Fast Breeding (guru management)

[jyb]

Originally Posted by swellman

Thanks for checking and queuing the polys. My hand calculations for C239_150_41 gave x^6+150 as a possible poly (with appropriate Y1 and Y0) though yoyo ultimately settled on 6x^6+625. Glad you found a superior choice. Like you and axn, I'm curious as to the performance of the various polys when swapping cn and c0. I'll run a few comparisons tonight.

Test sieving - yoyo test sieves over a range of 2000 spec_Q in poly selection. I've watched yoyo run a lot of test sieving over the years and I think this is a decent metric for comparison. Typically one or two polys will run nicely, with ETAs close and maybe one poly having a slightly better yield. The performance of the remaining poly(s) will typically be just awful. Test sieving it 5-10x longer isn't going to make it any better. One might argue for more extensive test sieving of the leading candidate polys but how much fine tuning is really needed on an SNFS 230 composite? I've read here in the forum that a minimum test sieving range of 1e5 is needed, preferably over 3-5 samples spread through the anticipated spec_Q range. A lot of work for a ~1% improvement via poly select. Maybe for high difficulty NFS efforts?

Agreed, 1e5 test sieving sounds like an awful lot of work for the typical 14e candidate, given the expected total sieving time. (OTOH, the sieving for C202_123_83 is going sufficiently badly right now that perhaps more test sieving with some different polynomials would have been better.) It may indeed be reasonable for the bigger jobs.

[swellman]

Here are two more composites for 14e. I won't post any additional xyyx candidates until the grid grows hungry again, but these may tie into our previous discussion.

The first poly has simple characteristics, seems fairly noncontroversial.

The second poly is a bit uglier. My hand calculations looked worse! x^6+19044 popped out, but seemed to sieve slower. Does anyone see a more obvious, better poly?


C201_125_82
C234_138_82

n: 208619775005214841872901255277508087918295528349999331578186378063727571230932513421692519429944207236973367070389336554107228110726829756207670114399908202861452045440891937445812698048257603452031981
# 125^82+82^125, difficulty: 239.23, anorm: 4.47e+030, rnorm: 5.96e+053
# scaled difficulty: 243.08, suggest sieving rational side
# size = 2.980e-016, alpha = 0.000, combined = 4.288e-013, rroots = 1
type: snfs
size: 239
skew: 1.3797
c5: 1
c0: 5
Y1: -17763568394002504646778106689453125
Y0: 700400277682442761269690122161193848974377746432
rlim: 134000000
alim: 134000000
lpbr: 31
lpba: 31
mfbr: 62
mfba: 62
rlambda: 2.7
alambda: 2.7

n: 530294512697343408215308203117955179097758826435472262903487341111485349479428742320761636588771494814865173847693389305181857312882489411942396542055355115353744426226507822521151678628146666749224478114716494498314424567309478447377
# 138^82+82^138, difficulty: 240.73, anorm: 8.28e+038, rnorm: -8.34e+045
# scaled difficulty: 241.90, suggest sieving rational side
# size = 3.930e-012, alpha = 0.000, combined = 3.301e-013, rroots = 0
type: snfs
size: 240
skew: 1.7225
c6: 81
c0: 2116
Y1: -6357680009799417283726499850563660657152
Y0: 18482725587447593211734307
rlim: 134000000
alim: 134000000
lpbr: 31
lpba: 31
mfbr: 62
mfba: 62
rlambda: 2.7
alambda: 2.7

[jyb]

Originally Posted by swellman

Here are two more composites for 14e. I won't post any additional xyyx candidates until the grid grows hungry again, but these may tie into our previous discussion.

The first poly has simple characteristics, seems fairly noncontroversial.

The second poly is a bit uglier. My hand calculations looked worse! x^6+19044 popped out, but seemed to sieve slower. Does anyone see a more obvious, better poly?


C201_125_82
C234_138_82

The only controversy I can think of for the first candidate is whether a quintic is appropriate for numbers of this size. I tried sieving with x^6+82, and it was better for low values of sp-Q, but its yield dropped much more quickly than with the quintic, and it was substantially worse for higher values.

As for the second candidate, I also tried 4761x^6+16, which turned out to be marginally worse than either of the other polys you suggested. OTOH, I found x^6+19044 to sieve a tiny bit better than 81x^6+2116. The difference was small enough that it could easily go the other way for different ranges than I tried (as it apparently did for you).

[swellman]

I remembered (and found!) this post by Batalov in response to some problems we encountered with sieving. It seems relevant to the recent discussion.

[jyb]

Originally Posted by jyb

The only controversy I can think of for the first candidate is whether a quintic is appropriate for numbers of this size.

Speaking of quintics, I was moved to check on C202_123_83, since it's giving such awful yields right now.

- It's using a quintic, 83^3*x^5 + 123^3. Abysmal yield.

- Another obvious quintic would be 123^2*x^5 + 83^2. This one is even worse. (The SNFS difficulty goes up from 236 to 244, so unsurprising.)

- The sextic polynomial 83^3*x^6 + 123 is interesting. Much better performance (though lower yield) for low spec-Q. Slightly worse performance for higher spec-Q.

- The sextic 123*83^3*x^6 + 1 appears to be the best of all. Better performance and yield in all ranges I checked.

So what caused Yafu to choose a quintic when there was a better sextic available?

[jyb]

Originally Posted by swellman

I remembered (and found!) this post by Batalov in response to some problems we encountered with sieving. It seems relevant to the recent discussion.

Well the relevant part is this:

Originally Posted by Batalov

These unwritten rules were:
1. Y1 > 0
2. |Y1| <= |Y0|

Both of these "rules" are routinely violated in the polynomials you've been feeding to the grid. I think they all have Y1 < 0, and see C178_140_114, which just sieved, or C212_138_53 or C229_123_88 for examples with |Y1| > |Y0|.

I think that maybe the problems associated with these guidelines no longer apply, as Batalov implied.

[swellman]

Originally Posted by jyb

Speaking of quintics, I was moved to check on C202_123_83, since it's giving such awful yields right now.

...

So what caused Yafu to choose a quintic when there was a better sextic available?

Probably limitations on the nature of test sieving. And some composites just have ugly polynomials no matter what. The transition from quintic to sextic is not a clear line either, at least in my experience. At least C202_123_83 is almost sieved, apologies to all for the unnecessary sweat in getting it done.

We are approaching the end of 14e candidates in the xyyx project - less than 70 remaining at last check. Working on a better process for presenting candidates to the queue. I do not wish to offer up suboptimal polys, even if they are the exception more than the rule. One is too many! And 15e work will magnify the problem once we go there.

Jyb - I'll PM you if you are amenable, just to bounce a couple of ideas off of you.

[pinhodecarlos]

No worries about C202_123_83. I only think for the future we need to be more careful on choosing the polynomial and in case of doubt just report here for support.

[jyb]

Originally Posted by swellman

We are approaching the end of 14e candidates in the xyyx project - less than 70 remaining at last check.

Yes, and the last of the NFS-ready homogeneous Cunninghams is queued now. We're about to run out of candidates!

Originally Posted by swellman

Jyb - I'll PM you if you are amenable, just to bounce a couple of ideas off of you.

Sure, anytime.

[pinhodecarlos]

Jon,

We still have http://mersennus.net/fibonacci/.

[jyb]

Originally Posted by pinhodecarlos

Jon,

We still have http://mersennus.net/fibonacci/.

Are any of those appropriate for the 14e queue? It looks like their SNFS difficulties are all above 270.