My best poly (cpu-selected):

[CODE]# norm 1.539532e-16 alpha -7.087319 e 3.239e-13 rroots 5
skew: 33518269.72
c0: 2289333875874569327497038535389419976873388
c1: 382077774062248187325136662799008916
c2: 4894543817187396719305221893
c3: -975365628950895601351
c4: 2294158842579
c5: 202860
Y0: -602870618958276747402796697188929
Y1: 470565207875800817
[/CODE]

Two OPNs from the [URL=http://www.lirmm.fr/~ochem/opn/t600.txt]t600[/URL] file.

2899469274619^19-1 (C172) SNFS-225
3740221981231^19-1 (C179) SNFS-227

Here is another 14e/32 candidate. Yoyo@home is just finishing up ECM to a full t55.

I will run the postprocessing once the sieving is complete. Thank you.

[code]
n: 283191072481051249914583228194650177905740292063875589919551516909659396832663031861991559472215415672107338058778319830834676384387536217135281552494362019768235081706813041110232151987119291978490269
# 137^62+62^137, difficulty: 247.35, anorm: 2.16e+039, rnorm: 5.24e+046
# scaled difficulty: 248.58, suggest sieving rational side
# size = 7.319e-013, alpha = 0.000, combined = 9.909e-014, rroots = 0
type: snfs
size: 247
skew: 10.2559
c6: 1
c0: 1163678
Y1: -2329194047563391944849
Y0: 167883826163764944817996215305490271305728
rlim: 200000000
alim: 200000000
lpbr: 32
lpba: 32
mfbr: 64
mfba: 64
rlambda: 2.8
alambda: 2.8
[/code]

C170 poly
 

@unconnected
CADO-NFS optimizes your poly quite a bit:
[code]
Y0: -602870617628107487170292489335813
Y1: 470565207875800817
c0: 405890601951855611817366374002328675248140
c1: 386640105807127966082616274304256764
c2: -3220985513457604782071787655
c3: -933216056338410174583
c4: 5161329338979
c5: 202860
skew: 35150350.24883
# lognorm 54.92, E 46.95, alpha -7.96 (proj -1.77), 5 real roots
# MurphyE=3.83902180e-13
[/code]Consider speed testing this one by actual sieving.

[QUOTE=RichD;453242]Two OPNs from the [URL=http://www.lirmm.fr/~ochem/opn/t600.txt]t600[/URL] file.

2899469274619^19-1 (C172) SNFS-225
3740221981231^19-1 (C179) SNFS-227[/QUOTE]

Never mind.
I mis-calculated the difficulty. They should be:
SNFS-237
SNFS-239
Which might be better suited for 15e.

But I do have another within range.

327668647153^19-1 (C172) SNFS-219

Best poly for c170 (other parameters suggested by yafu, I've increased alim/rlim a bit):
[CODE]n: 16155374118973955813091649522779062742170185143586034082882967704389689802848431254319353182125901255550801551714585711083348904636336944688336558457044065738232253533181
Y0: -602870617628107487170292489335813
Y1: 470565207875800817
c0: 405890601951855611817366374002328675248140
c1: 386640105807127966082616274304256764
c2: -3220985513457604782071787655
c3: -933216056338410174583
c4: 5161329338979
c5: 202860
skew: 35150350.24883
# lognorm 54.92, E 46.95, alpha -7.96 (proj -1.77), 5 real roots
# MurphyE=3.83902180e-13

rlim: 80000000
alim: 80000000
mfbr: 62
mfba: 62
lpbr: 31
lpba: 31
rlambda: 2.60
alambda: 2.60
lss: 0
[/CODE]

I am back from vacation, is there anything that needs pushing to the queues? I see that 15e is getting a bit short ...

The following posts in this thread contain candidates which have yet to be enqueued

941
940
938
920
910
880
853


There may be others I missed.

I would like to propose the C171 from Aliquot sequence 829332:3638.

Max0526 came up with a number of polys using CADO (see the Polynomial Request Thread, thanks Max!) and the best sieving (0.30 seconds per relation per thread on my i7) was:

[CODE]Y0: -691735415860028161291242601067023
Y1: 25898420289952162105307
c0: 577300829383670786734653724089000359155200
c1: -45090526843823845959056529260126600
c2: -6637850955461852556600436653
c3: 111155248878476001023
c4: 42917566535268
c5: 5418720
skew: 12640532.26887
# MurphyE=3.05653198e-13[/CODE]

I found the following poly using msieve by CPU and it sieves much worse (0.60 seconds per relation per thread):

[CODE]# norm 1.433572e-016 alpha -8.545613 e 3.128e-013 rroots 5
n: 143078471890001396404975722954703592875148935188191068938072316014184174902812459038968421963880118593068060667758149846867638636307227896395788079777289956829055499772249
skew: 718798201.99
c0: -20927250992693086458259129496993713626586796400
c1: 23809337639420727499940642755002298868
c2: 325528092819547637374452732948
c3: -141143903779127307669
c4: -826446704440
c5: 84
Y0: -4428524236781113000924987068997327
Y1: 126683988140215801[/CODE]

I am unsure why the msieve poly sieves so badly compared with the CADO when the MurphyE scores are similar. I am also unsure whether this would be better handled by 14e or 15e. Thanks in advance for considering this number.

[QUOTE=swellman;453462]The following posts in this thread contain candidates which have yet to be enqueued

941
940
938
920
910
880
853


There may be others I missed.[/QUOTE]

853 (C187_141_61) pushed to 15e

880 not pushed - I'm really not happy with three-large-primes-both-sides, for that large a number I would definitely recommend 16e.

910 (C256_127_121) pushed to 15e

938 (C201_137_62) pushed for 14e

941 (a11040:10011) pushed for 14e

I appreciate I have been lazy and only pushed things where there was a code block with the explicit polynomial in ... I have run trivial trial sieving to check I was using the right siever and to get the range about right.

[QUOTE=richs;453484]I would like to propose the C171 from Aliquot sequence 829332:3638[/quote]

Thanks, I'm looking into it. For future advice, it would be useful to post the whole gnfs file (with lpbr and alim values) as well as the range sieved and yield obtained, along with time-per-relation figures, so I can just copy-and-paste the polynomial into the Web interface rather than having to repeat some of the trial sieving myself.

[quote]
I am unsure why the msieve poly sieves so badly compared with the CADO when the MurphyE scores are similar. I am also unsure whether this would be better handled by 14e or 15e. Thanks in advance for considering this number.[/QUOTE]

I think it's a 14e number, the yield-per-Q was something like 7 with 15e which feels a bit big. But I forgot to check the result from the 14e run before going home; I'll finish up in the morning.

This is more a matter of anecdotal observation than science, but I've found that very large skews (and yours is over 2^29) do tend to lead to rather slow sieving.