Some Somewhat Easier n^i Sequences Available for Termination

[gd_barnes]

Originally Posted by EdH

1352^50 went prime from 136.

@Gary: Are you still working on any 1352 exponents 51-55? I've started on 51 with the intention of going through 55, but I'll skip anything you still want to run.

Cool on 1352^50!

1352^49 got tough, real fast. Hit a hard C133 at 133/133 with a factor 3. My Ryzen is doing other stuff ATM so it will be a slog to get that one done. It will likely be tomorrow afternoon.

Status on 51 to 55:

I'm working on only 53. It's at 141/126. The C126 will split in a little while. I'll keep running that one.

I'm done with the others. I did my usual initialization on them. They all look tough; especially 54 and 55. You sure you want to take those on? :-)

ECM status on the others:
54: fully ECM'd the C127
51, 52, and 55: ECM to t35 on the three C150s

[gd_barnes]

1352^53, 131071^31, and 131071^37 terminate

Base 131071 is in the same boat that base 1352 is in. In its case, it will be added to the page up to exponent 35 since it's < 160 digits at exponent 30. Hence I've been doing work for exponents > 30.

But why would I work on exponent 37 with an opening sequence 190 digits? Well that was just a strange so-happen. I pulled it up and it was already at 138/138. When the bases are prime, the first iteration is already factored by another project that does factoring of (P^n-1)/(P-1) where P is prime. In this case, with a smallest factor of 46 digits, it dropped immediately to 139 digits. The workers did one more iteration to bring it to where I saw it at 138. My first test dropped it immediately to 118 digits. All told, it took maybe ~2 hours.

Here is what I think needs to be decided now:
Do we want to complete base 131071 by working on only exponents 33 and 35? Or do base 1352 where we'd have to do 4 exponents (after I complete 49 later today)? Or do we move on to something completely different?

Here is a comparison and status of opening sequences of the two bases:

Base 1352:
51: 157/155 t40
52: 163/154 t40
54: 170/127 full
55: 172/157 t40

Base 131071:
33: 161/138 full
35: 172/171 t40

The last column is ECM status.

I'm game for whatever you decide.

[EdH]

Gary,

I'm finishing the c155 for 1352^51, but it shouldn't be done prior to your report. I think we should at least look at the smaller composites for the higher 1352 exponents. My last c170 failed to complete by script, but finished manually. I think it may have taken about a week, so we may want to work elsewhere for more completion overall, but it would be nice to complete the base.

-Ed

[gd_barnes]

Originally Posted by EdH

Gary,

I'm finishing the c155 for 1352^51, but it shouldn't be done prior to your report. I think we should at least look at the smaller composites for the higher 1352 exponents. My last c170 failed to complete by script, but finished manually. I think it may have taken about a week, so we may want to work elsewhere for more completion overall, but it would be nice to complete the base.

-Ed

I just did a big edit and status report of that post. I'm not sure if you've seen it. You may have to hit refresh.

[EdH]

Here are some very rough timings for my system:

c150 ~8hrs
c155 ~14hrs
c160 ~32hrs
c165 ~45hrs
c170 ~82hrs
c175 ~145hrs

Looking at these times, I think we'd be more productive elsewhere. Let's revisit Jean-Luc's last couple of posts and your earlier suggestion for shotgunning. Let's see if any of your suggested areas of interest would allow us to quickly initialize a full base and maybe work toward that. If we step through a couple bases, maybe that can give more data overall to the larger harvest.

[gd_barnes]

Originally Posted by EdH

Here are some very rough timings for my system:

c150 ~8hrs
c155 ~14hrs
c160 ~32hrs
c165 ~45hrs
c170 ~82hrs
c175 ~145hrs

Looking at these times, I think we'd be more productive elsewhere. Let's revisit Jean-Luc's last couple of posts and your earlier suggestion for shotgunning. Let's see if any of your suggested areas of interest would allow us to quickly initialize a full base and maybe work toward that. If we step through a couple bases, maybe that can give more data overall to the larger harvest.

I tend to agree. Let's look at the shotgun approach. We can probably complete several bases fairly quickly with your resources. There has been a lot of changes in the number of sequences remaining by base since I last posted those totals because I've somewhat focused on looking at the ones with fewer remaining. Later today, I'll post an updated list.

Edit: If you want to continue 1352^51, I'm fine with picking it up at 135 digits. Or it's no big deal if you want to finish it yourself. I'd hate to see you use resources and not do anything with it.

I'm signing off for the day now. Catch you later.

[EdH]

I'm sure any of our current work won't be wasted, even if it sits for later.

I'll have some more thoughts for you when you get back.

[EdH]

Here are my current thoughts:

1) since I'm running 1352^51 and its term is less than 150, I'll finish taking it below 135.

2) (I think) one item Jean-Luc is interested in, is sequences that terminate with the base prime. All of the primes less than 250 have tables so we're already working them. There are 11 sequences remaining that are in these tables and are at a term less than 150 digits. They are:

29^109
163^69
167^77
173^71
179^71
191^65
199^65
227^65
229^65
239^73
241^63

Some are already below 145. I'll focus on bringing them all below 135.

I think all the remaining primes would be too high to work their bases right now. The lowest (other than 181 that Jean-Luc has reserved) is 251.

3) (I think) Jean-Luc is also interested in sequences that end in cycles, but studying the ones we already know, doesn't provide any indication of how to find more, so the only way is to work more sequences. We can work more sequences by working lower exponents, but we don't want to randomly poke around such that we can't easily create a fully initialized table.*

This brings us back to working at lower bases. All lower uninitialized bases are now composite, so this work won't satisfy #1 above, but we can get more matched parity sequences done and work toward turning up more cycles. You noted 102 in one of your posts, so let's initialize it (mixed parity to 110) and work on all matched parity sequences below 150 digits.

Then, let's evaluate how that is working and see if I may want to move some of my work into the initialization as well.

Just a point as to why I'm trying to keep initialization in mind - At some point, to maintain organization, we need to have tables in the project reflect what has been accomplished. Since Jean-Luc has requested initialization prior to adding a table in the past, I feel we should stick to that requirement to help keep the project organized. It we stray too far, it may be harder to swing back. An extra issue which I don't know, is whether the harvest relies on the tables to work efficiently. If we work a bunch of random sequences, it may be hard for Jean-Luc to include them.

Overall thoughts?

[gd_barnes]

1352^49 and 524287^31 terminate

This finishes my effort on the recently added bases except what you bring below 135 digits.

On 1352^51, I see that you have dropped it to 147/147 with no small prime. It will probably drop to below ~100 or 110 digits on the next iteration. Feel free to finish it off if you want to. You deserve some credit too! :-)

524287^31 was another one like 131071^37. It is larger than what will be shown on the web page but dropped quickly so was fairly easy to terminate.

I'm busy until late night. I did a cursory glance at your post. What I digested makes sense to me. I'll respond in detail late tonight including a list of all bases with 1 and 2 sequences remaining.

[EdH]

1352^51 is "quite" ready to fall, but I've moved to the list in my last post, so it's up for grabs.

[richs]

I'll take 1352^51.