New Generalized Fermat factors - Page 5

Batalov · 2012-10-26, 08:21

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)

Batalov · 2012-10-26, 17:20

4366097300905*2^114+1 is a Factor of GF(112,5)

firejuggler · 2012-10-26, 17:56

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!"

Batalov · 2012-10-27, 01:28

Don't complain, because you win some -- you lose some.
Law of nature.

lalera · 2012-10-30, 19:59

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)!!!!

Batalov · 2012-10-30, 20:30

Excellent! (The 2nd has a prime k, too: k=11517057315943.)

Batalov · 2012-11-05, 04:08

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)

Batalov · 2012-11-07, 18:11

322504582089*2^178+1 is a Factor of GF(173,12)

lalera · 2012-11-07, 18:18

factor for gfn12

813463720888202755571713
11837455107717*2^36+1 is a Factor of GF(30,12)!!!!

Batalov · 2012-11-07, 18:35

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

Batalov · 2012-11-10, 06:04

8689209*2^8459+1 is a Factor of GF(8458,10)

2012-10-26, 17:56	#47
firejuggler Apr 2010 Over the rainbow 3²·281 Posts	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

2012-11-05, 04:08	#51
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2×4,663 Posts	116472^107984+1 is a Factor of GF(107983,5) 115652^101166+1 is a Factor of GF(101164,11) 134852^110472+1 is a Factor of GF(110470,3) <-- was known from 2004. But not the other two. And one more (07-Nov): 192892^141945+1 is a Factor of GF(141944,6) And one more (09-Nov): 74900672^9196+1 is a Factor of GF(9195,10) Last fiddled with by Batalov on 2012-11-09 at 22:32*

2012-11-07, 18:35	#54
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2×4,663 Posts	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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2012-10-26, 17:20	#46
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2·4,663 Posts	4366097300905*2^114+1 is a Factor of GF(112,5)

2012-10-27, 01:28	#48
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2×4,663 Posts	Don't complain, because you win some -- you lose some. Law of nature.

2012-10-30, 19:59	#49
lalera Jul 2003 3·7·29 Posts	2 factors for gfn6 204723303114760756658177 119164646087892^34+1 is a Factor of GF(33,6)!!!! and 3165784609160494361608193 115170573159432^38+1 is a Factor of GF(37,6)!!!!

2012-10-30, 20:30	#50
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2×4,663 Posts	Excellent! (The 2nd has a prime k, too: k=11517057315943.)

2012-11-07, 18:11	#52
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2×4,663 Posts	322504582089*2^178+1 is a Factor of GF(173,12)

2012-11-07, 18:18	#53
lalera Jul 2003 3×7×29 Posts	factor for gfn12 813463720888202755571713 11837455107717*2^36+1 is a Factor of GF(30,12)!!!!

2012-11-10, 06:04	#55
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 10010001101110₂ Posts	8689209*2^8459+1 is a Factor of GF(8458,10)