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 2007-04-11, 23:49 #1 Prime95 P90 years forever!     Aug 2002 Yeehaw, FL 2×41×89 Posts 2- table Code: Size Base Exp - SNFSdif Ratio Notes 337 2 1207 - 363.3 0.926 297 2 1213 - 365.1 0.814 248 2 1217 - 366.3 0.675 284 2 1229 - 369.9 0.766 329 2 1231 - 370.5 0.886 303 2 1237 - 372.3 0.812 337 2 1243 - 340.1 0.989 /11q 326 2 1249 - 375.9 0.865 268 2 1253 - 323.3 0.827 /7 220 2 1255 - 302.2 0.726 /5q 309 2 1259 - 378.9 0.813 223 2 1265 - 346.1 0.644 /gnfs/11quint 385 2 1277 - 384.4 1 347 2 1283 - 386.2 0.897 348 2 1291 - 388.6 0.894 302 2 1297 - 390.4 0.772 Last fiddled with by Batalov on 2017-10-19 at 02:55 Reason: 2,1219- is done!
2007-04-14, 03:38   #2
bdodson

Jun 2005
lehigh.edu

20008 Posts

Quote:
 Originally Posted by Prime95 Since Bruce has rendered my tables obsolete, ....
I suppose so, for the curve counts. All of the Mn's and Pn's not
yet tested to the p50-level are running fairly hard towards t50.
There are just 80 left to finish, with 37 having between 251-digits
to 279-digits running on ninety P3's plus 88 xeons; and 43 having
between 280-digits to 355-digits (44 posted here was a mis-count,
which included M1061) running on some 450 xps (when they're not
doing other things). Both groups were 4300/7830 curves short,
of which most of the smaller ones are done with the first 2000 new
curves (leaving 2300 curves to go); and the larger ones done with 1300,
running on the next 1000.

But I've always found the tables on ecmm.htm and ecmp.htm to
give a much clearer picture of those parts of the 2- and 2+
Cunningham lists than either the main Cunningham file or appendix C
with the unfactored composite cofactors. I'm also finding Garo/Rogue's
tables (as maintained by Alex) useful, even without curve count updates
(a thanks-less task, presumably). Having the open indicies visible gives
us something to work towards; especially as each of the remaining
ones on ecmm/ecmp seem more likely to form hard sieving targets (as
ecm success becomes less --- and less --- and less yet! --- likely).

A part of the pages that looks quite different now than it did when
I was looking around for things to do after the cabal's 512-bit gnfs
and 768-bit snfs is the "no known factors" section of ecmm. There's
still just a fragment left on ecm.htm, in the account of M727. When
I was first looking, there was M727, M751, M809, M971 and M997,
in addition to M1061. I still see our M727 factorization on the old pages
Sam recently posted, page 88 from 2001, which looks like it just made it
into the 3rd Edition of the Cunningham tables book. There's likewise the
M997 and M971 entries on the ecmm page, under factors found using
prime95, the p59 from M997 being my first ecm record (which has just now
dropped to the 11th largest ecm factor, on Richard's Champs list, after the
p61 found earlier this month). We did M751 as a large CWI project;
and M809 was an early mark for Franke, et. al. All together, the focus
of quite an extended effort, with just M1061 left to fall. Perhaps soon?
-Bruce

2007-04-14, 18:47   #3
bdodson

Jun 2005
lehigh.edu

210 Posts

Quote:
 Originally Posted by bdodson ... There's likewise the M997 and M971 entries on the ecmm page, under factors found using prime95, the p59 from M997 being my first ecm record (which has just now dropped to the 11th largest ecm factor, on Richard's Champs list, after the p61 found earlier this month). ... -Bruce
Ooops. I checked various points as I was composing/typing, but the
record factor from M997 was a p57. The p59 record was from the
ecm-gmp-6.0 beta test, from 10^223-1. For the p57, it's still 16th
on Paul's top50 all-times, all-programs ecm list (which used to be a
top100 list, so is) found at

http://www.loria.fr/%7Ezimmerma/records/top100.html -Bruce

 2007-05-01, 13:03 #4 bdodson     Jun 2005 lehigh.edu 210 Posts p51 from M929, c214 left Here's p51 = 912388729886745263028357724939366731341350831028977 Not only is the c214 cofactor composite, but its test to p50 will finish in a few hours (the 3rd to finish of 37 left from ecmm/ecmp in c251-c279; only 34 numbers 2-/2+ with n < 1200 left to finish t50). -Bruce
2007-05-02, 18:51   #5
R.D. Silverman

Nov 2003

746010 Posts

Quote:
 Originally Posted by bdodson (the 3rd to finish of 37 left from ecmm/ecmp in c251-c279; only 34 numbers 2-/2+ with n < 1200 left to finish t50). -Bruce

Only 34 left in the range C251-c279 or only 34 left in the entire table??

The 2- factors seem hard to find these days..... The last previous one was
almost 8 months ago.....

2007-05-03, 06:41   #6
bdodson

Jun 2005
lehigh.edu

210 Posts

Quote:
 Originally Posted by R.D. Silverman Only 34 left in the range C251-c279 or only 34 left in the entire table?? The 2- factors seem hard to find these days..... The last previous one was almost 8 months ago.....
Indeed, it's been that way for a while --- the 2- list seems to have
been fairly well covered in previous searches. I gave a careful, but
extended, description in my 1st post on the 2LM thread of "28 April";
a revision of my reply to one of your earlier inquiries. I'll try again.

The approx size of the regular Cunningham list is c. 800 numbers.
The countdown to finishing t50 on all 800 is

34 numbers from 2- or 2+ with n < 1200, all of which are from
c251-c279, plus

136 + 3 from the generic c251-c299's, where "generic" means NOT
"from 2- or 2+ with n < 1200". These do include 2LMs. (I've added
3 composite cofactors omitted in the "28 april" count.)

So my answer this this question is "yes, 34" for "numbers from 2-/2+";
but no, there's another 139 that are not "2-/2+ for n < 1200". The
summary count would be 34+136+3 = 173 of the 800 left to go. That
may sound like a lot, but the number of curves needed on each is relatively
small. The 2-/2+ need at most 2300/7830 curves with b1 = 43M
(p50-optimal); while the generic c251-c299's need at most
4100/7830. I'm currently making 1000-curve passes (with a last
pass of 1300 or 1100, respectively), of which two already finished on
(the very last part of) 2-/2+. Two more passes through 2-/2+ and
four more passes through the generic c251-c299's. Perhaps I'll have
a short answer by Sept. Counted as percentages of p50-tests, just
83.3 left to go of the 800 --- nearly 90% done. -Bruce

 2007-05-11, 20:14 #7 Mischa     May 2007 3 Posts Some coordination required Hi all, actually I did not want to spent much time on this factoring issue, but things are running smooth and do not require much action from my side. Since in the meantime the calculations are producing enough heat to fuel a middle-size Austrian city (and everybody is talking about greenhouse effect), some effort for coordination from my side seems to be appropriate. I just summed up quick & dirty my results on http://home.tele2.at/kennmich/cunningham/page2.html So far I used http://www.mersenne.org/ecm.htm as starting point, but according to my probability estimations I must have found some factors, which I did not, so I guess, not all results are incorporated. Are there any ranges which are not covered or only little covered yet?
2007-05-12, 14:34   #8
bdodson

Jun 2005
lehigh.edu

20008 Posts

Quote:
 Originally Posted by Mischa Hi all, ... I just summed up quick & dirty my results on http://home.tele2.at/kennmich/cunningham/page2.html ... according to my probability estimations I must have found some factors, which I did not, so I guess, not all results are incorporated. Are there any ranges which are not covered or only little covered yet?
Congratulations on the p51 factor of M929, we can ask Sam about
dual credit (did you keep the lucky value of sigma?). Checking your
curve counts, I see that you're the person George was referring to
in the post that started this thread.

The only number for which pre-sieving factorization efforts are
no longer useful is M1061 = 2,1061- = 2^1061 -1. If you're using
B1 = 110M limits, any of M787, M821, M823 or M953 (from your
list) would seem to be candidates for more B1 = 110M curves.
The only slight issue with having focussed so much attention on
M827 (the 24.7K B1=110M curves) is that there's a good chance
that all of the factors are out of ecm range (above 256-bits,
77-digits, for example). Distributing the curves over a larger
collection of numbers would give you a better chance that at
least some of the numbers have a factor in range. While we do
hear some spectacular successes with efforts focused on just one
number (such as Richard Brent's p40 from F10; Aoki's p64 from R311),
these seem to be more once-in-a-decade results, rather than the
once-a-month (or better) rate at which ecm is happier.

2^n -1 for n > 1200; I believe some of George's recent posts
include pointers to the current status there. Among under-tested
mersenne numbers in the Cunningham range, you hit on one of the
last --- with M919 --- that hasn't already had a complete test to
p50. The remaining ones have between 251-digits to 279-digits,
and the countdown to all being done has dropped from 37 to 24,
with several of those being on their last 1000-curves (B1 = 43M).
That's not to say that a 2nd test to p50, still with p50-limits doesn't
have a chance --- or even a better chance (distributed over a larger
collection of inputs) than B1 = 110M (p55-limits) --- but more of
those curves are likely to be wasted --- the distortion of the
probability estimate you mention. We're comparing the chance of
a late p48-p52 factor (for which p50-limits are still optimal) with
an early p53-p57 factor (for which p55-limits would be better).
Taken over time, on a sufficiently large collection of inputs (20-or-so,
at least), B1 = 110M is more likely to be useful --- although the
usefulness may drift over to pre-sieving efforts, rather than to finding
factors, on many/most of the numbers.

I could ramble on, but perhaps these are the most relevant points,
as I see them. Good luck finding (more) new factors! -Bruce

 2007-05-15, 07:35 #9 Mischa     May 2007 112 Posts Sigma for p51|M929 Sigma = 1,145,424,951 B1 = 9,927,349 B2 = 28,911,973 (very nice for a p51 factor!) Yesterday I tried to calculate the exact group order with Pari, no chance with the ellap-function. There are about 2,000,000 canditates for B1, B2 above. Is there some efficient algorithmn? What is your sigma? Mischa
2007-05-24, 02:02   #10
bdodson

Jun 2005
lehigh.edu

102410 Posts
Help!

Quote:
 Originally Posted by Prime95 Since Bruce has rendered my tables obsolete, ...
Ooops! My attempts at making a case for the ecmm and ecmp
pages doesn't appear to have been successful. Both pages now
record only the factors found using prime95, and refer instead to the
"Cunningham Tables" forum --- no listing of the remaining Mn and Pn's
in the Cunningham range of n < 1200, just the statement that they've
been tested to p50.

In particular, since the Garo/Alex tables omitted the base-2's
except the 2LMs (2,2m+ for 1200 < 2m < 2400), there is now no listing
of these numbers, except for Sam's tables --- which aren't updated
nearly frequently enough. I could grep out the ' 2,'s then fgrep +
and maybe - (maybe not, pending being reserved) from appendix C
of Dec 06; perhaps with "cut -c 1-30" to give the first 13-or-so
digits. Then take a diff with the ecmnet cunningham.in, and track
down the diffs to see which were complete, which needed updating;
perhaps comparing with the two recent pages. That would give the
basic info; but there would still need to be a readable /code for posting,
and a sticky (which I've been nagging about for some time now, re
2+ discussion and 2- discussion). Or perhaps whoever would be doing
the posting/formatting would prefer to start themseleves, without my
mucking around.

In any case, this forum on Cunningham tables is now seriously
incompete! -Bruce

2007-05-24, 03:29   #11
Prime95
P90 years forever!

Aug 2002
Yeehaw, FL

2×41×89 Posts

The old ecmm file
Attached Files
 ecmm.txt (8.2 KB, 289 views)

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