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Old 2017-09-01, 03:01   #23
ryanp
 
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And, done:

Code:
Thu Aug 31 19:15:20 2017  p69 factor: 189544322054778406106783278305473855966156308749994212723035497262401
Thu Aug 31 19:15:20 2017  p129 factor: 269073025737038601189586073069718594269124014102942601018050284891961011087805779825917499111420125551704003880408433450484724161
http://factordb.com/index.php?id=1100000000192858108

which completes the factorization of http://factordb.com/index.php?id=1000000000012151704 among others...
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Old 2017-09-01, 06:25   #24
Batalov
 
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Phi(4,2^7658614+1)/2

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... Hopefully as an easy SNFS?
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Old 2017-09-02, 21:35   #25
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Any suggestions for further factoring efforts? A GNFS 213 seems excessive. And I've got no eye for some of these SNFS polys...
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Old 2017-09-03, 01:48   #26
Batalov
 
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There is at least one more composite actually easier than that c197 (which was a snfs-289 that was in turn easier than gnfs-197).

It is the M(3024) c256 cofactor. It is a snfs-260, really easy. (3024/2 is divisible by 21)
Code:
? t=x+1/x
(x^2 + 1)/x

? polcyclo(42)/x^6 - (t^6+t^5-6*t^4-6*t^3+8*t^2+8*t+1)
0

% simply use x = 2^72
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Old 2017-09-03, 12:01   #27
swellman
 
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Quote:
Originally Posted by Batalov View Post
There is at least one more composite actually easier than that c197 (which was a snfs-289 that was in turn easier than gnfs-197).

It is the M(3024)
Ryan is factoring it now. Others may be feasible going forward. Thanks for the fishing lesson!
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Old 2017-09-03, 16:54   #28
Batalov
 
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I once met someone who told me "Fear not; from henceforth thou shalt fish for men."

Oh... Wait... It was a dream.
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Old 2017-09-03, 17:45   #29
xilman
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Quote:
Originally Posted by swellman View Post
Ryan is factoring it now. Others may be feasible going forward. Thanks for the fishing lesson!
Light a man a fire and you warm him for a night. Set a man on fire and you warm him for the rest of his life.
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Old 2017-09-03, 18:07   #30
Batalov
 
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โ€œSuccess isn't a result of spontaneous combustion. You must set yourself on fire.โ€
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Old 2017-09-04, 20:39   #31
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ECM has revealed a p59 factor of M(8640), a c648, leaving a C590 cofactor. ECM continues. All found by Ryan Propper.

Code:
p59=40992157914500402652351432573337743164884786549994004382081
Results posted at factordb.

Last fiddled with by swellman on 2017-09-04 at 21:00
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Old 2017-09-06, 20:46   #32
swellman
 
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Quote:
Originally Posted by Batalov View Post
There is at least one more composite actually easier than that c197 (which was a snfs-289 that was in turn easier than gnfs-197).

It is the M(3024) c256 cofactor. It is a snfs-260, really easy. (3024/2 is divisible by 21)
Code:
? t=x+1/x
(x^2 + 1)/x

? polcyclo(42)/x^6 - (t^6+t^5-6*t^4-6*t^3+8*t^2+8*t+1)
0

% simply use x = 2^72
Ryan has factored this c256, thanks to Batalov's guidance here (and in an
old thread discussing cyclotomic factorizations
).

http://factordb.com/index.php?id=1100000000017309404

which completes http://factordb.com/index.php?id=1000000000012151536
and many others.

Always open to more suggestions!
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Old 2017-09-08, 07:37   #33
rcv
 
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Is the c156 of 2^1344+1 of interest? http://www.factordb.com/index.php?id...00000032321623

The exponent has one too many factors of 2 to be among William Lipp's "official" eleven-smooth numbers. (1344=2^6*3*7). And it's just beyond the official Cunningham Table limits. Factor isn't presently shown in factordb or jcrombie's database.
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