Index 1 Sequence Work for the "n^i" Aliquot Project

[garambois]

Originally Posted by EdH

How much of a priority would you place in advancing the list to term 2?

If we do all this work of raising all the indexes above 1, I will be able to resume some works that has been on hold for quite some time.
But I won't have the time to start that work quickly.
I won't do much serious work until November - December.

[charybdis]

Originally Posted by gd_barnes

As for the recent base 100-195 effort, there were next to zero index 1's there because most bases in that range are prime. For prime bases, the index is always >= 2 due to another factoring project.

The real reason is that index 1 can be done by SNFS if the base is prime. For bases under 100, these would have been done as part of the Brent project, but I don't think bases above 100 are part of any other project. They've probably largely been done by individuals who like doing relatively easy SNFS jobs.

There are still a few SNFS targets in Ed's list, namely index 1 of 137^89, 173^83 and 193^83.

[EdH]

I've queued the three base 6 entries to run after the current sequence I'm working on. They should be done by tomorrow. I intend to work upwards through the bases as interest permits. I may skip over >150 composites for now, unless I feel like completing a base, like the c154 for 6^209.

[gd_barnes]

Some notes about this effort:

All same-parity exponents and double-square bases have been ECM'd to t35.
All opposite-parity sequences that are not double-square bases for bases >= 95 have been ECM'd to t35.

I'm not formally working on this effort yet but I do have an ongoing effort to initialize all medium and large opposite-parity exponents that results in factoring many sequences that are at index=1. I have done all bases >= 95 so far and am working my way downwards. Currently loaded up are bases 94 thru 90. The effort effectively ECM's everything to t35 on the last iteration of a sequence and continues until it can't completely factor a cofactor >= 110 digits.

Since the list was last updated, here is some work on base 95 that has been done to index=1:
Completely factored:
95^66, 70, 82, 84, 92, and 100

Partially factored:
95^74 and 98

Ed, since your list is auto-generated, do you need me to mention the partially factored exponents? In other words, will it automatically update the cofactor size if a sequence is not eliminated?

[EdH]

Originally Posted by gd_barnes

. . .
Ed, since your list is auto-generated, do you need me to mention the partially factored exponents? In other words, will it automatically update the cofactor size if a sequence is not eliminated?

This should be yes. The script takes the current list and strips the sizes, checks the db and if still at index 1 calculates the sizes from the new info and places it in a new list. Those that are no longer at index 1 are noted, but left off the new list. My only potential trouble is that each run uses up 1/3 of my db limit. I can add new bases easily. I may add a countdown to show progress. There shouldn't be many new sequences of workable size ever added. It should be a true countdown with just a few upticks.

I'll start a t35 ECM effort from the bottom up. We can meet along the way.

[EdH]

Everything up through 69^100 has been ECMed to t35. I'll start with the next one heading up further tomorrow. Overnight I'm running 12^145 via NFS.

[gd_barnes]

Originally Posted by EdH

Everything up through 69^100 has been ECMed to t35. I'll start with the next one heading up further tomorrow. Overnight I'm running 12^145 via NFS.

My opposite-parity initializing is done down through base 93. I'm entering everything now for bases 93-94. It will run down thru base 90. It generally completes ~2 bases a day since it's doing a lot more exponents on each base than are just in the index=1 effort.

Having everything ECM'd to t35 gives us a much better idea of the scope of this effort. So much stuff falls quickly to ECM at this point. Then it's just a matter of testing our way up the cofactor size list. Everything up to 115 digits would have sufficient ECM. After eliminating all sequences with cofactors <= 115 digits, we could do another mass ECM effort on the remaining ones to t40. Then everything up to ~130 digits would have enough. Or...we could just start testing sequences individually with everything at t35.

You might consider having a second list sorted by cofactor.

Eventually we could do an index=2 effort. :-) That would be much bigger because all of the prime bases come into play and that would be a load of them!

[gd_barnes]

I'm now done with my other initialization effort down thru base 92. Here are the index 1's affected for bases 92 to 94 in the last day:

Done:
92^63, 67, 69, 71, 73, 75, 79, 83, 87, & 89
93^64, 74, 78, 80, 92, & 94
94^71, 87, & 89

Partially factored:
92^91, 93, & 99
93^96
94^85 & 93

Ed, I started a process to ECM only the index 1's down thru base 80. I'll stop it there and you can take care of the 70's. It's a separate effort from my other initialization effort that will finish quickly.

Question: When you partially factor one of these, I assume that you are entering the factor in the DB. Is that correct? It is what I do so that we know the remaining cofactor size. I want to make sure that we are on the same page.

[kruoli]

How complex and time consuming is it to set up an ECM server for those?

[gd_barnes]

I'm nearly done with the aforementioned ECM effort down to base 80. I'll report here when it's done. I'm estimating ~2 hours from this post. Note that all cofactors for index 1 will be C>=110 but it stops immediately before doing anything with index 2. I run QS/GNFS on anything below that for index 1.

At this point, I'm assuming that you don't really need the details on everything that is either fully or partially factored.

[EdH]

Originally Posted by gd_barnes

. . .
You might consider having a second list sorted by cofactor.

Eventually we could do an index=2 effort. :-) That would be much bigger because all of the prime bases come into play and that would be a load of them!

I thought of a sorted list, too, but haven't implemented it yet.

The index 1 effort is based on some research Jean-Luc is doing with the factors of index 1. We've factored some large ones in the past to validate some things. I don't believe index 2 will gain us the extra insight to warrant a sub-project, at least not in the near future.

Originally Posted by gd_barnes

Ed, I started a process to ECM only the index 1's down thru base 80. I'll stop it there and you can take care of the 70's. It's a separate effort from my other initialization effort that will finish quickly.

Question: When you partially factor one of these, I assume that you are entering the factor in the DB. Is that correct? It is what I do so that we know the remaining cofactor size. I want to make sure that we are on the same page.

Do know yoyo's intention with the "70" bases? I always check his list of currently worked sequences when I make my lists, but he reserved the entire base for several of the "70s" recently. I may leave those for now and run t40 on the leftovers from yesterday's efforts. I'll also start running NFS on any c135-c145s you left in the "90" region.

All factoring efforts are worked directly with the db. All factors found are uploaded at that point.

Originally Posted by gd_barnes

At this point, I'm assuming that you don't really need the details on everything that is either fully or partially factored.

I agree. My list has no dependence on any of those bits, although some are interesting to us. The script just looks for index 1 being open.

Originally Posted by kruoli

How complex and time consuming is it to set up an ECM server for those?

I looked at ECMnet a long time ago and it seemed more complicated than I was interested in at the time. I was looking at it for a LAN only setup, with no outside access.