Status - Page 3

ryanp · 2017-09-01, 03:01

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...

Batalov · 2017-09-01, 06:25

... Hopefully as an easy SNFS?

swellman · 2017-09-02, 21:35

Any suggestions for further factoring efforts? A GNFS 213 seems excessive. And I've got no eye for some of these SNFS polys...

Batalov · 2017-09-03, 01:48

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

swellman · 2017-09-03, 12:01

Quote:

Originally Posted by Batalov

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!

Batalov · 2017-09-03, 16:54

I once met someone who told me "Fear not; from henceforth thou shalt fish for men."

Oh... Wait... It was a dream.

xilman · 2017-09-03, 17:45

Quote:

Originally Posted by swellman

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.

Batalov · 2017-09-03, 18:07

“Success isn't a result of spontaneous combustion. You must set yourself on fire.”

swellman · 2017-09-04, 20:39

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.

swellman · 2017-09-06, 20:46

Quote:

Originally Posted by Batalov

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!

rcv · 2017-09-08, 07:37

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.

2017-09-03, 01:48	#26
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2749₁₆ Posts	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^5-6t^4-6t^3+8t^2+8t+1) 0 % simply use x = 2^72

2017-09-04, 20:39	#31
swellman Jun 2012 2³·13·37 Posts	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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2017-09-01, 06:25	#24
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 89×113 Posts	... Hopefully as an easy SNFS?

2017-09-02, 21:35	#25
swellman Jun 2012 3848₁₀ Posts	Any suggestions for further factoring efforts? A GNFS 213 seems excessive. And I've got no eye for some of these SNFS polys...

2017-09-03, 16:54	#28
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 89×113 Posts	I once met someone who told me "Fear not; from henceforth thou shalt fish for men." Oh... Wait... It was a dream.

2017-09-03, 18:07	#30
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 10057₁₀ Posts	“Success isn't a result of spontaneous combustion. You must set yourself on fire.”

2017-09-08, 07:37	#33
rcv Dec 2011 11×13 Posts	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=2^637). And it's just beyond the official Cunningham Table limits. Factor isn't presently shown in factordb or jcrombie's database.