We are taking a break from subfield 3 and resuming the search over subfield 6.

The main reason for this is we have not found anything new in about 6 months. It's hard to put a percentage on it, but I am 99.99% confident that this search over sf3 is complete. It seems resources would be better spent on a search that will actually find new fields.

We can always finish sf3 at a later time, if for no other reason than to say it is complete with 100% confidence.

In my opinion it is either 100% complete with 100% confidence, or mathematically incomplete. If there actually isn't anything more to discover, that means we set a bound that is too loose, which could be interesting to investigate.

I also want to ask a question. Are there any peer-reviewed publications/grants/awards/anything related to NumberFields@home 2019-2022? If we kept finding nothing, using the resources more wisely can be a great idea.

We are using the best known theoretical bounds. So yes, they might be too loose, but someone smarter than me would have to find a way of making them tighter.

We had a journal article published back in 2019 for degree 7 fields. The plan was to eventually publish the results of the current degree 10 searches. We would most likely complete the search over sf3 before publication.

Can you guys create some progress bars to tell how the search progress is? As a non-math guy, it's hard for me and other people like me to understand what the subfield is, how many subfields are there, and how large is each subfield. Just curious about the it, and I do understand if you guys are busy and don't have time for this.
Go sun devils!

Can you guys create some progress bars to tell how the search progress is? As a non-math guy, it's hard for me and other people like me to understand what the subfield is, how many subfields are there, and how large is each subfield. Just curious about the it, and I do understand if you guys are busy and don't have time for this.
Go sun devils!

Have you taken a look at the batch status tables:
https://numberfields.asu.edu/NumberFields/batch_status.html

There were originally 7 subfields, now only 3 remain: 3, 6, and 7. Each row in the tables represents a separate search for a specific discriminant bound. The 2 dimensional version of the tables shows the sub-batches better, but the linear version gives the progress information, you just need to scroll down to the line that's active (currently sf6 DS10x12).

I hope that helps!

Thank you so much! Batch status is what I was looking for. Sorry about missed it... Great work!

Row 10 of subfield 6 is nearing completion. After that we will be moving to row 13 of subfield 7. The first case, DS13x11, was generated before the improved apps, so it will run faster than usual.

When can we get back to subfield 3 and finish it up?

When can we get back to subfield 3 and finish it up?

Row 13 of subfield 7 is the last of the batches that were generated years ago, so that's the main reason for closing those out.

Finishing subfield 3 could come after that, but I haven't decided yet.

We are now working on DS14x12, at time of writing there is 530 days (1 year 5.42 months) remaining until this will be completed. 1% has already been completed

In preparation for the final row of the sf6 search, I will be dumping a relatively small number of tasks (~60k). These are for the 16x7 case. The first part of row 16 was run years ago with the inefficient app, so this quick search is necessary to get proper timing stats with the latest app.

After that, it's back to row 15, which should keep us busy through the end of the summer.

Thanks for the update.
It's nice to know what's going on and why.

---

Grant
Darwin NT, Australia.

Out of curiosity I tried to estimate how many years this project needs to complete with current compute power. I got about 16 years. Is that plausible?
(I used 13x12 and 14x12 as a source for 16x11, 16x12 and 15x12, while 15x11 was used for 16x10, 16x9 and 16x8)

Out of curiosity I tried to estimate how many years this project needs to complete with current compute power. I got about 16 years. Is that plausible?
(I used 13x12 and 14x12 as a source for 16x11, 16x12 and 15x12, while 15x11 was used for 16x10, 16x9 and 16x8)

That is in the ball park. In about 1 year we should have everything except 13x12,14x12,15x12,16x11, and 16x12. At that point, given the redundant nature of the algorithm and various tests I can perform, I will be able to say with a high degree of confidence if every field has been found. After 6 more years everything should be done except for 16x12, and at that point my confidence level will be extremely high. I estimate it will take another 5 to 7 years to complete 16x12.

I thought that after 15x11 we'll be getting 13x12 and 14x12 as they are bolded in batch plan, but instead we are now starting to get 15x12. Is that right and was there change of plan?

I thought that after 15x11 we'll be getting 13x12 and 14x12 as they are bolded in batch plan, but instead we are now starting to get 15x12. Is that right and was there change of plan?

As we did with 13x12 and 14x12, we will be doing the first of 25 sub-searches on 15x12. Seeing how many new fields are found gives a good idea how close we are to having the complete set of fields for that row. After that we will start the 16th (and last) row. This is the best way to get the most fields with however much time we have left (before the hardware fails). After completing most of the 16th row, we can then start completing the 12th column starting with 13x12. Hope that helps explain the ordering of the searches.

I thought that after 15x11 we'll be getting 13x12 and 14x12 as they are bolded in batch plan, but instead we are now starting to get 15x12. Is that right and was there change of plan?

As we did with 13x12 and 14x12, we will be doing the first of 25 sub-searches on 15x12. Seeing how many new fields are found gives a good idea how close we are to having the complete set of fields for that row. After that we will start the 16th (and last) row. This is the best way to get the most fields with however much time we have left (before the hardware fails). After completing most of the 16th row, we can then start completing the 12th column starting with 13x12. Hope that helps explain the ordering of the searches.

Just small clarification: Last row or last rows? sf6 has 5 rows for M=16 and sf7 has one row for M=16.

So if I understand it right we'll have following order of searches:
"Quick" sampling of 15x12
16x{8;12} or sf7:16x12
13x12 and 14x12 and the other set from previous line

Did I get it right?

Many thanks for answering my questions.

I thought that after 15x11 we'll be getting 13x12 and 14x12 as they are bolded in batch plan, but instead we are now starting to get 15x12. Is that right and was there change of plan?

As we did with 13x12 and 14x12, we will be doing the first of 25 sub-searches on 15x12. Seeing how many new fields are found gives a good idea how close we are to having the complete set of fields for that row. After that we will start the 16th (and last) row. This is the best way to get the most fields with however much time we have left (before the hardware fails). After completing most of the 16th row, we can then start completing the 12th column starting with 13x12. Hope that helps explain the ordering of the searches.

Just small clarification: Last row or last rows? sf6 has 5 rows for M=16 and sf7 has one row for M=16.

So if I understand it right we'll have following order of searches:
"Quick" sampling of 15x12
16x{8;12} or sf7:16x12
13x12 and 14x12 and the other set from previous line

Did I get it right?

Many thanks for answering my questions.

I was referring to the 2D representation: https://numberfields.asu.edu/NumberFields/batch_status_2dim.html

This is the current order plan:
sampling of 15x12, 16x8 -> 16x10, sampling of 16x11, sampling of 16x12, 13x12, 14x12, 15x12, 16x11, 16x12

If/when Gerasim comes back, sf7_16x12 will be done over there. But at some point we may finish it here.

I forgot about 2D representation. It's clear now.

Thank you for the answers.