11- table

[garo]

Size    Base    Index    -    Diff.    Ratio
289	11	307	-	319.7	0.9	
251	11	311	-	323.8	0.99	
273	11	313	-	325.9	0.83	
319	11	317	-	330.1	0.96	
241	11	323	-	336.3	0.71	
344	11	331	-	344.7	0.99	
289	11	341	-	322.8	0.89	/11
294	11	347	-	361.3	0.81	
294	11	349	-	363.4	0.8

[akruppa]

10408 curves at B1=44M on 11,239- c246. Adds 8.02467 to p45, 1.35679 to p50 and 0.20739 to p55.

Alex

[bdodson]

Originally Posted by garo

Base	Index	Size	11M(45digits)	43M(50digits)	110M(55digits)	260M(60digits)	Decimal
11	227-	C195	27(1.05723)	40(0.205612)	630(0.0359772)	0(0.00565555)	984469958461669946331134175269535972678581291606947369505641093816179538386729583149733726284922487111763208303176785082052328807982992331143932131504453741826471251119859743518755983034989796049
11	229-	C217	14(0.270473)	0(0.0527035)	165(0.00921839)	0(0.00148122)	2280535465910720786775600820467952780151520584989210953191513809529995832534442428104555605819675075601827186776697522052785839359025772719189070007046448589601858667341500520544021900960186671447742425444326260994871
11	233-	C181	0(2.09174)	1500(0.38003)	590(0.0622008)	0(0.00529647)	3638029526867914815923489594587285626797533753146123743162290727610791298136033326483795137129428275721080608101533487077148138403910269514725873267506285639199648447372043817068739
11	235-	C182	0(2.09174)	1500(0.38003)	590(0.0622008)	0(0.00529647)	
10835100551974326032210703501349541965554864985688179195139946010601062261364483337942047398597258367633530485886544962131653246266840532801890865424245150043991345331435626089587731
11	239-	C246	0(0.267423)	0(0.0522979)	165(0.00921839)	0(0.00148122)

Speaking of factors of low index Cunninghams (cf 7+ list, p53 today),
here's a 4th hole, and the first report of an 11- factor,

p49 = 1795306125519308524148513029485573280444347858061

finishes 11, 235- C182, difficulty 195. This is also the first 2007 factor
for the old_and_tired P3-cluster (after none from c155-c169s with
difficulty under 220). If I recall, this was a degree 4, so well worth
removing from the snfs list. -Bruce

[bdodson]

Originally Posted by garo

Base	Index	Size	11M(45digits)	43M(50digits)	110M(55digits)	260M(60digits)	Decimal
...
11	251-	C258	0(0.267423)	0(0.0522979)	165(0.00921839)	0(0.00148122)	
487523988211783979202896039197591186290497247428788133724621419935480861329576209528082685233122161122376035778982182492664437004371964856890659726059972977717372420401692847726975957040423244869600265675076595382016275592550169879312507062175071226146047667
...

Short list, more than a year since the last factor; not actually any
shorter after

p51 = 219716501365259540843452614863811940554249320274071

from 11, 251- C258, leaving a c208. -Bruce

[mdettweiler]

Ran 2 curves at B1=11000000, B2=30114149530 on 11,293- C300. No factors found.

[bdodson]

Originally Posted by Anonymous

Ran 2 curves at B1=11000000, B2=30114149530 on 11,293- C300. No factors found.

I hope that you're neither surprized nor dissapointed. I completed tests
to p45 on the complete Cunningham list some time ago, then tests to
t50. More recently, working toward complete tests to 2*t50, I
completed testing the Cunningham numbers at/above C300 to 2*t50. There
are only a few ranges below 2*t50, with still some numbers in c251-c265
that have only been tested to 1.0*p50; and the rest of c266-c299.9
at/above 1.5*t50. [That's with your B1 = 11M being p45-optimal; and
p50-optimal being B1=43M, with t50 taking some 7,700 curves, and 2*t50
representing twice that effort.]

By contrast, the BMtR list is still giving up factors in p45-p49; and several
of the other factoring projects offer even better prospects. Of course,
I might have missed something ....

-Bruce

[mdettweiler]

Originally Posted by bdodson

I hope that you're neither surprized nor dissapointed. I completed tests
to p45 on the complete Cunningham list some time ago, then tests to
t50. More recently, working toward complete tests to 2*t50, I
completed testing the Cunningham numbers at/above C300 to 2*t50. There
are only a few ranges below 2*t50, with still some numbers in c251-c265
that have only been tested to 1.0*p50; and the rest of c266-c299.9
at/above 1.5*t50. [That's with your B1 = 11M being p45-optimal; and
p50-optimal being B1=43M, with t50 taking some 7,700 curves, and 2*t50
representing twice that effort.]

By contrast, the BMtR list is still giving up factors in p45-p49; and several
of the other factoring projects offer even better prospects. Of course,
I might have missed something ....

-Bruce

Oh, I see. One thing I'm a bit confused about, though (being new to factoring and all): if you did all that work, then how come it's not shown in the first post of this thread? (Or is it shown, and I just didn't interpret the data right?)

[bdodson]

Originally Posted by Anonymous

Oh, I see. One thing I'm a bit confused about, though (being new to factoring and all): if you did all that work, then how come it's not shown in the first post of this thread? (Or is it shown, and I just didn't interpret the data right?)

If you're interested in ECM factoring, then you know that success
with ecm reflects its nature as a random algorithm. A link on my home
page reports

An analysis of the ECM efforts for the year 1998, when the first factor of more than 49 digits was found, is given in [link]. The count of 40 - 49 digit factors was Dodson 22; Zimmermann 18; Montgomery 12, but the only factor that counted was Curry's 53 digit factor.

where the link is to one Richard Brent's early lists that you could find
from the ECMNET pages. By contrast, I used just a few months of
cpu time on 3 pcs to set my first record ECM factor in 2003. But,
as distinct from record ECM factors, mid-range ECM factors correlate
well with the amount of work done. The same page reports
"During November 1, 2003 to December 31, 2004 there were 122 Cunningham
factors found by ECMNET, of which 42 were found by Dodson using ....".

If you check the 3rd post from Garo on the "2.0" thread, you'll see that
most of the curves reported in the initial files in each of the sticky
threads in the "Cunningham Tables" sub-forum resulted from emails
between myself and Bob Silverman (first), and then between myself
and Rogue, which were then tabulated by Garo. It was a major effort
on his part, which has provided starting points for most of the posts
in this sub-forum. But the Tables all start from Jan 1, 2005, and no one
has considered updating the curve counts to be worth the effort --- even
keeping the unfactored numbers up to date has been a major effort, in
this case on Alex's part. The fourth, and (so far) the last post on the
2.0-thread is one of my early forum posts, dated 4 July 06, which records
the t45 test I was bringing to your attention in my first reply to your post.
If nothing else, you'd get a flavor of what Garo and Rogue were dealing
with, when they set the initial curve counts.

The factors during 2004 were obtained on a cluster of P3s, and were
mostly obtained from Cunningham numbers of size below 175-digits.
Finishing the t45 test resulted from the release of GMP-ECM-6,
a 64-bit binary supplied by Torbjorn and the arrival here of a cluster
of Opterons (a NFS grant for "major research instrumentation"). Finishing
t50 used a new condor pc/grid, some 700 pcs. Recent work continuing
on the pc/grid brought the 100 smallest Cunninghams up to 7*t50
(including all numbers below c190); the numbers from c190-c233 below
difficulty 250 up to 4*t50, the rest up to 3*t50; and the numbers from
c234-c250 up to 2*t50. The latter parts of that reflected a "life-cycle"
upgrade that replaced some P4s with core2duos, bring the pc count up
to 1000. Finally, many of the curves in the region above c250 I was referring
to in my previous post were done on a quadcore cluster (that has
since been switched over to sieving with a ggnfs binary and .poly povided
by Greg; cf the msieve thread).

So if you want curve counts, you get counts! The counts themselves
are not considered especially interesting; but systematically raising
curve counts (along with B1 bounds/default_B2) tends over time to
remove the smallest factors first. If you click the "by date" link on
the "quick start" page from ECMNET, you'll see that Cunningham factors
below p40 no longer appeared; then that factors below p45 became
rarer; and the most recent 30 factors show that it's more likely to
find a factor of 60-digits or more than to find a factor below 50-digits.
(At least until the most recent quadcore factors from numbers above
c250.) -Bruce

[mdettweiler]

Ah, I see. Yes, I knew that ECM finds factors in a random way, but I had always thought that there was an "optimal number of curves" to do at a certain B1 value before moving on to the next level. Thanks for the explanation, though!

[R.D. Silverman]

Originally Posted by Anonymous

Ah, I see. Yes, I knew that ECM finds factors in a random way, but I had always thought that there was an "optimal number of curves" to do at a certain B1 value before moving on to the next level.

There is. Nothing Bruce said contradicted this.
You need to read my joint paper with Sam Wagstaff Jr:
"A Practical Analysis of the Elliptic Curve Factoring Algorithm"
in Math. Comp.

It discusses two different optimizations.

(1) How to select parameters when you are going to spend a
*fixed* amount of time.
(2) How to select parameters to maximize the probability of success
per unit time spent.

[bdodson]

Originally Posted by bdodson

If you're interested in ECM factoring, ...

If you click the "by date" link on
the "quick start" page from ECMNET, you'll see that Cunningham factors
below p40 no longer appeared; then that factors below p45 became
rarer; and the most recent 30 factors show that it's more likely to
find a factor of 60-digits or more than to find a factor below 50-digits.
(At least until the most recent quadcore factors from numbers above
c250.) -Bruce

ECMNET/loria.fr was down over the weekend, and my recollection
was flawed here. There were a bunch of smallish factors from my
run towards a 2nd t50 on the c251-c384 Cunninghams; but even
those were more likely to be p5x than p4x. The link I was referring
to is

http://www.loria.fr/~zimmerma/cgi-bin/last.cgi?date

which lists 767 Cunningham factors reported to the ECMNET page
since Jan 1, 2000. Nov 1, 2003 is at #354; which is where the
count of factors from the P3 cluster started (iirc). The last 30 reports
(which included most of the least tested range) is #738-#767 of which
there are two factors below p50 (both p48s) and two factors above
p59.99 (p62 and p66), the rest p5x's. Looks like I was recalling a somewhat
earlier stretch, which included the p60 at #735, but not the p48 at
#731.

So the claim that there were "more p6x's than p4x's" is correct for
a range of 30 factors starting after #731, which gives 3-to-2, with
the other 25 being p5x's. Checking the Cunningham site of recent
factors (all methods), page 108 has the five most recent ECMNET/Dodson
factors; two from the tail end of the 3rd t50 on c190-c234; two
from the quadcore run on c251-c279 (with c266-c279 complete to
1.5*t50, the +0.5*t50 only partial on c251-c265) and the most recent
p57 from the current Childers/Dodson number. Checking the previous
page 107 fills in the two most recent p48s at #5587 and #5592 (in Sam's
numbering) and the last three ECMNET/Dodson factors were all from
c266-c299.

Hmm. So the most recent 30 (as distinct from a somewhat earlier
"most recent" 30) reflects two recent p48s, and bunches of small
p5xs, with no quadcore p6x. Anyway. It's clear that the p45-optimal
B1 = 11M is not the most likely place to look. By contrast, the current
#1 on the top10 of 2008 was found by PaulZ, a p66 with p50-optimal
B1=43M; but I'd bet that the number of curves was in 5-digits, maybe
6-digits. -Bruce