73 digit ECM factor

[xilman]

Originally Posted by bdodson

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

Do we know the group order? It's possible that only a small fraction of the (normally) indicated B2 range was run.


Paul

[Mini-Geek]

Originally Posted by xilman

Do we know the group order? It's possible that only a small fraction of the (normally) indicated B2 range was run.


Paul

[ <2, 4>, <3, 1>, <11, 1>, <20021, 1>, <556007, 1>, <717419, 1>, <2342731, 1>, 
<3724261, 1>, <61043881, 1>, <245849333, 1>, <84498517303, 1> ]

Min. B1 ~= 2.46e8, min. B2 ~= 8.45e10

[bdodson]

Originally Posted by Mini-Geek

[ <2, 4>, <3, 1>, <11, 1>, <20021, 1>, <556007, 1>, <717419, 1>, <2342731, 1>, 
<3724261, 1>, <61043881, 1>, <245849333, 1>, <84498517303, 1> ]

Min. B1 ~= 2.46e8, min. B2 ~= 8.45e10

So B1=3e9 with B2=103971375307818 = 1.04e14 would have more
than sufficed. This number wasn't on their June curve count list for
B1 = 3e9. Maybe they wanted a smaller number for a test case with
the new B1? Uhm, err ... or perhaps the c212 was a gnfs candidate?

-Bruce

[Batalov]

Command line unix ecm "found" the p59 too, - with a default param curve at B1=260e6 (3e9 would have been 11 times longer)
Step 1 took 1474 048ms
Step 2 took 681 698ms

[xilman]

Originally Posted by Batalov

Command line unix ecm "found" the p59 too, - with a default param curve at B1=260e6 (3e9 would have been 11 times longer)
Step 1 took 1474 048ms
Step 2 took 681 698ms

Mystery solved. Paul (the other one) has posted a report from Thorsten that B1 was actually 2.6e8 and that the factor was found on a PC.

Paul (this one)

[bdodson]

Originally Posted by xilman

Mystery solved. Paul (the other one) has posted a report from Thorsten that B1 was actually 2.6e8 and that the factor was found on a PC.

Paul (this one)

Yes, thanks. The cgi line is now saying

260e6

too. Just to remove any possible question, here's the log Thorsten
sent to PaulZ and Sam (as posted to ECMNET by PaulZ)

Input number is 
49065003020440088020233565530981034575278730829197795102034752497286737689958440672064128091671366305592919451423049625508883886628462923775201492141273267361171535761978676893172985484995759934256009764879575937 
(212 digits)
Using B1=260000000, B2=3178559884516, polynomial Dickson(30), 
sigma=260003949
Step 1 took 3020468ms
Step 2 took 1116034ms
********** Factor found in step 2: 
46654722984595033623595915319018639089714063407438899506169
Found probable prime factor of 59 digits: 
46654722984595033623595915319018639089714063407438899506169
Probable prime cofactor 
1051662080099391159250990850668031334695175372192528921233670913813412325120288431142374453093538999808223119264936281688325783724087706106729415181782473 
has 154 digits

so step1 was done on the "pc". This number is from the range that got
just barely over t55 (at c. 6t50), so the p59 no longer appears to have
arrived out of order; right in-range for a search of ecm factors in [p57,p62]
after no (more) factors found in t55. -Bruce

[bdodson]

Originally Posted by bdodson

Here's the (n+1)st:

p59=46654722984595033623595915319018639089714063407438899506169
2^937-1  C212	260e6	260003949	2010-10-18  BKLM

[corrected!] -Bruce

Here's another BKLM pc factorization

2, 953- c215 210604142476977747806569755290105170291449495120790656457721
. p115 Bos+Kleinjung+Lenstra+Montgomery ECMNET

also

p60 = 210604142476977747806569755290105170291449495120790656457721	
2^953-1	260e6	260008981 2010-11-07 J.Bos,T.Kleinjung,A.Lenstra,P.Montgomery

-Bruce

[R. Gerbicz]

It is interesting: c215=p60*p115.

[bdodson]

Originally Posted by R. Gerbicz

It is interesting: c215=p60*p115.

Sam's page had c212 = p59 * p212 on the previous epfl pc factor, for
a few days; of equal interest. The ECMNET reports, including PaulZ's
emails, don't include cofactors. -bd

[bdodson]

Originally Posted by bdodson

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. ... -Bruce

After two ECMNET pc factors; here's the next one that appears to
have larger step1, like the ones done on the PS3 network

5978  2, 961- c254 8685373022907062443109907561762261051459356481790933999405609
. p193 Bos+Kleinjung+Lenstra+Montgomery ECMNET

with

p61 = 8685373022907062443109907561762261051459356481790933999405609
2^961-1 1e9 3000011437 2010-11-23 J.Bos,T.Kleinjung,A.Lenstra,P.Montgomery

If the report is correct; the 1e9 is new/smaller than the 3e9 of the previous
PS3 factors, but the sigma looks PS3-ish. -bd

[fivemack]

I had that down as a possible SNFS candidate (to the point that I'd determined parameters), but Bos+Kleinjung+Lenstra+Montgomery have saved a CPU-decade or so.