First ECM in 2 Months!

[R.D. Silverman]

Aoki just found a 60-digit factor of 2,2098M with ECM.

This is the first new ECM factor in two months and I believe
is the longest period without a Cunningham ECM factor since
ECM was invented.

Unfortunately, the cofactor is still composite......

[Andi47]

Congrats to Aoki!

Just curious: What is the factor and the cofactor?

[bdodson]

Originally Posted by Andi47

Congrats to Aoki!

Just curious: What is the factor and the cofactor?

Google reports

2,2098M c281 = p58 * c224, on September 28, 2005

where the p58 is PaulZ's p58 Cunningham p-1 record. So a new
p60 would be 224-60 = 164 +/- 1. The p60 isn't up on either
Sam's or Paul's pages (Cunningham & ecmnet, respectively). Maybe
the p60 ruined a gnfs prospect in the c224? -Bruce

[xilman]

Originally Posted by bdodson

Google reports

2,2098M c281 = p58 * c224, on September 28, 2005

where the p58 is PaulZ's p58 Cunningham p-1 record. So a new
p60 would be 224-60 = 164 +/- 1. The p60 isn't up on either
Sam's or Paul's pages (Cunningham & ecmnet, respectively). Maybe
the p60 ruined a gnfs prospect in the c224? -Bruce

I've not heard of the details yet, so it won't be on my pages for that reason.

Paul

[xilman]

Originally Posted by bdodson

Google reports

2,2098M c281 = p58 * c224, on September 28, 2005

where the p58 is PaulZ's p58 Cunningham p-1 record. So a new
p60 would be 224-60 = 164 +/- 1. The p60 isn't up on either
Sam's or Paul's pages (Cunningham & ecmnet, respectively). Maybe
the p60 ruined a gnfs prospect in the c224? -Bruce

Further, I note that a C164 is a reasonable target by GNFS but that a C224 would be remarkably hard.


Paul

[R.D. Silverman]

Originally Posted by bdodson

Google reports

2,2098M c281 = p58 * c224, on September 28, 2005

where the p58 is PaulZ's p58 Cunningham p-1 record. So a new
p60 would be 224-60 = 164 +/- 1. The p60 isn't up on either
Sam's or Paul's pages (Cunningham & ecmnet, respectively). Maybe
the p60 ruined a gnfs prospect in the c224? -Bruce

Huh? It certainly is on Paul's pages.....

http://webloria.loria.fr/~zimmerma/c.../last.cgi?date

[bdodson]

Originally Posted by xilman

Further, I note that a C164 is a reasonable target by GNFS but that a C224 would be remarkably hard.

Paul

p60 = 237192716367319808525419681995440718925568206987372271548097

from the ecmnet page (quickstart; factors-by-date). B1 = 43M, p50-optimal.

The factor is Aoki's, as-in our current snfs record and the Cunningham
gnfs record c176. He previously found a p64 in pretesting for the kilobit
snfs. c224 would be a chance to consolidate post-rsa786 (c233)
observations, perhaps? -Bruce

PS - Ah, Paul's point isn't that Aoki mightn't consider c224 gnfs, so
much as that 2,2098M is now a much more "reasonable" factorization
after the p58 and p60. This p60 is useful; even though it left a
composite cofactor to finish.

(Sorry for the miss-info, I only checked the top10; looks like Bob
had this one before PaulZ's gotten to it!)

[Raman]

Originally Posted by bdodson

p60 = 237192716367319808525419681995440718925568206987372271548097

Is Prof. Sam really aware of this factor? He hasn't included this factor in his web pages so far. Did anybody send a reminder to him up?

I sent an information about this factor by my side. He hasn't responded, even in his web pages.

What happened to him up? Perhaps, has he gone away so for a long vacation, without any access to the internet?

PS: It has been already 5 days. Perhaps, has he also missed out all the factor that were being reported after at this one too?

[bdodson]

Originally Posted by Raman

Is Prof. Sam really aware of this factor? He hasn't included this factor in his web pages so far. Did anybody send a reminder to him up?

I sent an information about this factor by my side. He hasn't responded, even in his web pages.

What happened to him up? Perhaps, has he gone away so for a long vacation, without any access to the internet?

PS: It has been already 5 days. Perhaps, has he also missed out all the factor that were being reported after at this one too?

Relax already. I had an email from him last week. He was reporting having
driven by this part of Pennsylvania, on what sounded like an extended
vacation. For academics not teaching in summer school (or having recently
finished, like myself), we're in a brief break before the start of the new
academic year. He's (almost) certain to catch up on emails by early
September, presuming no unusual interruptions. Also, I don't believe that
we've had additional factor reports. -bd
--

Ah, also, PaulZ's been away for a while; so the ecmnet report (from which
Sam would likely first hear of the factor) just posted this morning. For eg,
the top10 is now updated. Ecmnet factors are reported automatically on
the cgi page referred to above (no worry about them being misplaced). Many
sieving results get reported by email, with multiple copies; as well as being
reported here (and again ...).

[Batalov]

Congratulations to Bruce, too!
348131628285692590860028784957527660987485049321208797343 (p57)
and a top10 hit.

[R.D. Silverman]

Originally Posted by Batalov

Congratulations to Bruce, too!
348131628285692590860028784957527660987485049321208797343 (p57)
and a top10 hit.

Yep. Very nice.

Unfortunately, the cofacor is composite and still too big
to tackle with GNFS.