ECM Efforts

[Mystwalker]

According to Dario Alpern's applet, it is.

[R.D. Silverman]

Originally Posted by bdodson

Ah, you'd think that I would have looked there first; just there
didn't seem to be any recent activity on this thread. But now that
I have the current counts, the three remaining Pn's on Bob's list
have already been over-run. Montgomery reports that these
have snfs difficulty 194; 199 and 204 (with the one that factored
at 190; figures that the hard ones would be left), which is likely
the reason Bob's chosen them. The effort spent on ecm pretesting
is way past the optimal percentage of the sieving time, so perhaps
Bob agrees that he's willing to risk sieving without further ecm, freeing
up the curves for something more likely to have a factor in ecm range?

If so, do we know where testing on the other three,

> 2,1322M, 2,1334L, 2,1342L

stands? Incidently, an update on this morning's post, Sean Irving
has added the new c135 to his gnfs queue, so we may reliably expect
factors in the near future.
Bruce

Hi,

I agree that we have run enough trials on the 2+ numbers. I am about
70% done with 2,749+. 2,791+ is queued. I will then do 2,969+ and
2,993+ before doing the LM's.

I only have 3 PC's..... (and one is part time)

The recent (and excellent!) work by Bruce still shows that there are
p45 to p50 factors remaining in the base 2 tables (he just found 3 more,
finishing 2,1091- and 2,943+ and finding a p49 of 2,1157+)

I wish I had his resources......

[bdodson]

Originally Posted by rogue

Both have enough curves at B1=11e6. 1334L has 40 curves at B1=43e6 and 630 at 11e7.

2,1342L had this factor submitted recently 312689963186011191785543941405234534125118895633. I believe that the cofactor 312119007097134742328978209700769058421902458121821582805367454109670158835039663246756558186935608062761438029523087241093 is prime.

Ah, these are the 2LM's with smallest exponent; 2,1322M C175 and
2,1334M C186. And those curve counts sound rather familiar, since
they're my curves? I was wondering about curves run by someone else,
perhaps in response to this thread. Also, the C175 "curves at B1=11e6"
were 2500 curves at B1=43e6, for c. 1.75-times a test to p45. By
contast, the 40 curves at B1=43M and 630 at 11e7 was my equivalent of
"curves to B1=11e6," rather than an addition to a previous test to p45.
Or do you know of someone else (possibly a group of someones) having
run a complete test to p45 on either of these numbers? The previous
2+ counts should be OK, since neither you nor Bob mentioned translating
my curve counts and reporting them to George?

I was happy to share curve counts for other people running curves to
know which limits to set, but ambiguities leading to double counts aren't
good --- in particular, for deciding whether numbers are ready for sieving.

Bruce

[rogue]

Originally Posted by bdodson

2,1334M C186. And those curve counts sound rather familiar, since
they're my curves? I was wondering about curves run by someone else,
perhaps in response to this thread. Also, the C175 "curves at B1=11e6"
were 2500 curves at B1=43e6, for c. 1.75-times a test to p45. By
contast, the 40 curves at B1=43M and 630 at 11e7 was my equivalent of
"curves to B1=11e6," rather than an addition to a previous test to p45.
Or do you know of someone else (possibly a group of someones) having
run a complete test to p45 on either of these numbers? The previous
2+ counts should be OK, since neither you nor Bob mentioned translating
my curve counts and reporting them to George?

Yes, those are your curve counts. You indicated to me (via PM) that all composites under 176 digits had enough curves at 11e6. Did I misintepret your statement? I don't have the PM in front of me, so I do recall your exact wording.

Paul Zimmerman's site doesn't indicate that additional curves were run. I'm unaware of anyone else running curves for those numbers. If they are, then they haven't reported them in the ECM Status forum. I have not sent any curve counts to George. When garo returns from vacation, we will try to get the curve counts (for all composites) straightened out and get the info to George and Paul.

[geoff]

Originally Posted by bdodson

Ah, these are the 2LM's with smallest exponent; 2,1322M C175 and 2,1334M C186. And those curve counts sound rather familiar, since they're my curves? I was wondering about curves run by someone else, perhaps in response to this thread.

On 2,1334L I have done 1763 curves at B1=11e6 and 202 curves at B1=43e6 that don't show in the c120-355 curve counts yet.

edit: Also, on 2,1342M (now third hole) I have done 600 curves at B1=43e6.

[R.D. Silverman]

Originally Posted by bdodson

Ah, these are the 2LM's with smallest exponent; 2,1322M C175 and
2,1334M C186. And those curve counts sound rather familiar, since
they're my curves? I was wondering about curves run by someone else,
perhaps in response to this thread. Also, the C175 "curves at B1=11e6"
were 2500 curves at B1=43e6, for c. 1.75-times a test to p45. By
contast, the 40 curves at B1=43M and 630 at 11e7 was my equivalent of
"curves to B1=11e6," rather than an addition to a previous test to p45.
Or do you know of someone else (possibly a group of someones) having
run a complete test to p45 on either of these numbers? The previous
2+ counts should be OK, since neither you nor Bob mentioned translating
my curve counts and reporting them to George?

I was happy to share curve counts for other people running curves to
know which limits to set, but ambiguities leading to double counts aren't
good --- in particular, for deciding whether numbers are ready for sieving.

Bruce

I did translate the curve counts (from your email) and sent them to George.
He has already added them into his tables.

[Prime95]

Originally Posted by R.D. Silverman

I did translate the curve counts (from your email) and sent them to George.
He has already added them into his tables.

Based on that email I added 6000 curves at 44 million to the tables (and marked 11,000,000 done). So any curves at 44,000,000 in excess of 6,000 was done by other users.

[bdodson]

Originally Posted by rogue

Yes, those are your curve counts. You indicated to me (via PM) that all composites under 176 digits had enough curves at 11e6. Did I misintepret your statement? I don't have the PM in front of me, so I do recall your exact wording.

Paul Zimmerman's site doesn't indicate that additional curves were run. I'm unaware of anyone else running curves for those numbers. If they are, then they haven't reported them in the ECM Status forum. I have not sent any curve counts to George. When garo returns from vacation, we will try to get the curve counts (for all composites) straightened out and get the info to George and Paul.

There is an ambiguity about reporting 11e6 as being done, based on
translations of curves run with larger limits. For the c192, my email reported
the 40 curves with B1=43M and c. 600 curves with B1=110M (all ecm6
curves). My intention would have been to have 11e6 marked as "no
additional curves needed" --- "not needed", for short. But when I
read "DONE" in the 11e6 column of ecmp.htm, I took that to mean that
someone actually ran 10,600 curves with b1=11M (or some translation
of that, to curves with B2=100*B1), in addition to the curves I ran.

George's post (if I'm now reading correctly), says P969 had (an equivalent
of) 10753 - 6000 = 4753 B1=44M total curves (including, perhaps, some
combination of 11M curves and 44M curves), with the "Done" in the
11e6 column to be ignored. I suppose you and garo had better follow
that format as well! Likewise, P993 has 8155 - 6000 = 2155. Since
CWI/Montgomery are sieving numbers of this difficulty after c. 25% of
a test for p50's, which is c. 5000 b1=44M with b2=100*b1 curves, the
ecm pretesting conclusion on these two seems to be OK. (For a better
margin, 33% would have been c. 6500, and we're also past that.)
[Since Bob has mis-reported my counts on these numbers (see below),
P969 is OK, but P993 may still be a bit short.]

This reduces the unknowns here to how Bob arrived at 6000 B1=44M
curves (and a few minor issues such as why he neglected to wait for
my reply when he said "I'll translate these counts and send them to
George, OK?"). For readers aside from Mark and Bob, the 6000's added
at various locations in the Mn and Pn tables are supposed to mean, first,
that the remaining cofactor is between c136 and c195. The actual curves
and limits depend upon 3 subdivisions (five if one wishes to be picky
and/or precise), c136-c145, c146-c175 and c176-c195; but the executive
summary is that all of these had enough curves run to mark 11e6 as
"Done". If that means 10600*11e6, then a factor of (11e6/44e6) applied
to 10600 would suggest 2650*44e6. Ooops. So Bob OUGHT to be
reporting 6000 curves on just one of the five divisions, c146-c155. For
c136-c145 and c176-c195, "Done" in 11e6 and 2650 in 44e6 is the
correct use of George's system, and for c156-c175 "Done and 4690".
(Bob's prefered factor of 2 for translation double counts the B2 difference
between prime95 and ecm6, since my report to him already included a factor
for that difference.) That's for base-2. Since the tables for larger
bases are using ecm6 curves, seems like keeping the original curves
(except for ecm5-to-ecm6 translation) is better.

About Paul's counts from the ecmnet page, only the c136-c145's have
been reported, since I was still working on c146-c175 and c176-c196
until recently.

Bruce (if you'd like to be really mislead, ask Bob about how well
block Lanczos on snfs/gnfs matrices parallelizes! See my colleague
Xilman's recent post for references. Or perhaps Bob's revised his
views since the RSA200 matrix? Sorry, this is off-thread.)

[bdodson]

Originally Posted by bdodson

There is an ambiguity about reporting 11e6 as being done, based on
translations of curves run with larger limits. For the c192, my email reported
the 40 curves with B1=43M and c. 600 curves with B1=110M (all ecm6
curves). My intention would have been to have 11e6 marked as "no
additional curves needed" --- "not needed", for short. But when I
read "DONE" in the 11e6 column of ecmp.htm, I took that to mean that
someone actually ran 10,600 curves with b1=11M (or some translation
of that, to curves with B2=100*B1), in addition to the curves I ran.

George's post (if I'm now reading correctly), says P969 had (an equivalent
of) 10753 - 6000 = 4753 B1=44M total curves (including, perhaps, some
combination of 11M curves and 44M curves), with the "Done" in the
11e6 column to be ignored. I suppose you and garo had better follow
that format as well! Likewise, P993 has 8155 - 6000 = 2155. Since
CWI/Montgomery are sieving numbers of this difficulty after c. 25% of
a test for p50's, which is c. 5000 b1=44M with b2=100*b1 curves, the
ecm pretesting conclusion on these two seems to be OK. (For a better
margin, 33% would have been c. 6500, and we're also past that.)
[[This assumes that P969 and P993 were among the numbers Bob asked
George to add 6000 to, on my behalf. But they shouldn't have been.
Corrections could be made using other assumptions, but the point at
the moment is that I'm still not able to determine what the correct count
should be, or how my curves were recorded. ]]

This reduces the unknowns here to how Bob arrived at 6000 B1=44M
curves (and a few minor issues such as why he neglected to wait for
my reply when he said "I'll translate these counts and send them to
George, OK?"). For readers aside from Mark and Bob, the 6000's added
at various locations in the Mn and Pn tables are supposed to mean, first,
that the remaining cofactor is between c136 and c195. The actual curves
and limits depend upon 3 subdivisions (five if one wishes to be picky
and/or precise), c136-c145, c146-c175 and c176-c195; but the executive
summary is that all of these had enough curves run to mark 11e6 as
"Done". If that means 10600*11e6, then a factor of (11e6/44e6) applied
to 10600 would suggest 2650*44e6. Ooops. So Bob OUGHT to be
reporting 6000 curves on just one of the five divisions, c146-c155. For
c136-c145 and c176-c195, "Done" in 11e6 and 2650 in 44e6 is the
correct use of George's system, and for c156-c175 "Done and 4690".
(Bob's prefered factor of 2 for translation double counts the B2 difference
between prime95 and ecm6, since my report to him already included a factor
for that difference.) That's for base-2. Since the tables for larger
bases are using ecm6 curves, seems like keeping the original curves
(except for ecm5-to-ecm6 translation) is better.

About Paul's counts from the ecmnet page, only the c136-c145's have
been reported, since I was still working on c146-c175 and c176-c196
until recently.

Bruce (if you'd like to be really mislead, ask Bob about how well
block Lanczos on snfs/gnfs matrices parallelizes! See my colleague
Xilman's recent post for references. Or perhaps Bob's revised his
views since the RSA200 matrix? Sorry, this is off-thread.)

The second paragraph in my original post ought to end with the above
comment in brackets, [[...]], rather than what's in the brackets [...]
there.

Bruce

[R.D. Silverman]

Originally Posted by bdodson

<snip>


This reduces the unknowns here to how Bob arrived at 6000 B1=44M
curves (and a few minor issues such as why he neglected to wait for
my reply when he said "I'll translate these counts and send them to
George, OK?").

Bruce (if you'd like to be really mislead, ask Bob about how well
block Lanczos on snfs/gnfs matrices parallelizes! See my colleague
Xilman's recent post for references. Or perhaps Bob's revised his
views since the RSA200 matrix? Sorry, this is off-thread.)

You reported 3000 ecm6 curves in your email. It has been agreed
that 1 ecm5/ecm6 curve ~ 2 prime95 curves. That's where the
6000 comes from.

As for your implications that I mislead people about parallel block Lanczos,

(1) Both CWI and NFSNET reported low (less than 50%) per processor
utiliization and CWI has stated in public that communication costs dominate
the computation. Peter Montgomery has presented graphs showing how
the per-processor utiliization decreases (somewhat dramatically) as the
number of processors increase.

My public comments have simply stated that B-L does not parallelize well.
I stick by that comment and it is backed by data presented by others.

(2) And it is quite unprofessional of you to accuse me of misleading others in
the manner you did.

[bdodson]

Originally Posted by Prime95

Based on that email I added 6000 curves at 44 million to the tables (and marked 11,000,000 done). So any curves at 44,000,000 in excess of 6,000 was done by other users.

Since Bob doesn't appear to have read my email, his report to you (submitted
without my agreement or approval) doesn't seem to me to be a postive
contribution to the counts reported on your pages ecmm.htm and ecmp.htm.
There are no numbers on which I ran 3000 ecm6 curves, and the 3000 ecm5
curves with B1=43M that I did run applies only to Cunningham composites
between 145- and 155-digits. There were, at that time, eight base-2
numbers, 2^n +/- 1 for n < 1200 in this range. Four have subsequently been
factored. So adding 6000 curves should at most have been applied to M1173
and P760, P820 and P1044.

If you were to email me any other numbers in Bob's email, I'd be happy to
supply a round number using Bob's factor of 2 that should replace the bogus
6000 value (if there were any numbers other than the above four in the
email you received). As I pointed out to Bob in the email he didn't wait
for (saying among other things that I'd be happier reporting my counts
myself), some care needs to be taken to be sure that a number in a given
range was actually in one of my input files. Of numbers that were run,
5000 would fit numbers from 156- to 175-digits, which is perhaps not so
serious a correction. Of numbers with 136- to 144-digits that I ran, Sean
Irvine's factorization of M949 finished the last number from the ecmm and
ecmp ranges (although there are some 20 numbers for other bases that
remain from the list of numbers run, not yet reserved by anyone). All of
these curves were run on a cluster of 1.1 Mhz Pentium 3.

The more recent Opteron curve counts are well below 6000 curves with
B1=44M, perhaps closer to 2650 curves, rounded to 2500, but with 11e6
(t45) marked as Done. Most numbers from 176- to 195-digits were run this
far (but not farther yet), the only exceptions being other people's recent
new composite cofactors. My recent base-2 factorizations were found by
applying just 165 ecm6 curves with B1=110M, which has finished on all of
c196-c384. I'm still working in this c196- range, so including counts seems
premature, but 3e6 (t40) is Done on the complete Cunningham list.

Bruce