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-   ElevenSmooth (https://www.mersenneforum.org/forumdisplay.php?f=31)

 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[/code]

[url]http://factordb.com/index.php?id=1100000000192858108[/url]

which completes the factorization of [url]http://factordb.com/index.php?id=1000000000012151704[/url] among others...

 Batalov 2017-09-01 06:25

... Hopefully as an [URL="http://factordb.com/index.php?id=1100000000964959181"]easy[/URL] SNFS? :rolleyes:

 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) [URL="http://factordb.com/index.php?query=2%5E864+%2B+2%5E792+-+2%5E648+-+2%5E576+%2B+2%5E432+-+2%5E288+-+2%5E216+%2B+2%5E72+%2B+1"]c256 cofactor[/URL]. 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 - ([COLOR=Blue]t^6+t^5-6*t^4-6*t^3+8*t^2+8*t+1[/COLOR])
0

% simply use x = 2^72
[/CODE]

 swellman 2017-09-03 12:01

[QUOTE=Batalov;466954]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) [/quote]

Ryan is factoring it now. Others may be feasible going forward. Thanks for the [url=https://en.m.wiktionary.org/wiki/give_a_man_a_fish_and_you_feed_him_for_a_day;_teach_a_man_to_fish_and_you_feed_him_for_a_lifetime]fishing lesson[/url]!

 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. :davieddy:

 xilman 2017-09-03 17:45

[QUOTE=swellman;466980]Ryan is factoring it now. Others may be feasible going forward. Thanks for the [url=https://en.m.wiktionary.org/wiki/give_a_man_a_fish_and_you_feed_him_for_a_day;_teach_a_man_to_fish_and_you_feed_him_for_a_lifetime]fishing lesson[/url]![/QUOTE]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
[/code]

Results posted at factordb.

 swellman 2017-09-06 20:46

[QUOTE=Batalov;466954]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) [URL="http://factordb.com/index.php?query=2%5E864+%2B+2%5E792+-+2%5E648+-+2%5E576+%2B+2%5E432+-+2%5E288+-+2%5E216+%2B+2%5E72+%2B+1"]c256 cofactor[/URL]. 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 - ([COLOR=Blue]t^6+t^5-6*t^4-6*t^3+8*t^2+8*t+1[/COLOR])
0

% simply use x = 2^72
[/CODE][/QUOTE]

Ryan has factored this c256, thanks to Batalov's guidance here (and in an [url=http://www.mersenneforum.org/showthread.php?t=17666]

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

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

Always open to more suggestions!

 rcv 2017-09-08 07:37

Is the c156 of 2^1344+1 of interest? [URL]http://www.factordb.com/index.php?id=1100000000032321623[/URL]

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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