Here are a few for 14e:

C194_137_54
C236_128_81
C231_129_74: sieve on -a side

Polynomials attached.

I should have another eight 14e candidates with polys tomorrow.

[QUOTE=XYYXF;441431][B]C284_135_127[/B] survived 20k+ curves at B1=300M. Maybe that's enough for 15e?[/QUOTE]

Poly for C284_135_127, if anyone thinks it's a feasible 15e candidate:

[code]
n: 51578930581067683364712246470648754575547859544204494416682639186369708191170511796813769844989815356030793636516951005823853033136843878040207423438777859531071980737682922658424237441847940477236250134159969973913839323836340914369119915173296697165060318712911689331475534604820059
# 135^127+127^135, difficulty: 286.14, anorm: 3.33e+040, rnorm: -4.26e+052
# scaled difficulty: 288.16, suggest sieving rational side
# size = 8.811e-015, alpha = 0.000, combined = 3.588e-015, rroots = 0
type: snfs
size: 286
skew: 4.9756
c6: 135
c0: 2048383
Y1: -19216834992144255601295030362371570981188252929
Y0: 545769345012110469286894653523921966552734375
rlim: 536000000
alim: 536000000
lpbr: 33
lpba: 33
mfbr: 66
mfba: 66
rlambda: 3.0
alambda: 3.0
[/code]

[QUOTE=swellman;441639]Here are a few for 14e:

C194_137_54
C236_128_81
C231_129_74: sieve on -a side

Polynomials attached.

I should have another eight 14e candidates with polys tomorrow.[/QUOTE]

Can I ask about the polynomial for C236_128_81? Seems like an odd choice. With a Y1 of -2^94 (instead of -2^92), the polynomial becomes just 9x^6 + 8. Is there a reason for the choices that were made here? Did it just sieve better?

[QUOTE=unconnected;441637]There are several [URL="http://stdkmd.com/nrr/c.cgi?q=reserved_and_submitted"]near-repdigit composites[/URL] reserved by Lionel a while ago. Two of them were cracked by ECM (18883_291 and 54441_248) and others received adequate ECM work and could be loaded into the 14e queue.

Also 90007_248 already done.[/QUOTE]

If you provide a .poly file for these, I'm sure they can be added.

Where is the information about the ECM factors which were found? The page to which you link and FactorDB both show 54441_248 as being a 249-digit composite, with no known factors at all.

[QUOTE=jyb;441705]Can I ask about the polynomial for C236_128_81? Seems like an odd choice. With a Y1 of -2^94 (instead of -2^92), the polynomial becomes just 9x^6 + 8. Is there a reason for the choices that were made here? Did it just sieve better?[/QUOTE]

Plugging into msieve, there is a huge difference between these two:
[CODE]skew 4.00, size 1.996e-012, alpha 0.120, combined = 2.036e-013 rroots = 0
skew 1.00, size 3.794e-012, alpha 1.337, combined = 3.174e-013 rroots = 0
[/CODE]
That is a 60% better score!

[QUOTE=swellman;441641]Poly for C284_135_127, if anyone thinks it's a feasible 15e candidate:[/quote]

I have done the trial sieving, and I don't think it is a feasible 15e candidate: in the best configuration, which is with 3 large algebraic primes and sieving on the rational side, the yield on quite a fast machine is

[code]
total yield: 8693, q=500010029 (1.50569 sec/rel)
[/code]

so we would be sieving 1000M special-Q to get a reasonable number of relations, and it would take 60% longer than C272_136_105 which I already thought was on the edge of feasibility.

[QUOTE=jyb;441705]Can I ask about the polynomial for C236_128_81? Seems like an odd choice. With a Y1 of -2^94 (instead of -2^92), the polynomial becomes just 9x^6 + 8. Is there a reason for the choices that were made here? Did it just sieve better?[/QUOTE]

The polynomial is an output from Yafu. It generates dozen of candidate polys and then test sieves the top three. I believe it compares the rational and algebraic norms for each poly, looking for the best balance. Ultimately Yafu compares ETA as the final determining factor.

While Yafu's poly select is a powerful tool, obviously it is not authoritative. If you believe the alternative poly is a better fit then we should use it. Yield and ETA from test sieving are the acid test!

[QUOTE=swellman;441718]The polynomial is an output from Yafu. It generates dozen of candidate polys and then test sieves the top three. I believe it compares the rational and algebraic norms for each poly, looking for the best balance. Ultimately Yafu compares ETA as the final determining factor.

While Yafu's poly select is a powerful tool, obviously it is not authoritative. If you believe the alternative poly is a better fit then we should use it. Yield and ETA from test sieving are the acid test![/QUOTE]

Okay, I've done a little test sieving. My tests show a substantially higher yield and 15-20% more relations per second with the simpler polynomial (i.e. the one I suggested rather than the one Yafu chose). So I'm switching it to that one.

[QUOTE=jyb;441750]Okay, I've done a little test sieving. My tests show a substantially higher yield and 15-20% more relations per second with the simpler polynomial (i.e. the one I suggested rather than the one Yafu chose). So I'm switching it to that one.[/QUOTE]

Good catch!

Here are the other eight candidates for 14e:

C229_123_88 use -a side
C227_124_85
C216_131_67
C224_136_106
C226_137_55
C212_138_53
C208_148_104 use -a side
C239_150_41

[QUOTE=swellman;441767]Good catch!

Here are the other eight candidates for 14e:

C229_123_88 use -a side
C227_124_85
C216_131_67
C224_136_106
C226_137_55
C212_138_53
C208_148_104 use -a side
C239_150_41[/QUOTE]

So are there any guesses as to what confidence we should have that these really are the best polynomials? (Where by "best" I really mean "within a few percent of the best".)

As you can maybe tell, I'm a little disturbed that Yafu would choose such a non-obvious polynomial that turns out to be clearly worse than the obvious one. It would be a shame if it's doing that routinely and we're wasting 15% of our computing resources during sieving.

Yafu does trial sieve, so it's *possible* that the original poly run was polluted somehow to came out with the wrong result. This is of course rather unlikely. I'll try and fiddle with it soon.