[QUOTE=jyb;526452]There are few remaining HCN composites which are in an appropriate range for factoring by NFS@Home, and which have had sufficient ECM to justify starting NFS on them. In case anyone is interested in helping to do ECM pre-testing on some of the harder candidates, I am running another ECMnet server (v2) on port 8195 of ecm.unshlump.com for this purpose. Alternatively, if anyone prefers to run ECM on their own, PM me for info on the composites and B1 level.[/QUOTE]

Huh? I have run a t55 on each of the first 5 holes except for 11,8 and 11,9 which
I will finish in the next month. I have also run a t55 on each composite under 200 digits.
Consider also all of the ECM run by YoYo. It is not finding many factors. I disagree
with your "have had sufficient ECM" comment.

[QUOTE=R.D. Silverman;526480]Huh? I have run a t55 on each of the first 5 holes except for 11,8 and 11,9 which
I will finish in the next month. I have also run a t55 on each composite under 200 digits.
Consider also all of the ECM run by YoYo. It is not finding many factors. I disagree
with your "have had sufficient ECM" comment.[/QUOTE]

Correction: Each of the "non-Aurefeuillan" composites under 200 digits.

One must also ask the (somewhat obvious) question: What is "in range"??

Based on non-HC numbers that have been done, up to GNFS-180 and SNFS-260
are "in range", as are quartics as small as SNFS-198 and as large as ~C235 [perhaps
a bit larger]

What is the lower limit for SNFS quintics/sextics? I would guess around C240.

By these criteria there are still many numbers that are "in range" for lasieved.

Back in 2015, Debroulx [url=https://www.mersenneforum.org/showpost.php?p=408161&postcount=167]published a list of suggested criteria[/url] for the 14e queue. I reproduce the list below for discussion purposes:
[quote]
* SNFS polynomials should have leading coefficients < 10^5
* SNFS tasks with degree 6 polynomials (preferred) should have 225 <= difficulty <= 250, ECM to 2/9 of SNFS difficulty
* SNFS degree 5 tasks should have 210 <= difficulty <= 235, ECM to 2/9 of (15+SNFS difficulty)
* SNFS degree 4 tasks should have 195 <= difficulty <= 220, ECM to 2/9 of (30+SNFS difficulty)
* GNFS tasks should have 155 <= difficulty <= 170, ECM to 2/7 of GNFS difficulty (a bit more than that for difficulty close to 170)[/quote]

These seem to hold up well after four years, though the GNFS limit has clearly grown. The recent GNFS 180 14e jobs were a real stretch, perhaps an upper limit of 175 is a sane compromise for GNFS.

If I recall correctly, these guidelines were lifted from [B]squalyl[/B]'s RSALS site when [B]debrouxl[/B] was the sub-administrator. That grid only ran the 14e siever. I believe [B]frmky[/B] has tweaked the sievers to get a little more juice from them. Looking at the results on NFS@home there has been a few jobs that squeezed the 14e to its limits.

[CODE]GNFS # of jobs
==== =========
180 5
179 3
178 3
177 4
176 1
175 3[/CODE]
One in each of the 179, 178 and 175 categories has the difficulty ending in .9 which could be counted in the next higher group. These are really pushing the siever. Perhaps [B]fivemack[/B] (or others) might have some comments.

[QUOTE=R.D. Silverman;526485]Correction: Each of the "non-Aurefeuillan" composites under 200 digits.

One must also ask the (somewhat obvious) question: What is "in range"??

Based on non-HC numbers that have been done, up to GNFS-180 and SNFS-260
are "in range", as are quartics as small as SNFS-198 and as large as ~C235 [perhaps
a bit larger]

What is the lower limit for SNFS quintics/sextics? I would guess around C240.

By these criteria there are still many numbers that are "in range" for lasieved.[/QUOTE]

Yes, this is a good question. I have been operating on the following guidelines:

- Lower limit for SNFS quintics/sextics is 230.
- Lower limit for SNFS quartics is about 205.
- Lower limit for GNFS is 150.

For 14e:
- Upper limit for SNFS quintics/sextics is low 250's.
- Upper limit for SNFS quartics is about 220 (14e can do higher, but 15e is likely to be more efficient).
- Upper limit for GNFS is around 175.

I don't have enough experience with 15e to have come up with good upper limits for it, but that doesn't really concern us here. There are plenty of HCN composites which are clearly appropriate for 15e. But the question is how much ECM should these have prior to adding to the 15e queue.

Any number which is within the 14e limits I describe above can probably be queued after a t55. (Maybe the largest of the GNFS jobs should have a little more ECM first.) However, I believe that anything above those limits (i.e. pretty much anything which is more appropriate for 15e) should get more before starting NFS. If you disagree, please give a specific amount of ECM which you think is appropriate for given digit counts/difficulties. Tom gave [URL="https://mersenneforum.org/showthread.php?p=525617#post525617"]this metric[/URL] recently, which seems pretty good, but of course it requires empirical data on runtimes. Do you have a better one?


[QUOTE=R.D. Silverman;526480]Huh? I have run a t55 on each of the first 5 holes except for 11,8 and 11,9 which
I will finish in the next month. I have also run a t55 on each composite under 200 digits.
Consider also all of the ECM run by YoYo. It is not finding many factors. I disagree
with your "have had sufficient ECM" comment.[/QUOTE]

You are of course free to disagree, but please be concrete: can you point to a specific HCN composite which qualifies under the limits I describe above? Also, the first 5 holes on which you ran a t55 are no longer the same first 5 holes in every case. Surely some of the numbers on which you did your work have since been factored, causing new numbers to become part of the first 5 holes. Do you have good data on exactly which numbers you finished? But even setting that aside, I think you'll find very few composites which have had even a t55 and which conform to the limits above, including among first 5 holes. (There are a few, mostly quartics which might actually be better as GNFS jobs.)

[QUOTE=jyb;526510]Yes, this is a good question. I have been operating on the following guidelines:

- Lower limit for SNFS quintics/sextics is 230.
- Lower limit for SNFS quartics is about 205.
- Lower limit for GNFS is 150.

For 14e:
- Upper limit for SNFS quintics/sextics is low 250's.
- Upper limit for SNFS quartics is about 220 (14e can do higher, but 15e is likely to be more efficient).
- Upper limit for GNFS is around 175.

I don't have enough experience with 15e to have come up with good upper limits for it, but that doesn't really concern us here. There are plenty of HCN composites which are clearly appropriate for 15e. But the question is how much ECM should these have prior to adding to the 15e queue.

Any number which is within the 14e limits I describe above can probably be queued after a t55. (Maybe the largest of the GNFS jobs should have a little more ECM first.) However, I believe that anything above those limits (i.e. pretty much anything which is more appropriate for 15e) should get more before starting NFS. If you disagree, please give a specific amount of ECM which you think is appropriate for given digit counts/difficulties. Tom gave [URL="https://mersenneforum.org/showthread.php?p=525617#post525617"]this metric[/URL] recently, which seems pretty good, but of course it requires empirical data on runtimes. Do you have a better one?




You are of course free to disagree, but please be concrete: can you point to a specific HCN composite which qualifies under the limits I describe above? Also, the first 5 holes on which you ran a t55 are no longer the same first 5 holes in every case. Surely some of the numbers on which you did your work have since been factored, causing new numbers to become part of the first 5 holes. Do you have good data on exactly which numbers you finished? But even setting that aside, I think you'll find very few composites which have had even a t55 and which conform to the limits above, including among first 5 holes. (There are a few, mostly quartics which might actually be better as GNFS jobs.)[/QUOTE]

I did not keep track of the "first 5" for which I ran ECM that have since been done.


I will go into the reservations page and extract those numbers that fall under the
guidelines discussed herein. It will take a bit of time. I will check the numbers
that I have done. We also need to check the numbers YoYo has done.


We agree that some of the quartics would be better as GNFS jobs.

[QUOTE=R.D. Silverman;526520]I did not keep track of the "first 5" for which I ran ECM that have since been done.


I will go into the reservations page and extract those numbers that fall under the
guidelines discussed herein. It will take a bit of time. I will check the numbers
that I have done. We also need to check the numbers YoYo has done.


We agree that some of the quartics would be better as GNFS jobs.[/QUOTE]

Let me save you some of that time. Here's the information I have.

GNFS jobs in range. All of these probably need more ECM, with the exception of 7+4,308, which has had a full t55 (probably done by you). The first two have had about half of a t50, which might be considered enough for GNFS-150.
[code]
Composite Digits
10+3_260 150
7+2_335 150
7+4_308 150
10+7_275 157
10+9_265 159
11+2_275 160
11+6_260 160
8-7_295 160
8-3_305 161
11+4_260 162
8+7_295 163
9-5_565M 163
9-5_575M 163
7+3_337 166
8+3_798M 167
5+4_425 168
8+3_762L 168
7+2_313 175
[/code]

SNFS (sextic) jobs in range. The first two have had a little more than t50, so they're probably ready. The rest need more ECM.
[code]
Composite SNFS Diff.
10+9_253 230.0
10-9_253 230.0
12+11_233 251.4
12-5_233 251.4
9+2_308 251.9
3+2_616 251.9
9+8_308 251.9
9+7_308 251.9
9+2_526L 252.2
9+2_526M 252.2
9+8_526L 252.8
[/code]

SNFS (quartic) jobs in range. These are all ready to go.
[code]
Composite SNFS Diff.
7-2_305 206.2
7+3_305 206.2
7+5_305 206.2
[/code]

GNFS jobs with pretesting done by Yoyo. All of these have had a t55. It's questionable whether that's enough for this size NFS job.
[code]
Composite Digits
12+5_975L 170
11-8_275 171
11+8_290 171
4-3_473 171
5+3_1395M 171
4-3_493 172
8-7_329 173
7-2_337 173
7+6_798M 173
9+7_320 174
11+3_248 174
6+5_365 175
12-5_275 175
8-5_335 175
10+7_305 175
9+5_268 175
3+2_637 175
10+9_750L 175
7+3_358 175
[/code]

[QUOTE=jyb;526524]Let me save you some of that time. Here's the information I have.

GNFS jobs in range.
All of these probably need more ECM, with the exception of 7+4,308, which has had a full t55 (probably done by you).
[/QUOTE]

See, e.g.

[url]http://www.rechenkraft.net/yoyo/download/download/stats/ecm/hc/wu_status[/url]

Many of these may have been run. I will check. YoYo is doing numbers in
order of size of the remaining composite and is currently up to C175. I have
not checked whether [b]ALL[/b] smaller numbers have also been run.


[QUOTE]

SNFS (sextic) jobs in range. The first two have had a little more than t50, so they're probably ready. The rest need more ECM.
[/QUOTE]

If any are within the first 5 holes, then I have run a t55 on them.

What about *quintics*?? i.e. those numbers with exponent divisible by 11?

Note also that in some cases numbers that *appear* to be "easiest" with quartics
will sometimes be faster with sextics! That is for (x^5-1)/(x-1) the rational norms
can be so large that it is worth increasing the algebraic degree to 6 to decrease
the rational norm even at the expense of increasing the algebraic norm. Quartics
are *distinctly* sub-optimal for numbers this size.


[QUOTE]
SNFS (quartic) jobs in range. These are all ready to go.
[code]
Composite SNFS Diff.
7-2_305 206.2
7+3_305 206.2
7+5_305 206.2
[/code]

GNFS jobs with pretesting done by Yoyo. All of these have had a t55. It's questionable whether that's enough for this size NFS job.

[/QUOTE]

Not IMO.

[QUOTE=R.D. Silverman;526534]See, e.g.

[url]http://www.rechenkraft.net/yoyo/download/download/stats/ecm/hc/wu_status[/url]

Many of these may have been run. I will check. YoYo is doing numbers in
order of size of the remaining composite and is currently up to C175. I have
not checked whether [b]ALL[/b] smaller numbers have also been run.[/QUOTE]

Yes, I have seen these. I'm the one who has fed these numbers to Yoyo. They're doing numbers in that order because that's the order in which I gave it to them.

Every one of the HCN's given to Yoyo has been fully factored, except for

1) The ones I showed you above.
2) 9 more which Yoyo hasn't started working on yet, but which are out of range for 14e.
3) 3 SNFS-250 quartics,which have received t55, but need more. These were the whole reason I started this conversation. They're out of range for 14e, of course.


[QUOTE=R.D. Silverman;526534]
If any are within the first 5 holes, then I have run a t55 on them. [/QUOTE]
Except that no, you don't really know that. For example, of the first five holes in the 10-3 table 14 months ago, 3 of them have been fully factored. So are those the ones you did a t55 on, or did you do that work more recently? What about the other tables? If you didn't keep any record of which composites you actually worked on, it's going to be very hard to know what still needs work.

[QUOTE=R.D. Silverman;526534]
What about *quintics*?? i.e. those numbers with exponent divisible by 11? [/QUOTE]
No quintics are in range. The slightly longer answer is that there are a bunch of composites which could be either quintics or sextics, but for the range of difficulties we're discussing, they will usually sieve better as sextics. But that can be tested when they actually get sieved. For brevity I just referred to these as "sextics" above, along with the ones which actually need to be sextics. There are, of course, also some obligatory quintics, but none of those is in range.

[QUOTE=R.D. Silverman;526534]
Note also that in some cases numbers that *appear* to be "easiest" with quartics
will sometimes be faster with sextics! That is for (x^5-1)/(x-1) the rational norms
can be so large that it is worth increasing the algebraic degree to 6 to decrease
the rational norm even at the expense of increasing the algebraic norm. Quartics
are *distinctly* sub-optimal for numbers this size. [/QUOTE]
Indeed, there are a handful of HCN's which fall into this category. E.g. 11-7,245 is an SNFS-204.1 quartic, but an SNFS-218.7 sextic. I know which way I would rather do it. However, none of these is in range (some are too easy, some too hard).


[QUOTE=R.D. Silverman;526534][QUOTE=jyb;526524]
GNFS jobs with pretesting done by Yoyo. All of these have had a t55. It's questionable whether that's enough for this size NFS job.[/QUOTE]
Not IMO.[/QUOTE]
Okay, then would you care to find polynomials for them? They're all GNFS jobs.

[QUOTE=jyb;526524]Let me save you some of that time. Here's the information I have.


SNFS (quartic) jobs in range. These are all ready to go.
[code]
Composite SNFS Diff.
7-2_305 206.2
7+3_305 206.2
7+5_305 206.2
[/code]

[/QUOTE]

What happened to: e.g.

11-7_245 167.0 204.1 Unreserved: click here to reserve
11-8_245 171.0 204.1 Unreserved: click here to reserve
5-2_365 201.1 204.1 Unreserved: click here to reserve
9-5_535M 181.8 204.2 Unreserved: click here to reserve
9-5_535L 182.4 204.2 Unreserved: click here to reserve
12+5_705M 194.2 204.3 Unreserved: click here to reserve

10+3_260 149.2 208.0 Unreserved: click here to reserve
12+11_245 151.1 211.5 Unreserved: click here to reserve
10+9_265 159.0 212.0 Unreserved: click here to reserve
8-7_295 159.5 213.1 Unreserved: click here to reserve
8+7_295 162.2 213.1 Unreserved: click here to reserve
5-2_385 143.9 215.3 Unreserved: click here to reserve
3-2_565 144.5 215.7 Unreserved: click here to reserve

11+6_260 159.3 216.6 Unreserved: click here to reserve
11+4_260 161.3 216.6 Unreserved: click here to reserve

8+5_305 141.3 220.4 Unreserved: click here to reserve
8+7_305 148.6 220.4 Unreserved: click here to reserve
8-3_305 160.8 220.4 Unreserved: click here to reserve

11+5_265 192.9 220.8 Unreserved: click here to reserve
11-7_265 195.1 220.8 Unreserved: click here to reserve
11+7_265 197.8 220.8 Unreserved: click here to reserve
11-9_265 206.7 220.8 Unreserved: click here to reserve
11+8_265 207.3 220.8 Unreserved: click here to reserve
11-5_265 216.4 220.8 Unreserved: click here to reserve

These are all "in range" quartics.

[QUOTE=R.D. Silverman;526556]What happened to: e.g.

11-7_245 167.0 204.1 Unreserved: click here to reserve
11-8_245 171.0 204.1 Unreserved: click here to reserve
5-2_365 201.1 204.1 Unreserved: click here to reserve
9-5_535M 181.8 204.2 Unreserved: click here to reserve
9-5_535L 182.4 204.2 Unreserved: click here to reserve
12+5_705M 194.2 204.3 Unreserved: click here to reserve

10+3_260 149.2 208.0 Unreserved: click here to reserve
12+11_245 151.1 211.5 Unreserved: click here to reserve
10+9_265 159.0 212.0 Unreserved: click here to reserve
8-7_295 159.5 213.1 Unreserved: click here to reserve
8+7_295 162.2 213.1 Unreserved: click here to reserve
5-2_385 143.9 215.3 Unreserved: click here to reserve
3-2_565 144.5 215.7 Unreserved: click here to reserve

11+6_260 159.3 216.6 Unreserved: click here to reserve
11+4_260 161.3 216.6 Unreserved: click here to reserve

8+5_305 141.3 220.4 Unreserved: click here to reserve
8+7_305 148.6 220.4 Unreserved: click here to reserve
8-3_305 160.8 220.4 Unreserved: click here to reserve

11+5_265 192.9 220.8 Unreserved: click here to reserve
11-7_265 195.1 220.8 Unreserved: click here to reserve
11+7_265 197.8 220.8 Unreserved: click here to reserve
11-9_265 206.7 220.8 Unreserved: click here to reserve
11+8_265 207.3 220.8 Unreserved: click here to reserve
11-5_265 216.4 220.8 Unreserved: click here to reserve

These are all "in range" quartics.[/QUOTE]

Note that some of them are also "in range" GNFS. I think that are also some
"in range" GNFS that might have been skipped, e.g.

9+7_266 153.3 217.6 Unreserved: click here to reserve

This (and several others) might be a little bit easier with SNFS, but the difference is small. Are we skipping these?