20080125, 03:44  #1 
Oct 2006
vomit_frame_pointer
2^{3}·3^{2}·5 Posts 
BrentMontgomeryte Riele numbers
I'm curious how much ECM CPU time has gone into the BrentMontgomeryte Riele extensions of the Cunningham tables (see the link at Zimmerman's page). They aren't mentioned much around here.
Bound to be some factors less than 50 digits among those composites, assuming no huge university clusters have ground away at them for months. Last fiddled with by FactorEyes on 20080125 at 03:45 
20080125, 05:09  #2  
Jun 2005
lehigh.edu
2^{10} Posts 
Quote:
p1/p+1 pass (check Paul's records page). CWI's been grinding through them for years; two of the top10 from 2007 were from B&P's large run with epfl's machines, including the largest, p65. We think that they're less tested than the Cunningham list; but I wouldn't rule out factors under 50 digits there either. [Ooops, looks like Alex's p4x's have gotten bumped out of the top10 p1's; check Richard's list.] Bruce (Ah, Richard's factors.txt reports that there was an ECMNET server running during 20032006; then further factors up to Feb 2007, a whole lot of CWI reports. There are surely easier targets.) 

20080125, 15:30  #3  
(loop (#_fork))
Feb 2006
Cambridge, England
1100011001110_{2} Posts 
Quote:
I believe huge university clusters have precisely ground away at these for months. The lowesthanging fruit on the firstholes list, which are reasonable personalSNFS targets  an S190 is probably no more than a week on a dualcore  are the 133=7x19 and 121=11x11 powers, and then there are some small prime or {2^kp,+} ones: Code:
24 139 + 191.85 62 107 + 191.79 15 163  191.70 (NB bdodson found a P47 factor on 2/2/08, this is now a C136) * 13 172 + 191.60 (finished by bdodson with a P43, 4 Feb 08) 42 118 + 191.54 * 55 121  191.44 (finished by bdodson with a P52, 14 Feb 08) 46 133 + 189.55 37 133  178.77 Code:
* 60 113  143 200.93 1.405 finished by bdodson 08 Feb with a P49 * 90 101  139 197.38 1.420 finished by FactorEyes 25 Apr with a P58 28 137  139 198.26 1.426 69 106 + 136 194.92 1.433 * 10 232 + 160 232.00 1.450 < Cunningham number done by Irvine with a P61 * 57 113 + 136 198.41 1.459 finished by bdodson 21 Feb with a P49 97 119  138 202.65 1.468 67 127  154 231.91 1.506 88 118 + 147 229.45 1.561 57 139  154 244.07 1.585 Last fiddled with by fivemack on 20080518 at 10:52 Reason: added list of gnfsfirst targets 

20080125, 17:19  #4 
"Nancy"
Aug 2002
Alexandria
2467_{10} Posts 
Arjen Lenstra's students Aniruddha Bhargava and Sylvain Pelissier have run a lot of ECM on the BMteR tables lately. Peter and I did P1 with B1=10^11 and B2=10^16 on a lot of these numbers. Some time ago I did a lot of the easiest SNFS numbers, difficulty <150 or so. Running the remaining numbers in comps.gz through phi finds 2 of difficulty < 160 and and bunch more of difficulty <170:
Code:
*15 204+ 86477846399689043464683717029156090048861048967246028346542762082353766287850823568159598684691797717310021500567119657051941720885202081 *19 186+ 22064611336630037993441645496728842220556437573639879717180732956862218596945115207666437591234151129886605991653966248694423179304531921 *13 219 29789227638967279719753452653419330616492652498969823472736616044408900214492708666729753560650062601082073419281423838835993023775830992450981 *13 185+ 19198075398143282986521312292007210339867204517090997717056197733310096986428557713704819474579995542784067972998805981880984450916235431 *13 228+ 2727364713570059220279875144576079475403851873457637202751779519533254755818120824963764148419498582454672890891627002684180842305689354915715330067231473 *15 207 200605994644287593361720414946755526335253616754462308696719693457589547560338042130862594677649676700840237084637053616237004264766403 *15 213 2066957912511937223486278091004702307738903999738040895327891708741440460352478870799960031807639552756444103266055920366399429995356491667232049271148228943 21 183+ 840495924180053889480828320466090761213441850805869573117086685493441247366283840934405600405893270865405558261915109754194721889173519532934835841 21 186+ 129448909920304924867760651957761342407632280139510993404590115590731227274229350321955442652859842734192467044448256320420026040449 22 183 33729278874243768066840544721250443222501196317530015698928363277010534626968965932075117893701136762671962220930452920558918235076223828303 22 183+ 351010416794463810326290140143660929903016348764190934847996908678342762573046606988781625855854022779076505615077186221687482877124053812941707255710443993153 23 155 1292173230767983005217310792141279567315609093128659129811853603939453351326699352608650846291286206367038097373538248391276807239103602200053634786305032277311 24 183 230223670658996925410197108966943754873294412852520219733667714294040308902808805182130471548678423014030764227959005924733050709589604158581136447396195437843529 24 145+ 311441749661125508779820860518393021783979989185535491637993981358479318102572173944478467494082073940288514845644498147791776561021 26 177 2757741899316066474467784735435019764295890940462946536735922314883399017882238830573494413902454692484010569377381856131203764553973815504158711464979910875761 28 145 4170520752643080302572797397982189273322959084449683008329127991951508969382319811864004350667257313721289791997219726648505628447871 31 159+ 8609758383766875992363295671475401342328692516921317342527073312610917766014707705872645275542074221651105886525040933678985711470145517798716401841 33 159+ 86776601947035139102955966706432585170964953534415262702221079534253696018529937121075589336461240895008116430976702815560542378049790290790661512428751068801 Alex Last fiddled with by fivemack on 20080518 at 10:50 Reason: Added stars by completed numbers 
20080128, 16:08  #5  
Jun 2005
lehigh.edu
2^{10} Posts 
Quote:
with on the BrentMontgomeryteRiele numbers was first introduced two or three posts above (in your post). Paul has never kept these factors, so far as I know. But that doesn't make this forum the next most likely place to check. The tables have been maintained for many years by Richard Brent (that would be as in OPN's Brent), and it appears to me that CWI (including Montgomery and Herman teR.) were sending monthly updates. The Feb 2007 update includes >> 22 148 12595083615719740205913831870057576586969 CWI 20070222 which seems to be a p41. While it is true that Bhargava and Pelissier have gotten large ecm factors, many/most seemed to have come from the smaller numbers on the tables. If someone has tested the complete list up to p45 (to probability .62), I haven't heard. I'm not saying that it hasn't; and I'd be interested to hear if it has. Back in October, Alex was reporting a p42 and a p44; and then a p44 and a p46; but only by p1/p+1; which will certainly not get all [p42..p46]'s. Seems to me that one wouldn't start a 3 week sieving project without more info and/or more ecm; much less two months or so. Bruce PS  well, are we discussing difficulty < 170? Then you may not mind finding a p45. the "3 months" and checking Paul rather than Richard Brent was the part that had me puzzled. Last fiddled with by bdodson on 20080128 at 16:21 Reason: ps from rechecking Alex's post, above 

20080128, 16:30  #6 
(loop (#_fork))
Feb 2006
Cambridge, England
14316_{8} Posts 
Sorry, I clearly need to rewrite this at some point. Paul Zimmermann is clearly not the right contact point. Brent's list of holes has some of them marked up with people/organisation names, which I presume are reservations.
I'm vaguely tempted to set up another copy of my homogenousCunningham reservation server with the 1037 comps.gz numbers in it, though I'd want to check that that didn't step on Brent's toes. http://wwwmaths.anu.edu.au/~brent/ft...ors/ecmnet.txt was last updated in February 2007 since ecmnet moved on to other projects; the firstholes file was updated much more recently (20080121), so seemed a safer source for numbers not yet done. A p45 on a single number is 5000 curves at 11e7, which I think of as taking five CPUdays, or around enough time for a C120 GNFS or difficulty170 SNFS; I can see that it'd be worth doing more ECM on the GNFSnumbers, and perhaps on my sublist of SNFSable first holes, but akruppa's list of SNFS candidates look adequately presieved. Last fiddled with by fivemack on 20080128 at 16:30 
20080128, 20:00  #7  
Jun 2005
lehigh.edu
1024_{10} Posts 
Quote:
BMteR tables, but reports and reservations(?) perhaps ought to include a copy to him  if for no other reason than that other people (not necessarily on this forum) would check with him. The reservations on the 1st holes file are taken from Sam's "who's doing what"  only Cunninghams, base < 13, are listed as reserved. Doesn't appear that there's an online place for reserving 19,186+, and perhaps you'd be done with it before it'd be updated anyway? If I'm reconstructing things correctly, the ecmnet from 20032006 was Xilman's. Then CWI decided that I'd ruined the Cunningham list (according to a lecture of Peter's in Berlin, just before the ANTS; at a conference in Brent's honor, organized by Paul Zimmermann, among others), and switched to BMteR. Not sure which came first, but Xilman seems to have decided that the BMteR tables had gotten too hard, and switched to homog Cunninghams (or was that you?). Quote:
before xilman's server was taken down? sixteen in the first report. Then a whole bunch in April; another chunk in May, then a bunch in June. Then nothing until October; the mess, a bunch of duplicates submitted more than once, from more than one person; nothing from CWI in Nov, then 3 monthly reports, Dec 06, Jan 07 and Feb 07; at which point the ecmnet server has been gone for a while, and Richard discontinues the online file. Again, "ecmnet" is Xilman's server (perhap it doesn't help that there's more than one Paul involved?); Paul Zimmermann's never run/listed the BMteR's. So looks like there's another 17orso on Alex's list; I could probably run the t45's with B1=110M (p55optimal limits) without much distraction if there's interest in cleaning these ones up. Richard would likely be glad to have them done/removed. Bruce 

20080128, 20:33  #8  
Bamboozled!
May 2003
Down not across
17·593 Posts 
Quote:
Paul 

20080129, 03:11  #9  
Jun 2005
lehigh.edu
2^{10} Posts 
Quote:
would be to use 110e6 = 11e7, p55optimal. Not so efficient for finding p45's, but we expect p52orso to be a more likely factor size. Using 250Mb P4's, k=20 seems to work here, and Alex's v gives Code:
GMPECM 6.1.1 [powered by GMP 4.2.1] [ECM] Input number is 1022589...5200558598087 (237 digits) Using MODMULN Using B1=110000000, B2=961969548556, polynomial Dickson(30), sigma=634450470 dF=65536, k=20, d=690690, d2=17, i0=143 Expected number of curves to find a factor of n digits: 20 25 30 35 40 45 50 55 60 65 2 4 10 33 131 594 3028 17145 107134 723404 500Mb P4's are using B1=110000000, B2=769593044236 with k=16; for which the p45 and p50 columns are 613 and 3133; and 620 curves looks good. For the 250's here's two days of curves: > rwrr 660 20080126 09:35 out613asm56pup.a4.1 > rwrr 666 20080126 22:24 out613asm56pup.b4.1 > rwrr 668 20080127 07:53 out613asm56pup.c4.1 > rwrr 673 20080127 17:08 out613asm56pup.d4.1 two numbers each, 800 curves, so c. 3000 curves/24hrs, for five p45 tests. For the 500's, two days worth: > rwrr 706 20080126 09:46 outhdk613c7079pd.a1h.1 > rwrr 701 20080126 16:50 outhdk613c7079pd.a2h.1 > rwrr 730 20080126 23:09 outhdk613c7079pd.a3h.1 > rwrr 700 20080127 04:15 outhdk613c7079pd.a4h.1 > rwrr 703 20080127 09:32 outhdk613c7079pd.a5h.1 > rwrr 754 20080127 16:30 outhdk613c7079pd.a6h.1 two numbers each, 500 curves, so another 3000 curves/24 hrs, five p45 tests. I could try 2*t45 for five numbers a day, around four days for all 17 numbers (1 below diff 160, 16 below diff 170). Suppose 15, 204+ would be next? Care to nominate four more for the first set of five? Bruce 

20080131, 19:13  #10 
(loop (#_fork))
Feb 2006
Cambridge, England
2·5^{2}·127 Posts 
You're presumably offering to run these curves on the cluster. One curve at 11e7 on 15,204+ is 815+300 seconds on the core2 on which 19+186 took 120 hours, admittedly using around 500M memory, so 600 would be 185 CPUhours. Though, since the factor is a P52, it might have picked it up.
I'd be happy running with no more ECM on numbers as SNFSeasy as the ones in akruppa's table; if it were my time to allocate, I'd set the cluster off on the five easiest firstholes from my original post (with SNFS difficulties 180192) Last fiddled with by fivemack on 20080131 at 19:19 
20080201, 18:12  #11  
Jun 2005
lehigh.edu
10000000000_{2} Posts 
Quote:
on whether/which of the difficulty < 170's were likely to be first, I started on the smallest. They're _really_ small! In fact, I'd bet that these small ones were more than adequetly pounded on by previous runs. On the other hand, t45's aren't hard to come by, so not much (if any) loss running them. So in addition to the c137 already mentioned, I did 2*t45 on two c132's from Alex's list; and 1*t45 on four more, c133, c135, c137 and c140. Hoping not to find a record ecm, since it wouldn't meet Richard (Brent's) ratio restriction for a Champion factor (c155orso, or larger). So anyway, now that I know that the (current) sieving candidates are from the first_holes list; rather than running a 2nd t45 on the above, I'm switching to the ones from your post, eight numbers. Starting with the smallest first (unless/until I hear otherwise); first two qued. Bruce 

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