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

[Cruelty]

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 PRP record page

Current status:

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

List of found primes and PRPs (since 2010):

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

[Cruelty]

Software: head to this page and download latest LLR version.
In order to start search you have to download gmfcandidates.zip 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

TestGM=1
TestGQ=1

to your llr.ini - 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.

[Cruelty]

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

[grobie]

how do you know what ranges are available.

[Cruelty]

I am assuming that ranges above GM37 are available for testing - I am not 100% sure though
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

[grobie]

Originally Posted by Cruelty

I am assuming that ranges above GM37 are available for testing - I am not 100% sure though
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

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.

[Cruelty]

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.

[grobie]

Originally Posted by Cruelty

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.

send me the 295 exponents.
Thanks
Tony

[Cruelty]

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...
Jean, if you want I can send you the 48-bit result file to replace your 32-bit file

[Cruelty]

I am reserving 1.21M-1.22M range.

[grobie]

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