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Old 2012-10-26, 08:21   #45
Batalov
 
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Phi(4,2^7658614+1)/2

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And one more, ...a good test for 0.27 (almost the verge of the new range):
Code:
GF(176,5) has a factor: 50553187030816197905138650389585873825862849611206916638597185537 [TF:214:215:mmff-gfn5 0.27 mfaktc_barrett215_F160_191gs]
found 1 factor for k*2^177+1 in k range: 200000000000 to 274877906943 (215-bit factors) [mmff-gfn5 0.27 mfaktc_barrett215_F160_191gs]
 
pfgw -f -gxo -q"263899949763*2^177+1"
PFGW Version 3.6.0.64BIT.20111222.x86_Dev [GWNUM 26.6]
263899949763*2^177+1 is a Factor of GF(176,5)
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Old 2012-10-26, 17:20   #46
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4366097300905*2^114+1 is a Factor of GF(112,5)
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Old 2012-10-26, 17:56   #47
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why don't I find any factor? tell me whyyyyyyyyy.

_____
SB: As they say at some card tables, "if you lost so much, you must be lucky with women!"

Last fiddled with by Batalov on 2012-10-26 at 18:15
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Old 2012-10-27, 01:28   #48
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Don't complain, because you win some -- you lose some.
Law of nature.
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Old 2012-10-30, 19:59   #49
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2 factors for gfn6

204723303114760756658177
11916464608789*2^34+1 is a Factor of GF(33,6)!!!!
and
3165784609160494361608193
11517057315943*2^38+1 is a Factor of GF(37,6)!!!!
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Old 2012-10-30, 20:30   #50
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Excellent! (The 2nd has a prime k, too: k=11517057315943.)
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Old 2012-11-05, 04:08   #51
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11647*2^107984+1 is a Factor of GF(107983,5)
11565*2^101166+1 is a Factor of GF(101164,11)
13485*2^110472+1 is a Factor of GF(110470,3) <-- was known from 2004. But not the other two.

And one more (07-Nov):
19289*2^141945+1 is a Factor of GF(141944,6)

And one more (09-Nov):
7490067*2^9196+1 is a Factor of GF(9195,10)

Last fiddled with by Batalov on 2012-11-09 at 22:32
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Old 2012-11-07, 18:11   #52
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322504582089*2^178+1 is a Factor of GF(173,12)
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Old 2012-11-07, 18:18   #53
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factor for gfn12

813463720888202755571713
11837455107717*2^36+1 is a Factor of GF(30,12)!!!!
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Old 2012-11-07, 18:35   #54
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Both factors have quite large n-m (see stats at the bottom of GFN12 page). That's rare and nice.
Code:
                Count of factors according to difference n − m 
                      n − m   = 1,  2,  3,  4,  5, 6, 7, 8 
Frequency 144, 66, 50, 20, 14, 2, 4, 1
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Old 2012-11-10, 06:04   #55
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8689209*2^8459+1 is a Factor of GF(8458,10)
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