42645*2^85628+1 is a Factor of xGF(85625,10,9)
36255*2^85678+1 is a Factor of xGF(85676,3,2)

(This is from the reserved range 80000<=N<=1e5, 3e4<k<5e4; I am expecting a few more.)

gaaa! I hate you!
(doing the range below, only k 1e4<k<3e4)

I found many shiny trinkets, so the search was not entirely futile. I have seven and I am only half done. This also means that you will find on average two times more of them in your range, i.e. over two dozen. What's there to hate?

[QUOTE="Ladies and gentlemen of the class of '99"]
“Don't waste your time on jealousy. Sometimes you're ahead, sometimes you're behind. The race is long, and in the end, it's only with yourself.”
[/QUOTE]

Sieved up to 48.73e12 so far with ppsieve cuda. Am I doing something wrong?
I have around 7M candidate left (and checking with pfgw).
If you are already half done, how many core did you spend on it?

It was a significant amount of cores.

Full results for 80000<N<=10^5, 30000<k<50000 (odd):

[CODE]Found primes : 6443 (expected 6438)
Found xGF factors: 10 (expected 6.1 )
Found GF factors : 0 (expected 0.8 )
Found Fermat factors: 0 (expected 0.17)

Factors:
37027*2^82664+1 is a Factor of xGF(82663,7,2)
49763*2^84445+1 is a Factor of xGF(84444,4,3)
42645*2^85628+1 is a Factor of xGF(85625,10,9)
36255*2^85678+1 is a Factor of xGF(85676,3,2)
45185*2^89463+1 is a Factor of xGF(89462,11,2)
30089*2^89579+1 is a Factor of xGF(89577,11,8)
45267*2^91332+1 is a Factor of xGF(91331,7,6)
47595*2^96095+1 is a Factor of xGF(96093,9,5)
35655*2^96137+1 is a Factor of xGF(96134,3,2)
40311*2^98955+1 is a Factor of xGF(98954,10,7)[/CODE]

I have also reserved 9000<N<=10^4, 5e6<k<5.2e6; and it's done:
30488 primes found (expected 30360). No factors of any kind (expected 0.25).

I have also reserved 100e3<N<=150e3, 1e4<k<2e4; and it's in progress.
So far, found a GF (of the xGF type, GF(11) don't have a special webpage):
[FONT=Courier New]11565*2^101166+1 is a Factor of GF(101164,11)[/FONT]
[FONT=Courier New]17467*2^101822+1 is a Factor of xGF(101820,8,5)[/FONT]

my first xGF factor...
submitted to the prime database and soon to W.Keller once I get a fistfull.
23705*2^80025+1 is a Factor of xGF(80024,10,3)!!!!

MM127
 

[CODE][Tue Oct 30 02:40:04 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 8200T to 8250T (181-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]
[Wed Oct 31 20:26:54 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 8250T to 8300T (181-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]
[Fri Nov 02 14:14:55 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 8300T to 8350T (181-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]
[Sun Nov 04 08:02:03 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 8350T to 8400T (181-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]
[Tue Nov 06 01:49:34 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 8400T to 8450T (181-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]
[Wed Nov 07 19:36:28 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 8450T to 8500T (181-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]


[Tue Oct 30 02:13:57 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 8500T to 8550T (181-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]
[Wed Oct 31 20:00:48 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 8550T to 8600T (181-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]
[Fri Nov 02 13:47:51 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 8600T to 8650T (181-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]
[Sun Nov 04 07:35:22 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 8650T to 8700T (181-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]
[Tue Nov 06 01:22:59 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 8700T to 8750T (181-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]
[Wed Nov 07 19:10:10 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 8750T to 8800T (181-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]


[Wed Oct 31 15:51:42 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 10000T to 10100T (182-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]
[Fri Nov 02 05:20:09 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 10100T to 10200T (182-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]
[Sat Nov 03 18:27:16 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 10200T to 10300T (182-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]
[Mon Nov 05 06:10:46 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 10300T to 10400T (182-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]
[Wed Nov 07 01:53:16 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 10400T to 10500T (182-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]


[Wed Oct 31 13:20:55 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 10500T to 10600T (182-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]
[Fri Nov 02 06:19:26 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 10600T to 10700T (182-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]
[Sat Nov 03 17:19:42 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 10700T to 10800T (182-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]
[Mon Nov 05 03:55:37 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 10800T to 10900T (182-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs]
[Tue Nov 06 14:31:32 2012]
UID: aketilander/OBD, no factor for MM127 in k range: 10900T to 11000T (182-bit factors) [mmff 0.26 mfaktc_barrett183_M127gs][/CODE]

[CODE]no factor for k*2^88+1 in k range: 281000000000000 to 281474976710655 (136-bit factors) [mmff 0.26 mfaktc_barrett140_F64_95gs]
no factor for k*2^88+1 in k range: 281474976710656 to 562949953421311 (137-bit factors) [mmff 0.26 mfaktc_barrett140_F64_95gs]
no factor for k*2^88+1 in k range: 562949953421312 to 1000000000000000 (138-bit factors) [mmff 0.26 mfaktc_barrett140_F64_95gs]
[/CODE]

[CODE]no factor for k*2^96+1 in k range: 281000000000000 to 281474976710655 (144-bit factors) [mmff 0.26 mfaktc_barrett152_F96_127gs]
no factor for k*2^96+1 in k range: 281474976710656 to 562949953421311 (145-bit factors) [mmff 0.26 mfaktc_barrett152_F96_127gs]
no factor for k*2^96+1 in k range: 562949953421312 to 1000000000000000 (146-bit factors) [mmff 0.26 mfaktc_barrett152_F96_127gs]
[/CODE]

[CODE]no factor for k*2^45+1 in k range: 1000000000000000 to 1125899906842623 (95-bit factors) [mmff 0.26 mfaktc_barrett96_F32_63gs]
no factor for k*2^45+1 in k range: 1125899906842624 to 2000000000000000 (96-bit factors) [mmff 0.26 mfaktc_barrett96_F32_63gs]

no factor for k*2^48+1 in k range: 1000000000000000 to 1125899906842623 (98-bit factors) [mmff 0.26 mfaktc_barrett108_F32_63gs]
no factor for k*2^48+1 in k range: 1125899906842624 to 2000000000000000 (99-bit factors) [mmff 0.26 mfaktc_barrett108_F32_63gs][/CODE]