[QUOTE=jyb;243422]I calculate that it needs about 3300 curves with B1 = 43e6. It's received about 110 via Paul's ECMnet server. No idea if anyone else has thrown more curves at it.[/QUOTE]

Thanks. I have run ~2200@11e6 overnight and will switch to 43e6 now.

Is there a way to get the ECM statistics of Paul's ECMnet server?

[QUOTE=Andi47;243446]Thanks. I have run ~2200@11e6 overnight and will switch to 43e6 now.

Is there a way to get the ECM statistics of Paul's ECMnet server?[/QUOTE]
[url]http://207.192.74.48:8194/[/url]


Paul

[QUOTE=xilman;243462][url]http://207.192.74.48:8194/[/url]


Paul[/QUOTE]

thanks!!!

11,6,235- c128
 

11,6,235- c128 = p61*p68 via GNFS:

[code]prp61 factor: 5211907482166741854589248371911529534402043859881657306177041
prp68 factor: 14242818812591555317393439967379540697889965598423126596248717623571
[/code]

[QUOTE=Andi47;243446]Thanks. I have run ~2200@11e6 overnight and will switch to 43e6 now.

Is there a way to get the ECM statistics of Paul's ECMnet server?[/QUOTE]

3240@43e6 and 42@26e7, no factor. Switching to SNFS.

edit: poly f =
[code]n:
100306814899904714076693496677114788947208958618141076068483677260474467176017256197514918743719724022199520107701972965399638594181462697660563452279820102258288582611745055060802380538252546923924881
c6: 1
c5: 0
c4: -7
c3: 0
c2: 14
c1: 0
c0: -7
Y1: 8683513829059386822166052864
Y0: -255476698618766184698924625112226297
skew: 1.383
rlim: 33554431
alim: 33554431
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6[/code]

skew should be somewhere near |c0|^1/6=1.383?

edit2: g=x^6-x^5+x^4-x^3+x^2-x+1 gives somewhat more relations per q (same parameters, but with skew=1, sieved -f 20000000, -c 1000) than f, but with g it should be diff. 230, and with f diff. should be 213?

edit3: I just see that I should sieve f on the -r side, or even on both sides.

[QUOTE=Andi47;244215]3240@43e6 and 42@26e7, no factor. Switching to SNFS.

edit: poly f =
[code]n:
100306814899904714076693496677114788947208958618141076068483677260474467176017256197514918743719724022199520107701972965399638594181462697660563452279820102258288582611745055060802380538252546923924881
c6: 1
c5: 0
c4: -7
c3: 0
c2: 14
c1: 0
c0: -7
Y1: 8683513829059386822166052864
Y0: -255476698618766184698924625112226297
skew: 1.383
rlim: 33554431
alim: 33554431
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6[/code]

skew should be somewhere near |c0|^1/6=1.383?

edit2: g=x^6-x^5+x^4-x^3+x^2-x+1 gives somewhat more relations per q (same parameters, but with skew=1, sieved -f 20000000, -c 1000) than f, but with g it should be diff. 230, and with f diff. should be 213?

edit3: I just see that I should sieve f on the -r side, or even on both sides.[/QUOTE]

Is f the polynomial you meant when you referred above (post #977) to the "obvious sextic poly"? I don't understand where it came from; can you explain the derivation? Your polynomial g is the one which I would have thought was the obvious sextic. And I'm pretty sure its difficulty is 213; I don't see where 230 would come from.

[QUOTE=jyb;244388]Is f the polynomial you meant when you referred above (post #977) to the "obvious sextic poly"? I don't understand where it came from; can you explain the derivation? Your polynomial g is the one which I would have thought was the obvious sextic. And I'm pretty sure its difficulty is 213; I don't see where 230 would come from.[/QUOTE]

When I talked about "the obvious sextic" in the first time, I was also thinking about g - I didn't see f in the first time. I have just read the difficulty given at the [URL="http://www.chiark.greenend.org.uk/ucgi/~twomack/homcun.pl"]Homogenius Cunningham Reservation Page[/URL] without doublechecking.

Later I saw that there is another poly in this (which I was referring to as f).

How the polys are derived (let the homogeneous cunningham be c=a^n+b^n):

[B]g[/B] is quite easy: n is divisible by 7, so one can [B]divide c by the algebraic factor (a^(n/7)+b^(n/7))[/B] and get the poly g as result for the algebraic side. The rational side poly is b^(n/7)*x – a^(n/7).

to get [B]f[/B], I did this in Pary gp (intention: use that n is divisible by 14, divide by (x^2+1) (note: in pari it seems that I have to calculate for the special case (x^14+1), substitute t=(x^2+1)/x):

[code](09:05) gp > A=factor(x^14+1)[2,1]
%7 = x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
(09:06) gp > t=(x^2+1)/x
%8 = (x^2 + 1)/x
(09:07) gp > x^6*t^6-A
%9 = 7*x^10 + 14*x^8 + 21*x^6 + 14*x^4 + 7*x^2
(09:07) gp > (x^6*t^6-7*t^5)-A
%10 = (7*x^15 + 14*x^13 + 21*x^11 - 7*x^10 + 14*x^9 - 35*x^8 + 7*x^7 - 70*x^6 -70*x^4 - 35*x^2 - 7)/x^5
(09:08) gp > (x^6*t^6-7*t^4)-A
%11 = (7*x^14 + 14*x^12 + 21*x^10 + 7*x^8 - 21*x^6 - 42*x^4 - 28*x^2 - 7)/x^4
(09:08) gp > (x^6*t^6+7*t^5)-A
%12 = (7*x^15 + 14*x^13 + 21*x^11 + 7*x^10 + 14*x^9 + 35*x^8 + 7*x^7 + 70*x^6 +70*x^4 + 35*x^2 + 7)/x^5
(09:09) gp > x^6*(t^6-7*t^5)-A
%13 = -7*x^11 + 7*x^10 - 35*x^9 + 14*x^8 - 70*x^7 + 21*x^6 - 70*x^5 + 14*x^4 - 35*x^3 + 7*x^2 - 7*x
(09:09) gp > x^6*(t^6-7*t^4)-A
%14 = -14*x^8 - 21*x^6 - 14*x^4
(09:09) gp > x^6*(t^6-7*t^4+14*t^2)-A
%15 = 7*x^6
(09:10) gp > x^6*(t^6-7*t^4+14*t^2-7)-A
%16 = 0
(09:10) gp > (x^14+1)/(x^12-x^10+x^8-x^6+x^4-x^2+1)
%17 = x^2 + 1
(09:18) gp > (x^7+1)/(x+1)
%18 = x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
[/code]

Hmmm... I'm not sure what I did (or mis-did?) to calculate the difficulties. Maybe you are right and the difficulty of g is indeed 213. :question:

[QUOTE=jyb;244388]Is f the polynomial you meant when you referred above (post #977) to the "obvious sextic poly"? I don't understand where it came from; can you explain the derivation? Your polynomial g is the one which I would have thought was the obvious sextic. And I'm pretty sure its difficulty is 213; I don't see where 230 would come from.[/QUOTE]

Oh wait, I see what you did. You took the polynomial you got from dividing out the algebraic factor and considered it to be of 12th degree, then you did the degree-halving trick. Huh, it wouldn't have occurred to me to not just consider the quotient polynomial to be of 6th degree and stop right there.

In any case, I believe that either way the SNFS difficulty is 213, so if g appears to be sieving better, then I'd use that.

Edit: just saw your reply. I guess you didn't think about it quite the way I thought you did, but you got the same result.

BTW, you can run this number through akruppa's phi program, and it will happily generate g for you. It also conveniently reports that g's difficulty is 212.44.

11^238+4^238 factored
 

11^238+4^238 factored

poly f
[code]n:
100306814899904714076693496677114788947208958618141076068483677260474467176017256197514918743719724022199520107701972965399638594181462697660563452279820102258288582611745055060802380538252546923924881
c6: 1
c5: 0
c4: -7
c3: 0
c2: 14
c1: 0
c0: -7
Y1: 8683513829059386822166052864
Y0: -255476698618766184698924625112226297
skew: 1.383
rlim: 33554431
alim: 33554431
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6[/code]

(polynomial g mentioned in post #984 might have been faster, but when I recognized my miscalculation of the difficulty of f and g, I was well into sieving with f and thus didn't want to start over.)

sieved from 1.4M to 17M on the -r side and from 2M to 3M on on the -a side.

[code]Fri Jan 14 07:02:03 2011 Msieve v. 1.47
Fri Jan 14 07:02:03 2011 random seeds: 929ab758 1769fac0
Fri Jan 14 07:02:03 2011 factoring 100306814899904714076693496677114788947208958618141076068483677260474467176017256197514918743719724022199520107701972965399638594181462697660563452279820102258288582611745055060802380538252546923924881 (201 digits)
Fri Jan 14 07:02:04 2011 searching for 15-digit factors
Fri Jan 14 07:02:04 2011 commencing number field sieve (201-digit input)
Fri Jan 14 07:02:04 2011 R0: -255476698618766184698924625112226297
Fri Jan 14 07:02:04 2011 R1: 8683513829059386822166052864
Fri Jan 14 07:02:04 2011 A0: -7
Fri Jan 14 07:02:04 2011 A1: 0
Fri Jan 14 07:02:04 2011 A2: 14
Fri Jan 14 07:02:04 2011 A3: 0
Fri Jan 14 07:02:04 2011 A4: -7
Fri Jan 14 07:02:04 2011 A5: 0
Fri Jan 14 07:02:04 2011 A6: 1
Fri Jan 14 07:02:04 2011 skew 1.00, size 2.058e-010, alpha 2.845, combined = 5.347e-012 rroots = 6
Fri Jan 14 07:02:04 2011
Fri Jan 14 07:02:04 2011 commencing relation filtering
Fri Jan 14 07:02:04 2011 estimated available RAM is 8125.4 MB
Fri Jan 14 07:02:04 2011 commencing duplicate removal, pass 1

relation errors snipped

Fri Jan 14 07:06:11 2011 found 11797144 hash collisions in 53907251 relations
Fri Jan 14 07:06:11 2011 commencing duplicate removal, pass 2
Fri Jan 14 07:07:02 2011 found 12967922 duplicates and 40939329 unique relations
Fri Jan 14 07:07:02 2011 memory use: 330.4 MB
Fri Jan 14 07:07:02 2011 reading ideals above 21954560
Fri Jan 14 07:07:02 2011 commencing singleton removal, initial pass
Fri Jan 14 07:11:19 2011 memory use: 1378.0 MB
Fri Jan 14 07:11:21 2011 reading all ideals from disk
Fri Jan 14 07:11:21 2011 memory use: 793.1 MB
Fri Jan 14 07:11:23 2011 commencing in-memory singleton removal
Fri Jan 14 07:11:25 2011 begin with 40939329 relations and 41265475 unique ideals
Fri Jan 14 07:11:47 2011 reduce to 18308784 relations and 15005754 ideals in 22 passes
Fri Jan 14 07:11:47 2011 max relations containing the same ideal: 27
Fri Jan 14 07:11:48 2011 reading ideals above 720000
Fri Jan 14 07:11:49 2011 commencing singleton removal, initial pass
Fri Jan 14 07:14:16 2011 memory use: 376.5 MB
Fri Jan 14 07:14:16 2011 reading all ideals from disk
Fri Jan 14 07:14:16 2011 memory use: 628.7 MB
Fri Jan 14 07:14:18 2011 keeping 17662978 ideals with weight <= 200, target excess is 116097
Fri Jan 14 07:14:19 2011 commencing in-memory singleton removal
Fri Jan 14 07:14:20 2011 begin with 18308876 relations and 17662978 unique ideals
Fri Jan 14 07:14:36 2011 reduce to 18302603 relations and 17656268 ideals in 10 passes
Fri Jan 14 07:14:36 2011 max relations containing the same ideal: 200
Fri Jan 14 07:14:44 2011 removing 2491971 relations and 2236140 ideals in 255831 cliques
Fri Jan 14 07:14:45 2011 commencing in-memory singleton removal
Fri Jan 14 07:14:46 2011 begin with 15810632 relations and 17656268 unique ideals
Fri Jan 14 07:15:01 2011 reduce to 15477648 relations and 15080092 ideals in 12 passes
Fri Jan 14 07:15:01 2011 max relations containing the same ideal: 180
Fri Jan 14 07:15:08 2011 removing 1812252 relations and 1556421 ideals in 255831 cliques
Fri Jan 14 07:15:09 2011 commencing in-memory singleton removal
Fri Jan 14 07:15:10 2011 begin with 13665396 relations and 15080092 unique ideals
Fri Jan 14 07:15:21 2011 reduce to 13464991 relations and 13319434 ideals in 10 passes
Fri Jan 14 07:15:21 2011 max relations containing the same ideal: 164
Fri Jan 14 07:15:27 2011 removing 128961 relations and 118077 ideals in 10884 cliques
Fri Jan 14 07:15:27 2011 commencing in-memory singleton removal
Fri Jan 14 07:15:28 2011 begin with 13336030 relations and 13319434 unique ideals
Fri Jan 14 07:15:35 2011 reduce to 13335052 relations and 13200378 ideals in 6 passes
Fri Jan 14 07:15:35 2011 max relations containing the same ideal: 162
Fri Jan 14 07:15:38 2011 relations with 0 large ideals: 9666
Fri Jan 14 07:15:38 2011 relations with 1 large ideals: 290
Fri Jan 14 07:15:38 2011 relations with 2 large ideals: 7176
Fri Jan 14 07:15:38 2011 relations with 3 large ideals: 74467
Fri Jan 14 07:15:38 2011 relations with 4 large ideals: 416673
Fri Jan 14 07:15:38 2011 relations with 5 large ideals: 1386230
Fri Jan 14 07:15:38 2011 relations with 6 large ideals: 2837511
Fri Jan 14 07:15:38 2011 relations with 7+ large ideals: 8603039
Fri Jan 14 07:15:38 2011 commencing 2-way merge
Fri Jan 14 07:15:47 2011 reduce to 8038760 relation sets and 7904086 unique ideals
Fri Jan 14 07:15:47 2011 commencing full merge
Fri Jan 14 07:17:57 2011 memory use: 960.5 MB
Fri Jan 14 07:17:57 2011 found 4135138 cycles, need 4122286
Fri Jan 14 07:17:58 2011 weight of 4122286 cycles is about 288631818 (70.02/cycle)
Fri Jan 14 07:17:58 2011 distribution of cycle lengths:
Fri Jan 14 07:17:58 2011 1 relations: 604316
Fri Jan 14 07:17:58 2011 2 relations: 530686
Fri Jan 14 07:17:58 2011 3 relations: 496076
Fri Jan 14 07:17:58 2011 4 relations: 431961
Fri Jan 14 07:17:58 2011 5 relations: 364318
Fri Jan 14 07:17:58 2011 6 relations: 309529
Fri Jan 14 07:17:58 2011 7 relations: 262271
Fri Jan 14 07:17:58 2011 8 relations: 215804
Fri Jan 14 07:17:58 2011 9 relations: 177654
Fri Jan 14 07:17:58 2011 10+ relations: 729671
Fri Jan 14 07:17:58 2011 heaviest cycle: 28 relations
Fri Jan 14 07:17:58 2011 commencing cycle optimization
Fri Jan 14 07:18:03 2011 start with 23497715 relations
Fri Jan 14 07:18:41 2011 pruned 454924 relations
Fri Jan 14 07:18:41 2011 memory use: 783.6 MB
Fri Jan 14 07:18:41 2011 distribution of cycle lengths:
Fri Jan 14 07:18:41 2011 1 relations: 604316
Fri Jan 14 07:18:41 2011 2 relations: 539472
Fri Jan 14 07:18:41 2011 3 relations: 509556
Fri Jan 14 07:18:41 2011 4 relations: 438682
Fri Jan 14 07:18:41 2011 5 relations: 370506
Fri Jan 14 07:18:41 2011 6 relations: 311468
Fri Jan 14 07:18:41 2011 7 relations: 262838
Fri Jan 14 07:18:41 2011 8 relations: 214540
Fri Jan 14 07:18:41 2011 9 relations: 175868
Fri Jan 14 07:18:41 2011 10+ relations: 695040
Fri Jan 14 07:18:41 2011 heaviest cycle: 28 relations
Fri Jan 14 07:18:45 2011 RelProcTime: 1001
Fri Jan 14 07:18:45 2011
Fri Jan 14 07:18:45 2011 commencing linear algebra
Fri Jan 14 07:18:46 2011 read 4122286 cycles
Fri Jan 14 07:18:52 2011 cycles contain 13193699 unique relations
Fri Jan 14 07:20:02 2011 read 13193699 relations
Fri Jan 14 07:20:18 2011 using 20 quadratic characters above 536870910
Fri Jan 14 07:21:18 2011 building initial matrix
Fri Jan 14 07:23:23 2011 memory use: 1589.5 MB
Fri Jan 14 07:23:28 2011 read 4122286 cycles
Fri Jan 14 07:23:29 2011 matrix is 4122108 x 4122286 (1226.5 MB) with weight 355924854 (86.34/col)
Fri Jan 14 07:23:29 2011 sparse part has weight 280301302 (68.00/col)
Fri Jan 14 07:24:05 2011 filtering completed in 2 passes
Fri Jan 14 07:24:06 2011 matrix is 4118939 x 4119117 (1226.3 MB) with weight 355842772 (86.39/col)
Fri Jan 14 07:24:06 2011 sparse part has weight 280278205 (68.04/col)
Fri Jan 14 07:24:18 2011 matrix starts at (0, 0)
Fri Jan 14 07:24:19 2011 matrix is 4118939 x 4119117 (1226.3 MB) with weight 355842772 (86.39/col)
Fri Jan 14 07:24:19 2011 sparse part has weight 280278205 (68.04/col)
Fri Jan 14 07:24:19 2011 saving the first 48 matrix rows for later
Fri Jan 14 07:24:20 2011 matrix includes 64 packed rows
Fri Jan 14 07:24:21 2011 matrix is 4118891 x 4119117 (1176.6 MB) with weight 285990568 (69.43/col)
Fri Jan 14 07:24:21 2011 sparse part has weight 267248176 (64.88/col)
Fri Jan 14 07:24:21 2011 using block size 65536 for processor cache size 8192 kB
Fri Jan 14 07:24:36 2011 commencing Lanczos iteration (6 threads)
Fri Jan 14 07:24:36 2011 memory use: 1112.0 MB
Fri Jan 14 07:25:05 2011 linear algebra at 0.0%, ETA 21h 6m
Fri Jan 14 07:25:14 2011 checkpointing every 200000 dimensions
Sat Jan 15 03:50:39 2011 lanczos halted after 65133 iterations (dim = 4118889)
Sat Jan 15 03:50:44 2011 recovered 33 nontrivial dependencies
Sat Jan 15 03:50:44 2011 BLanczosTime: 73919
Sat Jan 15 03:50:44 2011
Sat Jan 15 03:50:44 2011 commencing square root phase
Sat Jan 15 03:50:44 2011 reading relations for dependency 1
Sat Jan 15 03:50:45 2011 read 2060261 cycles
Sat Jan 15 03:50:48 2011 cycles contain 6594198 unique relations
Sat Jan 15 03:51:42 2011 read 6594198 relations
Sat Jan 15 03:52:10 2011 multiplying 6594198 relations
Sat Jan 15 03:56:58 2011 multiply complete, coefficients have about 152.46 million bits
Sat Jan 15 03:56:59 2011 initial square root is modulo 296117
Sat Jan 15 04:03:06 2011 sqrtTime: 742
Sat Jan 15 04:03:06 2011 prp92 factor: 36927255648095989951985774656987568839655052931187682592268434062028505862220007198170243309
Sat Jan 15 04:03:06 2011 prp109 factor: 2716335485523052784316697212187945556566795988731539322457259443328172259035412769964680225310630228996873909
Sat Jan 15 04:03:06 2011 elapsed time 21:01:03[/code]

Update posted
 

I have just posted another set of updated tables which include 14 new factorizations which have been found in the last ten weeks. Apologies for taking so long to post this update.

This update is also the first to which I've contributed for a very long time. Jon Becker found a p51 factor of 12,7,224+ leaving a c142 which I then finished off with GNFS.

The ECMNET server 207.192.74.48:8194 has also been updated. It is now handing out tasks with B1=43M, optimal for finding p50 factors.

Paul

Dang
 

10^247-3^247 was a GNFS 169:

[CODE]Fri Apr 8 20:44:43 2011 prp56 factor: 34581288406972979570753537571251434845112681479616761361
Fri Apr 8 20:44:43 2011 prp114 factor: 186319210949268336029587590143841461202656359110020729733953908458147826268188552190529829616472561587026505541707[/CODE]

My biggest ECM miss to date. Ran 28000 curves at B1=11e7, which gave me a better than 50/50 shot at the bastard.

Shoulda', coulda', woulda'.

Hell!