mersenneforum.org Factoring humongous Cunningham numbers
 Register FAQ Search Today's Posts Mark Forums Read

2021-02-08, 15:05   #1816
jyb

Aug 2005
Seattle, WA

29×59 Posts

Quote:
 Originally Posted by charybdis Ah yes, of course. In fact it's the same algebraic poly for 3+2_1494L. There's also 3+2_1566L at difficulty 250.
Yes, actually there are a bunch more of these:

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.

 2021-02-15, 05:11 #1817 jyb     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 2020-12-14 4+3 1299L C180 607755967434501568870695261077004931263987013678201460614628674339. P114 NFS@Home & S Wellman GNFS 2020-12-17 11+10 286 C184 7173956154365860711212202496723318801876594682689112326594444341. P120 R Balfour GNFS 2020-12-23 3+2 1458L C232 272778179581700214608940613130848043155524950157485759256767991922069865314923455527672324477. P140 NFS@Home & J Becker SNFS 2020-12-26 7+2 334 C281 1572086970565613985593372374878848957028731812522459870919029. C221 Yoyo@home ECM 2020-12-26 8+3 834L C216 5386615734827920616029575531764652188196347636472473209711568761. P152 NFS@Home & J Becker SNFS 2020-12-30 11+10 269 C185 67885338031643306133874275113686175257711072279110334310565761575819502743. P111 NFS@Home & J Becker GNFS 2021-01-03 11-8 283 C184 25757443172192581774724832290466401813631301331104722265517146931911797890420779056821787347. P93 R Balfour GNFS 2021-01-04 8-5 283 C227 464969267080074787461258396097781630167378756522966212957078194975297861002935363382383671. P137 NFS@Home & J Becker SNFS 2021-01-05 9+2 268 C217 142498277492679700462296895337558444538793533656900226962405681936401. P149 NFS@Home & R Dickerson SNFS 2021-01-11 11+2 277 C188 88590756731423307003438243887117477947340188631909874351901. P129 E Hall ECM 2021-01-13 5+2 427 C218 100680094404947719634117385125033732408343221066182601426750212111947841649. P144 NFS@Home & J Becker SNFS 2021-01-15 5-2 427 C220 96217143903778444213232889302950053378903523564203636295750346599109673025775414237. P137 NFS@Home & S Wellman SNFS 2021-01-19 5+2 830M C189 87194481537532219647451961506971310167337599587206670640874119313576546280898121241. P106 NFS@Home & J Becker SNFS 2021-01-21 11-8 287 C238 252913619349347588763877132448479425212438959990695903607339047594314326337. P164 NFS@Home & J Becker SNFS 2021-01-26 5+3 427 C248 16700096523299630893472388366118974723690274818074341769651328600601181666038611931. P166 NFS@Home & S Wellman SNFS 2021-01-26 3+2 1830M C188 37770194609070586001730845912294235047156885480703474181. C132 R Balfour ECM 2021-01-27 3+2 1830M C132 131213278246853941674923688720314447512564184463046996160762761. P70 R Balfour GNFS 2021-01-27 9+2 305 C211 33886426314493237523028241894757682498248211508090019580110200268685617316223681971361. P126 NFS@Home & J Becker SNFS 2021-01-28 11+3 287 C225 42665305442804211960901054513780679767624419132293851490443038684781251905807956131476818463955371699623. P121 NFS@Home & J Becker SNFS 2021-01-29 9-2 305 C197 413020446073576555908361881990070925701150917711393503147365776845747292981180280391. P114 NFS@Home & J Becker SNFS 2021-02-01 4-3 497 C253 33282325839230622131117390810912865176923802246998981830448662948858059087195223739086604472329614857070727957. P143 NFS@Home & J Becker SNFS 2021-02-01 8+3 307 C184 4034465893229948991017240237611887989468926643807749544311. P127 R Balfour GNFS 2021-02-02 11+9 244 C250 27629397626771432899477186319651600758864547022558510301569208366886795222177078053629518005040139761. P150 NFS@Home & J Becker SNFS 2021-02-04 11-3 287 C219 18496624888322543022162761135950249087378640019521785169232653369425835250009897448220711. P131 NFS@Home & J Becker SNFS 2021-02-08 5+3 433 C185 94414140295893398074672341688321994284592975267433041169947368634327222303526629750080826479. P93 NFS@Home & M Vang GNFS 2021-02-08 11+7 296 C290 471269492266311247705814157010450215250487473435313. C239 Yoyo@home ECM 2021-02-13 9+2 538L C198 254654820883764896593943831178564781224544416692849771917112077288998797. P127 NFS@Home & J Becker SNFS 2021-02-14 Last fiddled with by jyb on 2021-02-15 at 05:12
 2021-03-07, 14:45 #1818 richs     "Rich" Aug 2002 Benicia, California 4DB16 Posts 8p3_774M factored Code: p93 factor: 394919403261007891106577866024599716542953650239284344299419901724499859466699310235306392453 p131 factor: 25259855101428349320239531146314859153787374023516210467201845328330310463818470624024408683291807036810023175118643790052502663829 Also posted in NFS@Home 14d Results thread.
 2021-04-23, 16:11 #1819 jyb     Aug 2005 Seattle, WA 32578 Posts This just in... My ECMnet server just popped out a 71-digit 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 GMP-ECM. 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 backward-compatible, 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.
2021-04-23, 17:29   #1820
VBCurtis

"Curtis"
Feb 2005
Riverside, CA

477910 Posts

Quote:
 Originally Posted by jyb My ECMnet server just popped out a 71-digit factor of 8+7,316! Given the B1 value of 110M, this is a very surprising find.
Congratulations, sir! Nice find. Should be top-10 for 2021?

2021-04-23, 18:23   #1821
jyb

Aug 2005
Seattle, WA

29×59 Posts

Quote:
 Originally Posted by VBCurtis Congratulations, sir! Nice find. Should be top-10 for 2021?
Indeed, it currently comes in at #3 (and the only one so far not done by Sam or RyanP). Paul was nice enough to accept it, even without verifiability.

2021-04-23, 20:12   #1822
EdH

"Ed Hall"
Dec 2009

47×79 Posts

Quote:
 Originally Posted by jyb Indeed, it currently comes in at #3 (and the only one so far not done by Sam or RyanP). Paul was nice enough to accept it, even without verifiability.
Congrats! Nice work!

2021-04-24, 02:02   #1823
ryanp

Jun 2012
Boulder, CO

23×5×7 Posts

Quote:
 Originally Posted by jyb Indeed, it currently comes in at #3 (and the only one so far not done by Sam or RyanP). Paul was nice enough to accept it, even without verifiability.
Great find -- congrats!

 2021-04-24, 08:09 #1824 bur   Aug 2020 101001112 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.
2021-04-24, 11:10   #1825
axn

Jun 2003

10011011000002 Posts

Quote:
 Originally Posted by bur What does this notation mean: a+b,nL? I thought it meant a,nL + b,nL, but I coudln't find those in factordb.
I believe you're referring to numbers having Aurifeuillean factorization. There are special combination of a,b,n which have these formula-based 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.

2021-04-24, 13:09   #1826
charybdis

Apr 2020

263 Posts

Quote:
 Originally Posted by axn L & R
Actually L and M.

Jon has a detailed explanation on his page.

 Similar Threads Thread Thread Starter Forum Replies Last Post wpolly Factoring 26 2016-07-29 04:34 Xyzzy Cunningham Tables 42 2014-04-02 18:31 jasong GMP-ECM 6 2006-06-30 08:51 jasong Factoring 1 2006-04-03 17:18 jasong Factoring 27 2006-03-21 02:47

All times are UTC. The time now is 02:10.

Tue May 11 02:10:36 UTC 2021 up 32 days, 20:51, 1 user, load averages: 3.49, 3.22, 3.07