20210208, 15:05  #1816  
Aug 2005
Seattle, WA
29×59 Posts 
Quote:
3+2,1674L (266) 3+2,1782M (283) 3+2,1818L (289) 3+2,1890L (301) 3+2,1926L (306) 3+2,1926M (306) Of course, the difficulty starts to get pretty high, even for sextics. 3+2,1890L is particularly interesting, because it can be an octic at difficulty 240, which surely beats a sextic with difficulty 301. 

20210215, 05:11  #1817 
Aug 2005
Seattle, WA
29·59 Posts 
HCN tables updated
Another update. The tables and ECMnet server have been updated to reflect all factors reported to me through the end of February 14 (GMT). There were 28 new factors found since the last update, of which 25 completed the factorization of their respective numbers.
There are now 825 composites remaining in the tables. The minimum digit count remains 180, with one such composite currently unreserved (it may be easier by SNFS than GNFS). With the usual polynomial degrees, SNFS difficulties range from 233 to 310. As Robert pointed out above, there are several relatively easy SNFS jobs, with difficulties in the 230's that can use sextic polynomials. Here are the factors found since the last update, showing appropriate credit: Code:
4+3 424 C236 340224522413101377136425263820279171197505211595431135772877212742510692929. P162 NFS@Home & J Becker SNFS 20201214 4+3 1299L C180 607755967434501568870695261077004931263987013678201460614628674339. P114 NFS@Home & S Wellman GNFS 20201217 11+10 286 C184 7173956154365860711212202496723318801876594682689112326594444341. P120 R Balfour GNFS 20201223 3+2 1458L C232 272778179581700214608940613130848043155524950157485759256767991922069865314923455527672324477. P140 NFS@Home & J Becker SNFS 20201226 7+2 334 C281 1572086970565613985593372374878848957028731812522459870919029. C221 Yoyo@home ECM 20201226 8+3 834L C216 5386615734827920616029575531764652188196347636472473209711568761. P152 NFS@Home & J Becker SNFS 20201230 11+10 269 C185 67885338031643306133874275113686175257711072279110334310565761575819502743. P111 NFS@Home & J Becker GNFS 20210103 118 283 C184 25757443172192581774724832290466401813631301331104722265517146931911797890420779056821787347. P93 R Balfour GNFS 20210104 85 283 C227 464969267080074787461258396097781630167378756522966212957078194975297861002935363382383671. P137 NFS@Home & J Becker SNFS 20210105 9+2 268 C217 142498277492679700462296895337558444538793533656900226962405681936401. P149 NFS@Home & R Dickerson SNFS 20210111 11+2 277 C188 88590756731423307003438243887117477947340188631909874351901. P129 E Hall ECM 20210113 5+2 427 C218 100680094404947719634117385125033732408343221066182601426750212111947841649. P144 NFS@Home & J Becker SNFS 20210115 52 427 C220 96217143903778444213232889302950053378903523564203636295750346599109673025775414237. P137 NFS@Home & S Wellman SNFS 20210119 5+2 830M C189 87194481537532219647451961506971310167337599587206670640874119313576546280898121241. P106 NFS@Home & J Becker SNFS 20210121 118 287 C238 252913619349347588763877132448479425212438959990695903607339047594314326337. P164 NFS@Home & J Becker SNFS 20210126 5+3 427 C248 16700096523299630893472388366118974723690274818074341769651328600601181666038611931. P166 NFS@Home & S Wellman SNFS 20210126 3+2 1830M C188 37770194609070586001730845912294235047156885480703474181. C132 R Balfour ECM 20210127 3+2 1830M C132 131213278246853941674923688720314447512564184463046996160762761. P70 R Balfour GNFS 20210127 9+2 305 C211 33886426314493237523028241894757682498248211508090019580110200268685617316223681971361. P126 NFS@Home & J Becker SNFS 20210128 11+3 287 C225 42665305442804211960901054513780679767624419132293851490443038684781251905807956131476818463955371699623. P121 NFS@Home & J Becker SNFS 20210129 92 305 C197 413020446073576555908361881990070925701150917711393503147365776845747292981180280391. P114 NFS@Home & J Becker SNFS 20210201 43 497 C253 33282325839230622131117390810912865176923802246998981830448662948858059087195223739086604472329614857070727957. P143 NFS@Home & J Becker SNFS 20210201 8+3 307 C184 4034465893229948991017240237611887989468926643807749544311. P127 R Balfour GNFS 20210202 11+9 244 C250 27629397626771432899477186319651600758864547022558510301569208366886795222177078053629518005040139761. P150 NFS@Home & J Becker SNFS 20210204 113 287 C219 18496624888322543022162761135950249087378640019521785169232653369425835250009897448220711. P131 NFS@Home & J Becker SNFS 20210208 5+3 433 C185 94414140295893398074672341688321994284592975267433041169947368634327222303526629750080826479. P93 NFS@Home & M Vang GNFS 20210208 11+7 296 C290 471269492266311247705814157010450215250487473435313. C239 Yoyo@home ECM 20210213 9+2 538L C198 254654820883764896593943831178564781224544416692849771917112077288998797. P127 NFS@Home & J Becker SNFS 20210214 Last fiddled with by jyb on 20210215 at 05:12 
20210307, 14:45  #1818 
"Rich"
Aug 2002
Benicia, California
4DB_{16} Posts 
8p3_774M factored
Code:
p93 factor: 394919403261007891106577866024599716542953650239284344299419901724499859466699310235306392453 p131 factor: 25259855101428349320239531146314859153787374023516210467201845328330310463818470624024408683291807036810023175118643790052502663829 
20210423, 16:11  #1819 
Aug 2005
Seattle, WA
3257_{8} Posts 
This just in...
My ECMnet server just popped out a 71digit factor of 8+7,316!
Given the B1 value of 110M, this is a very surprising find. I calculate a probability of less than 1 in 8 million that a single curve would produce this factor, and even the 14000 curves which have been thrown at it had only about a 1 in 600 chance of making this find. Now here's the bad news: the ECMnet client and server have never handled the modern format of the sigma value used by GMPECM. Thus the sigma value used for this curve has been lost forever. I have no way of proving that I found this factor by ECM! Upon realizing this, I immediately rewrote the relevant parts of the server and client to handle modern sigma values for my own use. Before deploying that, I need to make sure that it's backwardcompatible, so a corrected server can still work with an uncorrected client. In the future, anybody connecting to my server with a stock ECMnet client will continue to see this problem. The sigma value will only be preserved when both client and server are corrected. I'm pretty sure that rogue long ago stopped supporting ECMnet v2, so I don't know what the prospects are for getting this change deployed more broadly (probably not very good). But at least my own future finds will be reproducible. 
20210423, 17:29  #1820 
"Curtis"
Feb 2005
Riverside, CA
4779_{10} Posts 

20210423, 18:23  #1821 
Aug 2005
Seattle, WA
29×59 Posts 

20210423, 20:12  #1822 
"Ed Hall"
Dec 2009
Adirondack Mtns
47×79 Posts 

20210424, 02:02  #1823 
Jun 2012
Boulder, CO
2^{3}×5×7 Posts 

20210424, 08:09  #1824 
Aug 2020
10100111_{2} Posts 
What does this notation mean: a+b,nL? I thought it meant a,nL + b,nL, but I coudln't find those in factordb.

20210424, 11:10  #1825 
Jun 2003
1001101100000_{2} Posts 
I believe you're referring to numbers having Aurifeuillean factorization. There are special combination of a,b,n which have these formulabased factorizations. They will have (typically) two components, referred to as L & R. You can just look up the main number (a^n+/b^n) in factordb. It should already contain the (possibly composite) factors.

20210424, 13:09  #1826 
Apr 2020
263 Posts 

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