20070411, 23:49  #1 
P90 years forever!
Aug 2002
Yeehaw, FL
2·3·1,193 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 20171019 at 02:55 Reason: 2,1219 is done! 
20070414, 03:38  #2 
Jun 2005
lehigh.edu
2^{10} Posts 
I suppose so, for the curve counts. All of the Mn's and Pn's not
yet tested to the p50level are running fairly hard towards t50. There are just 80 left to finish, with 37 having between 251digits to 279digits running on ninety P3's plus 88 xeons; and 43 having between 280digits to 355digits (44 posted here was a miscount, 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 thanksless 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 512bit gnfs and 768bit 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 
20070414, 18:47  #3  
Jun 2005
lehigh.edu
2^{10} Posts 
Quote:
record factor from M997 was a p57. The p59 record was from the ecmgmp6.0 beta test, from 10^2231. For the p57, it's still 16th on Paul's top50 alltimes, allprograms ecm list (which used to be a top100 list, so is) found at http://www.loria.fr/%7Ezimmerma/records/top100.html Bruce 

20070501, 13:03  #4 
Jun 2005
lehigh.edu
2000_{8} 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 c251c279; only 34 numbers 2/2+ with n < 1200 left to finish t50). Bruce 
20070502, 18:51  #5  
Nov 2003
2^{6}·113 Posts 
Quote:
Only 34 left in the range C251c279 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..... 

20070503, 06:41  #6  
Jun 2005
lehigh.edu
2^{10} Posts 
Quote:
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 c251c279, plus 136 + 3 from the generic c251c299'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 (p50optimal); while the generic c251c299's need at most 4100/7830. I'm currently making 1000curve 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 c251c299's. Perhaps I'll have a short answer by Sept. Counted as percentages of p50tests, just 83.3 left to go of the 800  nearly 90% done. Bruce 

20070511, 20:14  #7 
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 middlesize 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? 
20070512, 14:34  #8  
Jun 2005
lehigh.edu
2^{10} Posts 
Quote:
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 presieving 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 256bits, 77digits, 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 onceinadecade results, rather than the onceamonth (or better) rate at which ecm is happier. I don't know much about the larger exponents on your list, 2^n 1 for n > 1200; I believe some of George's recent posts include pointers to the current status there. Among undertested 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 251digits to 279digits, and the countdown to all being done has dropped from 37 to 24, with several of those being on their last 1000curves (B1 = 43M). That's not to say that a 2nd test to p50, still with p50limits doesn't have a chance  or even a better chance (distributed over a larger collection of inputs) than B1 = 110M (p55limits)  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 p48p52 factor (for which p50limits are still optimal) with an early p53p57 factor (for which p55limits would be better). Taken over time, on a sufficiently large collection of inputs (20orso, at least), B1 = 110M is more likely to be useful  although the usefulness may drift over to presieving 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 

20070515, 07:35  #9 
May 2007
3_{10} Posts 
Sigma for p51M929
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 ellapfunction. There are about 2,000,000 canditates for B1, B2 above. Is there some efficient algorithmn? What is your sigma? Mischa 
20070524, 02:02  #10 
Jun 2005
lehigh.edu
2^{10} Posts 
Help!
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 base2'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 130" to give the first 13orso 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 
20070524, 03:29  #11 
P90 years forever!
Aug 2002
Yeehaw, FL
15766_{8} Posts 
The old ecmm file

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