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 2017-09-01, 03:01 #23 ryanp     Jun 2012 Boulder, CO 52·17 Posts 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...
 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, 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^5-6*t^4-6*t^3+8*t^2+8*t+1) 0 % simply use x = 2^72
2017-09-03, 12:01   #27
swellman

Jun 2012

23×13×37 Posts

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!

 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, 17:45   #29
xilman
Bamboozled!

"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across

89×131 Posts

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.

 2017-09-03, 18:07 #30 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 1005710 Posts โSuccess isn't a result of spontaneous combustion. You must set yourself on fire.โ
 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
2017-09-06, 20:46   #32
swellman

Jun 2012

74108 Posts

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
).

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

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

Always open to more suggestions!

 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=2^6*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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