Search for prime Gaussian-Mersenne norms (and G-M-cofactors) - Page 6

Batalov · 2014-01-24, 20:23

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.

______________
*For a moment I was thinking that you were referring to EMs.
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 $3^p \pm 3^{{p+1} \over 2}+1$ ... That is, if it's not already done.

Cruelty · 2014-01-25, 08:56

Quote:

Originally Posted by Citrix

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.

Code:

TestGM=1
TestGQ=1
FactorOverride=54

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

Quote:

Originally Posted by Batalov

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.

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

Citrix · 2014-01-26, 00:14

Quote:

Originally Posted by Cruelty

Code:

TestGM=1
TestGQ=1
FactorOverride=54

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

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?

Citrix · 2014-01-26, 04:37

What does the 48 in

Code:

ABC 4^$a+1
1950017 48
1950037 48

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

Batalov · 2014-01-26, 08:11

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.

No GM yet.

Kosmaj · 2014-01-26, 08:55

Hi Batalov,

Congrats on your GQ! For the sake of completness can you post the number here. It's not published on PRP Top yet.

Thanks!

Cruelty · 2014-01-26, 21:10

Congratulations!

Batalov · 2014-01-26, 22:12

Channeling the inner davieddy: It's (going to be) number 9.

Cruelty · 2014-02-07, 10:20

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?

Batalov and Citrix: should you by any chance give up your ranges just let me know

Batalov · 2014-02-07, 18:02

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.

Citrix · 2014-02-07, 22:39

Quote:

Originally Posted by Batalov

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.

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.

2014-01-26, 04:37	#59
Citrix Jun 2003 2×7×113 Posts	What does the 48 in Code: ABC 4^$a+1 1950017 48 1950037 48 mean? Is this how deep it is already been sieved?

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2014-01-24, 20:23	#56
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2504₁₆ Posts	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. ______________ For a moment I was thinking that you were referring to EMs. 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 $3^p \pm 3^{{p+1} \over 2}+1$ ... That is, if it's not already done.

2014-01-26, 08:55	#61
Kosmaj Nov 2003 3622₁₀ Posts	Hi Batalov, Congrats on your GQ! For the sake of completness can you post the number here. It's not published on PRP Top yet. Thanks!

2014-01-26, 21:10	#62
Cruelty May 2005 2³·7·29 Posts	Congratulations!

2014-01-26, 22:12	#63
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 22404₈ Posts	Channeling the inner davieddy: It's (going to be) number 9.

2014-02-07, 10:20	#64
Cruelty May 2005 11001011000₂ Posts	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? Batalov and Citrix: should you by any chance give up your ranges just let me know

2014-02-07, 18:02	#65
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 22404₈ Posts	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.