[QUOTE=fivemack;524039]Place your bets: is a quartic of SNFS difficulty 258.31 going to be easier or harder than a GNFS 195.65?[/QUOTE]

GNFS will be superior. IMHO of course!

[B]QUEUED AS 307_109m1[/B]

C180 from the OPN t600 file.
307^109-1
[CODE]n: 219342985485631316265442071722550692243683588858554966031177608387883403841657934639060534768118755209418166071051802166246203883566248340153057709552356976051818594985665351142461
# expecting poly E from 8.41e-14 to > 9.67e-14
lss: 0
Y0: -51482716348094461165175706033366334
Y1: 119221644080049479
c0: 38646770029987535912516266391431194355905315
c1: 242833785516590445947812024793300718
c2: -589405154582811895754965332941
c3: 19394102442721694323918
c4: 368931528779254
c5: 606480
skew: 41743167.27
# size 1.574e-17, alpha -8.187, combined = 9.171e-14 rroots = 5
type: gnfs
rlim: 268000000
alim: 268000000
lpbr: 32
lpba: 32
mfbr: 64
mfba: 94
rlambda: 2.7
alambda: 3.7[/CODE]
Trial sieving 5K blocks.
[CODE] Q Yield
20M 11312
60M 11661
100M 9978
200M 9544
250M 8846
260M 8136[/CODE]

[QUOTE=fivemack;524039]Place your bets: is a quartic of SNFS difficulty 258.31 going to be easier or harder than a GNFS 195.65?[/QUOTE]
Count my vote for easier GNFS, pass the number and a suggested SNFS poly, and let's run a polyselect and test-sieve (if vebis and/or VBCurtis joins with CADO, GNFS should be easier, I will run a part of select and the spin).

The number is [url]http://www.factordb.com/index.php?id=1100000000216955821[/url]

[code]
44909292899933054639417823914025695557188367019208
84946505771634999063887745952445887475578875492666
80645513849582870575969680815200984485951826643783
7184140423450006769373462680041385370778722521
[/code]

SNFS is significantly quicker with 16e than with 15e, so you might want to make that comparison too. With the polynomial below, I get a yield of 1.7977 sieving with 16e from 400M to 400M+10k

[code]
n: 4490929289993305463941782391402569555718836701920884946505771634999063887745952445887475578875492666806455138495828705759696808152009844859518266437837184140423450006769373462680041385370778722521
skew: 0.447
c4: 25
c3: -25
c2: -10
c1: 10
c0: 1
Y1: -1
Y0: 16892574194241670428824570378554538679120491007541580961500624834
lpbr: 33
lpba: 32
mfbr: 96
mfba: 64
alambda: 2.6
rlambda: 3.4
alim: 400000000
rlim: 400000000
[/code]

The best polynomial I got after an overnight search was

[code]
n: 4490929289993305463941782391402569555718836701920884946505771634999063887745952445887475578875492666806455138495828705759696808152009844859518266437837184140423450006769373462680041385370778722521
# norm 2.782481e-19 alpha -8.139046 e 6.806e-15 rroots 3
skew: 1546232048.23
c0: -840275467664477384115030092092308912794938768818000
c1: -401623096793192586248782919178513646926916
c2: 1364798544769124532296446769656552
c3: 181953540629697374159247
c4: -493865460396230
c5: 170352
Y0: -121394160494208958424033844696497192557
Y1: 28307512268007061
lpbr: 32
lpba: 32
mfbr: 64
mfba: 96
alambda: 3.4
rlambda: 2.6
alim: 400000000
rlim: 400000000
[/code]

with a yield of 0.54 for 15e 400M..400M+1k ... doing trial sieving with a longer range and with 16e now.

I have a similarly interesting conundrum for how to sieve an HCN. Consider 8+3,750L (as it happens, 8+3,750M will have the same stats). This can be sieved in the following ways:

- GNFS-174
- SNFS-225.8 (quartic)
- SNFS-182.5 (octic)

Trial sieving with the octic suggests that it will require work similar to an SNFS-240 sextic.

So which one would you choose?

BTW, are the NFS@Home sieving applications able to handle octic polynomials?

[QUOTE=jyb;524178]BTW, are the NFS@Home sieving applications able to handle octic polynomials?[/QUOTE]

Yes, I have submitted a few p^17-1 using degree halving when the traditional sextic is SNFS-235 or better. But expect a higher dup rate like 30%.

[QUOTE=jyb;524178]I have a similarly interesting conundrum for how to sieve an HCN. Consider 8+3,750L (as it happens, 8+3,750M will have the same stats). This can be sieved in the following ways:

- GNFS-174
- SNFS-225.8 (quartic)
- SNFS-182.5 (octic)

Trial sieving with the octic suggests that it will require work similar to an SNFS-240 sextic.

So which one would you choose?[/QUOTE]

GNFS-174 most likely a 31 or 32 bit job for 14e.
SNFS-225 - I have an SNFS-229 quartic that will go to 15e (can't fit it in 14e).
SNFS-182 sounds like it might be a solid 31 bit job for 14e. (assuming SNFS-240 style).

[QUOTE=RichD;524210]GNFS-174 most likely a 31 or 32 bit job for 14e.
SNFS-225 - I have an SNFS-229 quartic that will go to 15e (can't fit it in 14e).
SNFS-182 sounds like it might be a solid 31 bit job for 14e. (assuming SNFS-240 style).[/QUOTE]

Agree on all counts. Quartics really seem to sieve better with 15e at relatively low difficulties. And yes, my test sieving was best with 31-bit LPs with 14e. I haven't tried 15e, though.

[QUOTE=RichD;524210]GNFS-174 most likely a 31 or 32 bit job for 14e.
SNFS-225 - I have an SNFS-229 quartic that will go to 15e (can't fit it in 14e).
SNFS-182 sounds like it might be a solid 31 bit job for 14e. (assuming SNFS-240 style).[/QUOTE]
15e queue is generally busier, which rules out the quartic- I'd rather send something to 14e even if it's 20% slower than 15e would be. (or is the quartic less than 20% slower on 14e than it is on 15e?)

I tried an octic in the 180s last fall; it needed 15e and something like twice as much sieving as my testing indicated. I didn't do a detailed exploration of what I did wrong with the test-sieving, but I'd consider an octic experimental still. If you're interested in blazing new ground, go for the octic but please do more detailed test-sieving than usual, as well as a post-mortem conclusions for future octic-reference.

I have GNFS-166 as the 14e cutoff between 31 and 32 LP, so I suggest you strongly consider 32LP if you take the GNFS-174 on 14e route. 350M relations on 32LP vs 210M relations on 31LP should come out better for 32LP. Perhaps a 31/32 hybrid with 275M targeted is worth a try, too.

[QUOTE=VBCurtis;524239]I have GNFS-166 as the 14e cutoff between 31 and 32 LP, so I suggest you strongly consider 32LP if you take the GNFS-174 on 14e route. 350M relations on 32LP vs 210M relations on 31LP should come out better for 32LP. Perhaps a 31/32 hybrid with 275M targeted is worth a try, too.[/QUOTE]

I was looking over the previous GNFS-170s job from the 14e queue. That was the extent for my exploration.

The smallest 32-bit job was GNFS-172 and the largest 31-bit job was GNFS-173. So a GNFS-174 most likely is a 32-bit job unless a 31/32 hybrid can be concocted, :smile:

[B]QUEUED AS 8p3_750L[/B]

SNFS-182.5 (octic) C174 HCN (8+3,750L), ECM to t55. For 14e.
[code]
n: 138139204578772262817881161412776719426048594117702059017435375546534529986395155457745750292325198676439045652909048323119316764386071853957726869247602569913388756432021001
skew: 1.63299316185545
lss: 0
c8: 81
c7: 324
c6: -1080
c5: -5184
c4: 2304
c3: 20736
c2: 0
c1: -24576
c0: 4096
Y1: 109561042308169728
Y0: -37778931863804450319011
rlim: 134000000
alim: 134000000
lpbr: 31
lpba: 31
mfbr: 62
mfba: 62
rlambda: 2.6
alambda: 2.6
[/code]
Trial sieving 10K blocks.
[code]
Q Yield
--- -----
20M 24257
35M 22426
50M 20620
65M 19917
80M 18360
95M 20317
110M 18383
125M 17954
140M 14396
155M 14863
170M 15875
185M 14690
200M 15282
215M 12890
230M 13332
245M 12260
[/code]
Recommend sieving special Q on algebraic side, 20M - 160M.