Bases 6-32 reservations/statuses/primes

[mdettweiler]

All this recent action with the one-or-two-k's-left bases in this range reminded me of my Sierp. base 23 reservation that's been stagnant for quite a while. It's currently at about 203K, only a bit higher than my last reported status of 200K. I should probably drop this reservation, but I would really prefer to have it at a more even n-level before doing that...

Hmm, I just had a thought about how I can make room for this base on my dualcore. It should move reasonably quickly once I do that.

[Siemelink]

My base 7 reservation has reached n=120,000. I'll leave it at this and release the reservation.
I have started on the remains of Riesel base 23. I'll take it from 180,000 to 200,000

Cheers, Willem

[Cruelty]

Base 10 (Riesel + Sierpinski) doublechecked till n=210000.

[gd_barnes]

Riesel base 22 is at n=170K; continuing to n=200K; one prime reported since last status.

Riesel base 27 is complete to n=200K; no primes for my reservation; now unreserved.

[Xentar]

Damn, primes are hiding..

Current status:
sierp-b17: one k remaining, n ~ 367K - a test needs about 6 hours now
sierp-b18: one k remaining, n ~ 274K - 2 hours per test

Sieved till ~ 100T. It's not very effective anymore.

Any ideas? :(

[gd_barnes]

I have no new ideas for you whatsoever. Your sieve depth sounds about correct.

Many of these bases, even the ones with 1-2 k's remaining, will not be proven in our lifetimes with current mathematical knowledge, even allowing for an increase in computer speed and capacity.

You could easily end up having to search to n>2M to find a prime on either one of or both of these. If a test at n=274K takes 2 hours, a test at n=2740K (2.74M) would take around 200 hours or over 8 days!

A prime for either base at this point would be CRUS's largest prime yet; eclipsing Rogue's base 11 n=~300K prime.

Good luck! I personally can't stomach much over 1 hour per test. The final k on Riesel base 27 had an FFTlen increase around n=~196K that jumped it from 3500 to 4000 secs. per test. Even if I hadn't planned to previously, I tested it to n=200K and then unreserved it.


Gary

[MrOzzy]

Originally Posted by Xentar

Any ideas? :(

Put more cores on it? :-)

[MrOzzy]

Originally Posted by gd_barnes

Many of these bases, even the ones with 1-2 k's remaining, will not be proven in our lifetimes with current mathematical knowledge, even allowing for an increase in computer speed and capacity.

You might want to give it a more positive approach. If you look at the bases with 1 or 2 k's remaining:

Riesel bases: 22, 23, 26, 27, 49, 72, 93, 94, 100, 109, 110, 123, 160, 170, 177, 181, 704, 989, 1019, 1021
Sierpinski bases: 9, 10, 12, 17, 18, 23, 27, 30, 33, 43, 57, 68, 72, 73, 86, 87, 99, 101, 183, 252, 781

Many of them might get proven soon(ish) once someone puts an effor to it. I just listed them to show how many bases there are with just a few k left.

[japelprime]

Update on my reservation.
Sierp. Base9. With remaining k = 2036.
I have tested more or less 300k-350k with Phrot. I am now dc this range with LLR.
I will send Gary the results when I have finished all first time check to 350k.

[gd_barnes]

Originally Posted by MrOzzy

You might want to give it a more positive approach. If you look at the bases with 1 or 2 k's remaining:

Riesel bases: 22, 23, 26, 27, 49, 72, 93, 94, 100, 109, 110, 123, 160, 170, 177, 181, 704, 989, 1019, 1021
Sierpinski bases: 9, 10, 12, 17, 18, 23, 27, 30, 33, 43, 57, 68, 72, 73, 86, 87, 99, 101, 183, 252, 781

Many of them might get proven soon(ish) once someone puts an effor to it. I just listed them to show how many bases there are with just a few k left.

I'm a realist. I agree completely on the positive approach as long as people are aware of what they are getting themselves into. But I disagree about "someone putting an effort" to them. Virtually all of the lower bases and even several of the higher bases have already had huge efforts put on them. All bases < 30 with 1-2 k's remaining have been searched to n>=170K. Only 2 of them are at n<200K...Riesel bases 22 and 23...and many of them are reserved to higher ranges. Base 22 is mine and I recently knocked out a k at n=~160K. On the other k, I've now reached n=177K at 2500 secs. per test (continuing to n=200K, which should take ~2-3 more weeks yet) and base 23 is Willem's, who just recently reserved it for n=180K-200K.

A search on bases > 20 at n>200K pushes 4000 secs. per test on a 2.6 Ghz Intel using Phrot. Base 27 hit 4000 secs. at n=~196K so it may be a little above n=200K for bases 21 thru 26.

Also keep in mind, as I'm sure you know, the higher bases take longer to search and are lower priority. The project direction originally was only for bases <= 32. I initially objected to expanding it further but realized that it would be a more fun project to open it up to all bases <= 1024.

Probably the most "behind" "lower" bases (< 35) with 1-2 k's remaining are Sierp bases 30 and 33 that are both at n=100K with 2 and 1 k respectively remaining. Max did a good job with base 33 taking it down from 3 to 1 k remaining by searching 3 k's from n=25K to 100K...no small effort. There is also Sierp bases 43 and 57 that are only at n=25K. Of course at the same search depth, it's generally best to search the smaller bases since they take less time.

As for higher bases > 32, I've been about the only one working on the Sierp side for a long time now and I'm not sure why. I'd encourage people to start doing some Sierp searching in that area. All of the Riesel bases <= 110 that you mentioned are at least at n=50K whereas there are many Sierp bases only at n=25K. I only have one more new Sierp base <=100 that I'm going to add over the next couple of months...base 88. All the others that haven't been searched yet will have many k's remaining at n=10K or 25K; likely 40-100 k's or more and so will be large undertakings.

All of this said, I had mentioned a long time back that it would be interesting to start a team effort to just sieve all of the bases with 1, 2, or 3 k's remaining. Of course this would require separate sieves. Then after that is done, start searching all of the bases at once in one monster team drive.

Of course there are logistical problems like different search depths, reservations, etc. It's just a matter of taking the time to coordinate such a large effort...the coordination of which would take a long time in and of itself.


Gary

[MrOzzy]

There are 3 things that make CRUS very interesting:
- You can start your own base from scratch
- You can select some base with a high conjecture and find lots of small and medium primes
- You can try to proove a conjecture of a low base or reduce the number of k's by finding one or more very large primes

With a combined effort CRUS also could offer top 5000 work (around 150.000 - 200.000 digits) for example using base 24 for both sierp and riesel primes.

I still like the idea of sieving multiple bases with a few k left and testing them using prpnet. Most interesting would be bases with very few k left for both Riesel and Sierp for example bases 10,22,23,26,27 and 49.

I might be able to help coordinate such efforts in a month or two once I've finished renovating, but no promices though.

Large primes and prooving conjectures helps exposing this project to the community, which results in more people joining, more large primes found, ect ...