Latest update posted.
 

The latest tables have just hit the web site. There have been 15 new factors found in the last couple of months and the number of composites has decreased to 647.

Paul

[QUOTE=xilman;261990]The latest tables have just hit the web site. There have been 15 new factors found in the last couple of months and the number of composites has decreased to 647.

Paul[/QUOTE]And yet another update has hit the web. There are six new factorizations since 6th May, all completions, so the number of composites has fallen to 641.

I'm away for a couple of weeks and it's likely that I won't be able to process email. Please continue to send any factorizations you find.

Paul

Another update has been uploaded. There are three new factors, 11^202+8^202 was factored by Andi47 by GNFS, whereas Jon Becker's ECMNET client found a p44 factor of 10^238+7^238238 and a p46 from 9^211-2^211. These were the first two ECM factors reported since early April. There are now 638 composites remaining.

As SSW says: keep the factors coming!


Paul

Update 2011-09-14
 

Another update has just hit the web pages. Nine new factors have been found, six by ECM from Jon Becker and three by SNFS from Ben Buhrow. There are now 628 composites remaining in the comps.gz file at [url]http://www.leyland.vispa.com/numth/factorization/anbn/main.htm[/url]

The ecmnet server has also been updated. Unfortunately, and as Jon notified me by email, 49 composites are missing and so only 579 are loaded there. This situation is harmless (those 579 composites still need factoring, after all) but very frustrating because I've no idea why some keep dropping out of the server's database. Presumably, a bug in the housekeeping scripts needs to be nailed.

Today's update was prompted by Jon finding two p49 factors earlier today!


Paul

[QUOTE=xilman;271730]Another update has just hit the web pages. Nine new factors have been found, six by ECM from Jon Becker and three by SNFS from Ben Buhrow. There are now 628 composites remaining in the comps.gz file at [URL]http://www.leyland.vispa.com/numth/factorization/anbn/main.htm[/URL]
[/QUOTE]

Just a slight correction because I forgot to tell you originally: 5-4 (C141) and 8+7 (C146) I did with GNFS, not SNFS.

[QUOTE=bsquared;271732]Just a slight correction because I forgot to tell you originally: 5-4 (C141) and 8+7 (C146) I did with GNFS, not SNFS.[/QUOTE]Thanks. I'll update the table here but won't bother changing the web page until there is at least one more factor to report.

Paul

Update 2011-10-23
 

Another month has passed and another ten factors found. There are now 618 composites remaining in the tables.[code]7+5 229 C124 17396621554951997707823828646184129755962069688281899828223. P66 P Leyland GNFS 2011-09-20
3-2 509 C154 1880785718228755501135514888227503963356750083. P109 J Becker ECM 2011-09-21
6-5 289 C169 36922083876294494809741478500353905181000406819. P122 R Silverman ECM 2011-09-24
9-5 229 C135 728215296524145287561585556252447094777937929. P90 J Becker ECM 2011-10-01
7+4 256 C172 14138620053270279171951987149801906201593040733468161. P120 J Becker ECM 2011-10-04
12+7 203 C170 63893624566549276691793351661070043093424607. P126 R Silverman ECM 2011-10-05
9-2 221 C184 25206285585387916305390146986278575883111867237891751. P131 J Becker ECM 2011-10-11
11+10 202 C172 20946300565328540029595701472835970642250264231640397. P120 R Silverman ECM 2011-10-20
10+9 212 C205 6962707396077029231074867935230216211226834081. C159 J Becker ECM 2011-10-23
7-3 257 C212 125679421318774800176550790999944344153383771. C168 J Becker ECM 2011-10-23
[/code]

Paul

Update 2011-11-22
 

Another months, another 12 factors, leaving 609 composites:
[code]
7+6 299 C224 758454365874703735212851865326938107200378758477. C176 J Becker ECM 2011-10-25
5-4 353 C175 153574619276768281361953123456121705535304060618051. P125 J Becker ECM 2011-10-29
7+4 298 C174 122318582929347535086799049709360958793558981. P130 J Becker ECM 2011-11-04
5-4 307 C173 4124589907808646546772506044389003672723432438379. P124 J Becker ECM 2011-11-05
8+5 218 C127 13328011195026361740979587698409481780030265738357381. P75 W Roonguthai GNFS 2011-11-11
8-5 211 C129 1090552902012511025449030624021355931957090167438954111. P75 W Roonguthai GNFS 2011-11-15
8+7 247 C129 73653887033110753242360428191174682847018401717804895141701039. P67 W Roonguthai GNFS 2011-11-18
10+3 221 C172 28897762414008705259244616945787152873685664359. P125 J Becker ECM 2011-11-18
7-5 269 C206 1017107053145780990377554374384538204187484317. P161 J Becker ECM 2011-11-19
7+6 233 C129 352644927097323230788916470919561095292281307619376202516597467. P67 W Roonguthai GNFS 2011-11-20
11+6 229 C215 10588018905652372555612288235991364930057828253. C169 J Becker ECM 2011-11-21
11-6 211 C184 21096938613015455752169001965568394486916175078245317. C132 J Becker ECM 2011-11-21
[/code]There are still quite a few relatively easy GNFS factors, but you should be careful to co-ordinate your work with Warut...

Paul

7^265+6^265 factored by SNFS
 

I factored 7[sup]265[/sup]+6[sup]265[/sup] by snfs.

poly was:
[CODE]n: 134032784829224188704805801954711437509488777852060587147730874530372834713663941606698531297582568354637016827625353091897166774095794261086503256231291
skew: 1
c4: 1
c3: -1
c2: 1
c1: -1
c0: 1
Y0: -616873509628062366290756156815389726793178407
Y1: 174588755932389037098918153698611839369216
rlim: 9500000
alim: 9500000
lpbr: 28
lpba: 28
rlambda: 2.6
alambda: 2.6
mfbr: 54
mfba: 54
[/CODE]

sieved on the -r side from Q=3M to 17M (with a gap of ~1M in between due to an apparently failed resume of a subrange) with the 13e siever. 21.59M raw relations, 3.4M free relations, 21.52M unique relations.

Matrix was:
[CODE]matrix is 1654500 x 1654725 (446.8 MB) with weight 116960755 (70.68/col)
sparse part has weight 107184595 (64.77/col)
[/CODE]

matrix solving step took ~7:40 hours on a C2D@2.0 GHz (2 threads)

Sqrt found the factors in the 4th dependency:

[CODE]prp65 factor: 25475823935618895744203100212826476959833250674725417368194279691
prp88 factor: 5261175660812560466410837393152937241913877737975905852396615560945428010316565519307601[/CODE]

A minor mystery
 

Can you help me solve a minor mystery?

Warut Roonguthai sent me a GNFS factorization for 11^229+6^229 C123. However, my tables had the cofactor as a C169 so was missing a P46 factor. Extensive searching of my email repository didn't find it.

Some detective work by Warut turned up [quote]According to [url]http://factordb.com/index.php?id=1100000000462981915[/url] the factor you are looking for is

P46 = 8073044562493033989204180312399123271715177323

and it was found by ECM no later than November 7, 2011, 7:12 am, clearly before Jon Becker found

P47 = 10588018905652372555612288235991364930057828253.[/quote]

Anyone here owning up to the discovery, or know who may have found it?

Paul

IP check to see who submitted it?