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

[Cruelty]

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

[Cruelty]

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

[Cruelty]

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

[Cruelty]

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

(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)

[Kosmaj]

Hi Cruelty,

Congrats on a nice find!

[Cruelty]

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

[Cruelty]

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

[Cruelty]

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

[Batalov]

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 forum. 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?

[Cruelty]

2-2.5M is not reserved so go ahead (I've got a feeling there is a prime)
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

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

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

[Citrix]

Originally Posted by Cruelty

2-2.5M is not reserved so go ahead (I've got a feeling there is a prime)
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

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

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

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.