73 digit ECM factor

[xilman]

Originally Posted by bdodson

So sounds like Eurocrypt gets the RSA768 paper?

It's not here. Not sure where it will appear. Crypto, perhaps, or Asiacrypt?


Paul

[tcadigan]

Originally Posted by xilman

It's not here. Not sure where it will appear. Crypto, perhaps, or Asiacrypt?


Paul

It's on the program for Crypto. rather more specifically at 10:55 Aug. 17th.

[tcadigan]

Originally Posted by tcadigan

It's on the program for Crypto. rather more specifically at 10:55 Aug. 17th.

Just to be complete:
Emmanuel Thome gave the presentation today. With focus on parallel block Wiedemann used in the Linear Algebra.

[warut]

The fourth factor has 68 digits.

5949  2,1139- c313 12947560801881275212486900476122097688373975262784709656768032387833. p246 Bos+Kleinjung+AKLenstra+Montgomery ECMNET

[bdodson]

Originally Posted by warut

The fourth factor has 68 digits.

5949  2,1139- c313 12947560801881275212486900476122097688373975262784709656768032387833. 
p246 Bos+Kleinjung+AKLenstra+Montgomery ECMNET

This would be the fifth BKLM factor (after the new coding). Plus the first
of the two p63's, listed just as Bos+Kleinjung, which is also B1=3e9/PS3/epfl.
There's also a Bos/Kleinjung p61 found with B1=260e6, which wasn't listed
on the epfl report of PS3 factors. That one was after the first p63/PS3, but
before the recoding. All but the p61 and the new p68 are easy to find;
listed in the top10.

Thanks for the early report! (Ah; from Sam's page. The above is from
the ECMNET reports.) -Bruce

(bumps my smaller p62.)

[warut]

Thanks for the correction. I forgot the actual fourth factor by BKLM because it was reported on another thread.

[warut]

Originally Posted by R. Gerbicz

It looks like it was a big luck, found the p66 divisor at the 624th(?) curve (B1=3e9).

Actually, for 2^1073-1, BKLM ran ~25,000 stage 1 on the PS3 cluster (plus an addition 1,460 stage 2 on conventional computers).

[bdodson]

Originally Posted by warut

The fourth factor has 68 digits.

5949  2,1139- c313 12947560801881275212486900476122097688373975262784709656768032387833. p246 Bos+Kleinjung+AKLenstra+Montgomery ECMNET

Here's the (n+1)st:

p59=46654722984595033623595915319018639089714063407438899506169
2^937-1  C212	260e9	260003949	2010-10-18  BKLM

That's B1 = 2.6e11 ... a large new jump again. Just in; I haven't seen
the cofactor (Sam's page isn't updated yet; this is from the ecmnet
cgi page.) -Bruce

[R.D. Silverman]

Originally Posted by bdodson

Here's the (n+1)st:

p59=46654722984595033623595915319018639089714063407438899506169
2^937-1  C212	260e9	260003949	2010-10-18  BKLM

That's B1 = 2.6e11 ... a large new jump again. Just in; I haven't seen
the cofactor (Sam's page isn't updated yet; this is from the ecmnet
cgi page.) -Bruce

The cofactor is prime.

[R.D. Silverman]

Originally Posted by R.D. Silverman

The cofactor is prime.

It's interesting that a p59 was missed at 3 x 10^9......

[bdodson]

Originally Posted by R.D. Silverman

It's interesting that a p59 was missed at 3 x 10^9......

I had a previous p57 ... does seem like the p59 could have been found
earlier. But do we know that 2,937- had a full run with B1=3e9? -Bruce