanks! Verification was a real pain though, as pfgw does not support resuming of n+1 tests, which I have learnt the "hard way" :bangheadonwall:

status report
 

GM & GQ: complete till n=1.9M, reserving 1.9M - 1.95M

Status
 

Update on GM+GQ search: completed till n=1.95M, reserving 1.95M-2M range :flex:

Status: GM
 

If it is not reserved, Borys, I'd like to take GM 2-2.5M range.

(I've also already done 3-3.1M before I found this thread. Didn't want to collide with existing effort, so I shot too high perhaps. I based the estimate on your Nov/2012 PRP in 1.88M vicinity.)

To the best of your knowledge, Borys, is this the best thread to coordinate this search? I've just noticed that there are vague ideas about GM/GQs on the Primegrid's [URL="http://www.primegrid.com/forum_thread.php?id=5398#71407"]forum[/URL]. EDIT: Not that it means that they are acting upon it... I meant to say that other people might be also running similar searches. Boris Iskra, too, maybe?

2-2.5M is not reserved so go ahead (I've got a feeling there is a prime) :smile:
I would encourage you to test both for GM and GQ - it will take more time but would be more complete and in line with my search so far. BTW: I can provide you with a 48-bit pre-factored file - just let me know where to send it :smile:

As far as coordination is concerned I am not aware of anyone else searching for GM/GQ at the moment, although it's not entirely impossible :smile:

Also AFAIR there is a GQ gap below n=1M that was not tested by anyone so far.

[QUOTE=Cruelty;365278]2-2.5M is not reserved so go ahead (I've got a feeling there is a prime) :smile:
I would encourage you to test both for GM and GQ - it will take more time but would be more complete and in line with my search so far. BTW: I can provide you with a 48-bit pre-factored file - just let me know where to send it :smile:

As far as coordination is concerned I am not aware of anyone else searching for GM/GQ at the moment, although it's not entirely impossible :smile:

Also AFAIR there is a GQ gap below n=1M that was not tested by anyone so far.[/QUOTE]

I have also been interested in GM/GQ for some time. I have tried to test 2-2.5M in the past (few months ago) but could not figure out how to set up LLR for factoring-so stopped.

If we could set up a PRPnet server for test GM/GQ that would help coordinate the search alot. I would also like to donate some CPU cycles to this search.

Ah, I see now, Borys. GQs are those cofactors*, and that's of course something that comes for free with LLR (because the whole calculation is done in 2^2p+1 and only the last modulo is taken mod GM and GQ). I am done with 2-2.3M GM/GQs, and I guess I will proactively reserve 2.5-3.5M at this time.

______________
*[I]For a moment I was thinking that you were referring to EMs[/I].
If I understand correctly, these are still being done in general form (in both pfgw and llr) and are quite slow. Come to think of it, maybe I'll try to hack LLR into doing EMs; all that's needed is to do squarings modulo 3^3p+1 and the last step mod 3^p+1, and mod [TEX]3^p \pm 3^{{p+1} \over 2}+1[/TEX]... That is, if it's not already done.

[QUOTE=Citrix;365285]I have also been interested in GM/GQ for some time. I have tried to test 2-2.5M in the past (few months ago) but could not figure out how to set up LLR for factoring-so stopped.

If we could set up a PRPnet server for test GM/GQ that would help coordinate the search alot. I would also like to donate some CPU cycles to this search.[/QUOTE]
[code]TestGM=1
TestGQ=1
FactorOverride=54[/code]
Insert above lines into llr.ini and you should be testing for both GMs and GQs. The last line refers to the factoring depth, and you can set it to whatever level you wish, or skip it entirely, however first versions of LLR tended to overfactor that's why this setting was introduced.
As for PRPnet server, I don't think it can properly handle the input file structure required by LLR to perform GM+GQ search, e.g.:
[code]ABC 4^$a+1
1950017 48
1950037 48[/code]
[QUOTE=Batalov;365302]Ah, I see now, Borys. GQs are those cofactors*, and that's of course something that comes for free with LLR (because the whole calculation is done in 2^2p+1 and only the last modulo is taken mod GM and GQ). I am done with 2-2.3M GM/GQs, and I guess I will proactively reserve 2.5-3.5M at this time.[/QUOTE]
Wow, that is fast! I guess you have commited a lot of resources - at this pace I expect the next GM by the end of February :tu:

[QUOTE=Cruelty;365336][code]TestGM=1
TestGQ=1
FactorOverride=54[/code]
Insert above lines into llr.ini and you should be testing for both GMs and GQs. The last line refers to the factoring depth, and you can set it to whatever level you wish, or skip it entirely, however first versions of LLR tended to overfactor that's why this setting was introduced.
As for PRPnet server, I don't think it can properly handle the input file structure required by LLR to perform GM+GQ search, e.g.:
[code]ABC 4^$a+1
1950017 48
1950037 48[/code]

[/QUOTE]
Thanks.

I would like to reserve 3.5-5.0M. Is it possible to do trial factor on GPU?

What range of GQ is not-tested for which a factor of the GM has been found. I am somewhat more interested in GQ than GM.
Is there a list of all the known GQ primes?

What does the 48 in

[code]
ABC 4^$a+1
1950017 48
1950037 48
[/code]

mean? Is this how deep it is already been sieved?

Yes. You can use the 32-bit LLR executable for prefactoring; it then produces the output file in this format. If you later use the output file as input and increase the FacTo=54 parameter (e.g.), the program will factor from 48 to 54 bits.

In the meantime, I found one of them GQs, submitted to the PRP top. It may take a few days to be approved. Ok, here it is:
[quote]You have submitted the following probable prime(s) to the PRP Top queue :
(2^2305781-2^1152891+1)/5 (694109 digits)

Comments :
A Gaussian-Mersenne norm cofactor. Found with LLR which can work with both G-M prime norms and their cofactors of 4^p+1.[/quote]No GM yet.

Hi Batalov,

Congrats on your GQ! For the sake of completness can you post the number here. It's not published on [URL="http://www.primenumbers.net/prptop/prptop.php"]PRP Top[/URL] yet.

Thanks!

Congratulations! :groupwave:

Channeling the inner davieddy: It's (going to be) number 9.
[YOUTUBE]LVf5Cr4M-F8[/YOUTUBE]

Since reservations have recently jumped from 2M to 5M I would like to reserve 5M-6M range. I'll start with pre-factoring and first I have to figure out the optimal depth - any suggestions for that? :smile:
Batalov and Citrix: should you by any chance give up your ranges just let me know :hello:

My range is now finished. There was just one GQ PRP.

Citrix: do you have an estimate how much time it will take you to finish your reservation? In general, it should be in good form to reserve something that one can do in a week, a month... not 10 years.

[QUOTE=Batalov;366382]My range is now finished. There was just one GQ PRP.

Citrix: do you have an estimate how much time it will take you to finish your reservation? In general, it should be in good form to reserve something that one can do in a week, a month... not 10 years.[/QUOTE]

I am going to put 2 i7 Haswell on it for sure.. maybe couple more if I can somehow get PRPnet to work for these numbers. I am not sure how long it is going to take.. I need to run some tests first. I don't think the range is large enough that it will take 10 years. If we can have GPU factoring.. that will save alot of time.

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! :smile:

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.

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 :tu:

[QUOTE=Citrix;367751]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.[/QUOTE]
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.

[QUOTE=Citrix;367751]Am I doing something wrong. [/QUOTE]
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. :unsure:

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.

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 :smile:
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:
[code]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)
[/code]
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?

[QUOTE=Cruelty;367848]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.
[/QUOTE]
This is consistent with what most other projects are doing and sounds just right to me.

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?

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

[QUOTE=Citrix;367906]Is anyone else interested in finishing the 700k - GM36 - available (GQ-only effort) range?[/QUOTE]

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?

[QUOTE=Thomas11;367932]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?[/QUOTE]

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...

latest status update
 

[code]till 600k - completed by Jean Penné (GQ-only effort)
600k - 700k - completed by Cruelty (GQ-only effort)
700k - GM36 - reserved by Thomas11 (GQ-only effort, factoring till 45 bits)
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 - 3.85M - reserved by Citrix (prefactored to 55 bits)
3.85M - 4M - reserved by Batalov

GM37-40M - pre-factored till 48 bits by Cruelty[/code]

@Thomas11 - sorry I haven't responded to your question earlier, and you've learned the "hard way" about testing/factoring for GQ-only effort :sad:
To the best of my knowledge there is no other file for the 700k-GM36 range. At the beginning of this effort I have pre-factored entire GM37-40M range till 48 bits so again, should anyone need it I can provide it :smile:

I completed factoring the range 700k-GM36 to 48 bits.
The number of candidates has significantly reduced from 19197 to 9544 (10152 at 45 bits).

I will continue factoring to 50 bits and perhaps a few bits higher until the elimination rate drops below the time for a primality test. Based on the timings at 700k and 992k I'm estimating that the whole range could be completed in about one month on a Core2Quad machine. That's much faster than I originally expected. :smile:

[QUOTE=Thomas11;367991]I completed factoring the range 700k-GM36 to 48 bits.
The number of candidates has significantly reduced from 19197 to 9544 (10152 at 45 bits).

I will continue factoring to 50 bits and perhaps a few bits higher until the elimination rate drops below the time for a primality test. Based on the timings at 700k and 992k I'm estimating that the whole range could be completed in about one month on a Core2Quad machine. That's much faster than I originally expected. :smile:[/QUOTE]

Thomas11, in your range, if LLR was used to test GM numbers then all numbers for which GM was tested, GQ would have automatically been tested. This should help eliminate some more tests.

I have had some luck with using p-1 for these numbers to sieve as 50-55 bits seems too low to sieve. P-1 is most useful when either a factor for GQ is know or GM is know and finding a new factor will eliminate the whole test. Also p-1 can be done on 64 bit computers, making the sieve more efficient. I am still working on how to process the output from prime95. Any suggestions?

[QUOTE=Citrix;368023]I have had some luck with using p-1 for these numbers to sieve as 50-55 bits seems too low to sieve. P-1 is most useful when either a factor for GQ is know or GM is know and finding a new factor will eliminate the whole test. Also p-1 can be done on 64 bit computers, making the sieve more efficient. I am still working on how to process the output from prime95. Any suggestions?[/QUOTE]
Wouldn't it be more beneficial to pre-factor e.g. to 60 bits rather than P-1?

[QUOTE=Cruelty;368035]Wouldn't it be more beneficial to pre-factor e.g. to 60 bits rather than P-1?[/QUOTE]

Yes if I had enough 32 bit machines. I only have one machine. P-1 will still be useful after factoring to 60 bits.

32-bit binary gladly runs on any computer. This is true for the llr and e.g. for NewPGen (which only exists as a 32-bit binary) - these are both linked statically.

There may be a problem with LLR when looking at both sides (GM and GQ) and factoring is done in stages, e.g. first to 48 bits, then to 50 bits, and so on.

Consider for example n=702433, and let's assume we are testing both sides, using the switches TestGM=1 and TestGQ=1.

There would be two factors, one for each side:
2^702433-2^351217+1 has a factor : 376119154717
(2^702433+2^351217+1)/5 has a factor : 348149222345417

If factoring is done in just one step up to 50 bits, then both factors would be found and this n would be eliminiated.

If, however, one decides to factor to 48 bits first and in a later step to 50 bits, then this n would survive, since in the 48->50 bit stage LLR has no record about the smaller factor (376119154717) found in the earlier stage. Only if both factors would be found during one and the same factoring run, the number would be eliminated.

In practice this would mean that there might be quite a few candidates accidentally surviving the factoring stages. Perhaps one could write some shell or Perl script for extracting the factors from the lresults.txt files and check for matching pairs...

When checking in GM=1 and GQ=1 mode LLR does not write the factors unless factors for both GM=1 and GQ=1 have been found. Writing a script will not help because LLR does not output the factors.

[QUOTE=Citrix;368055]When checking in GM=1 and GQ=1 mode LLR does not write the factors unless factors for both GM=1 and GQ=1 have been found. Writing a script will not help because LLR does not output the factors.[/QUOTE]

Well, then running a "prefactoring stage" (as Cruelty did with FacTo=48) seperatelly of the primality testing could be counterproductive...

You have two options.. either sieve from scratch everytime
OR sieve GM and GQ separately (which will take twice the time) and then combine using the script.

Since I have sieved to 55 bits on my range there is no way I can move ahead to 60 bits (without repeating the work), that is why I am looking into p-1.

Good point Thomas11 I haven't thought about it. From what I see, the original 32-bit pre-factored file found on jpenne.free.fr, does include information about GM-only or GQ-only factors, so perhaps there is an undocumented way to secure such information in factoring-only assignment?
As for my 48-bit effort it isn't completely useless, as there are less candidates to test, and at current range of "n" it doesn't take much time to again factor candidates till 48 bits and further.

(2^792061-2^396031+1)/5 is 3-PRP! (238434 digits) :smile:

Congratulations! :groupwave:

3.85M to 5M factored to 55 bits. Some numbers were done to 60 bits to make tests for efficiency.

(As mentioned above, I have unreserved this range). I hope this sieve file will be helpful to someone.

[QUOTE=Batalov;367928]I'll run the start of the slow range 3.85M-4.00M.[/QUOTE]
3.85M-4.00M is done, no primes.

Will continue to 4.3M now. (Sieved to 59 bits.)

latest status update
 

[code]till 600k - completed by Jean Penné (GQ-only effort)
600k - 700k - completed by Cruelty (GQ-only effort)
700k - GM36 - reserved by Thomas11 (GQ-only effort, 1 GQ found so far)
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 - 3.85M - reserved by Citrix (prefactored to 55 bits)
3.85M - 4.3M - completed by Batalov
4.3M - 4.7M - reserved by Batalov

3.85M - 5M - pre-factored till 55 bits by Citrix
GM37-40M - pre-factored till 48 bits by Cruelty[/code]

Stupid question. Can the factoring be done with a 64-bit linux machine? If so how to do it? I can put a core into the effort and forget about it.

[QUOTE=pinhodecarlos;368949]Stupid question. Can the factoring be done with a 64-bit linux machine? If so how to do it? I can put a core into the effort and forget about it.[/QUOTE]

Yes it can, simply use 32-bit executable :smile:

[QUOTE=Batalov;368905]Will continue to 4.3M now. (Sieved to 59 bits.)[/QUOTE]
4.0M-4.3M is done, no primes.

Will carry on to 4.7M.

I finished the range 700k-GM36 (GQ-only). 1 GQ found for n=792061 (already reported).