20170901, 03:01  #23 
Jun 2012
Boulder, CO
2^{3}·41 Posts 
And, done:
Code:
Thu Aug 31 19:15:20 2017 p69 factor: 189544322054778406106783278305473855966156308749994212723035497262401 Thu Aug 31 19:15:20 2017 p129 factor: 269073025737038601189586073069718594269124014102942601018050284891961011087805779825917499111420125551704003880408433450484724161 which completes the factorization of http://factordb.com/index.php?id=1000000000012151704 among others... 
20170902, 21:35  #25 
Jun 2012
3,203 Posts 
Any suggestions for further factoring efforts? A GNFS 213 seems excessive. And I've got no eye for some of these SNFS polys...

20170903, 01:48  #26 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9572_{10} Posts 
There is at least one more composite actually easier than that c197 (which was a snfs289 that was in turn easier than gnfs197).
It is the M(3024) c256 cofactor. It is a snfs260, really easy. (3024/2 is divisible by 21) Code:
? t=x+1/x (x^2 + 1)/x ? polcyclo(42)/x^6  (t^6+t^56*t^46*t^3+8*t^2+8*t+1) 0 % simply use x = 2^72 
20170903, 12:01  #27  
Jun 2012
3,203 Posts 
Quote:


20170903, 16:54  #28 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}·2,393 Posts 
I once met someone who told me "Fear not; from henceforth thou shalt fish for men."
Oh... Wait... It was a dream. 
20170903, 17:45  #29  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2ACC_{16} Posts 
Quote:


20170903, 18:07  #30 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2564_{16} Posts 
โSuccess isn't a result of spontaneous combustion. You must set yourself on fire.โ

20170904, 20:39  #31 
Jun 2012
110010000011_{2} 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 Last fiddled with by swellman on 20170904 at 21:00 
20170906, 20:46  #32  
Jun 2012
3,203 Posts 
Quote:
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! 

20170908, 07:37  #33 
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" elevensmooth 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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