Bases 33-100 reservations/statuses/primes

[rogue]

Originally Posted by mdettweiler

Reserving Sierp. base 33 for sieving to n=100K.

I was thinking that this would be an interesting base to run through PRPnet--we'd probably have it done in a very short time, and with only 3 k's remaining, there is a very good chance of proving this base in a short amount of time. What does everyone think about this?

(Note: even if we don't do it through PRPnet, I still plan to complete the sieving, which I started earlier today and is proceeding to finish probably sometime today or tomorrow. )

There are other bases with a single k left that have proven to be stubborn for n > 100K. The k for this base could be just as nasty.

My personal opinion is that we should try to get all bases to n = 100K and then throw everything left into PRPNet, with the exception of the bases that have more than a few dozen k left.

[gd_barnes]

I'm in favor of a combination of your guy's suggestions and part of it is something that I alluded to in another thread. At some point in the near future, for bases <= 100 that have not already been done, do the following initial processing:

1. Test all bases <= 100 that will clearly have <= 35 k's remaining at n=10K.

2. For bases in #1 that have 8-15 k's remaining at n=10K, test them to n=25K.

3. For bases in #1 that have 1-7 k's remaining at n=10K, test them to n=100K.

After completing the above, do the following final processing:

1. Put all bases that have 1-3 k's remaining into group 1. I'll rate each of these bases as having a > 50% chance of being proven in the next 10 years.

2. Put all bases that have 4-7 k's remaining into group 2. I'll rate these as having a 2-50% chance of being proven in the next 10 years.

3. Put all bases remaining that DID meet the criteria in #1 of the initial process but did NOT meet the criteria in #2 or #3 of the intial process or #1 or #2 of the final process into group 3. Most will have 8-35 k's remaining at either n=10K or 25K. I rate these as having < 2% chance of being proven in the next 10 years.

4. Sieve all of the above together as much as can be reasonably done. I don't know of a way to sieve multiple bases at once. Perhaps it can be done.

5. Put each group into a separate PRPnet server and let 'er rip. Group 3 may need to be broken down a little further as it will have a lot of bases and k's and will have been tested to a lower limit.

This will give us a good chance at proving a few bases, will also bring some tougher but not virtually impossible bases to a point at which future generations of prime searchers could reasonably prove them, especially with continued software improvements like Phrot and PRPnet, and will knock out many k's on the virtually impossible bases.

Personally, I can't get too excited about bases > 100 and don't recommend them for PRPnet. Actually, it took me quite a while to warm up to anything for bases > 32. Only the math of finding patterns in the partial algebraic factors got me more interested in them. Bases > 100 are great for individual efforts but are simply too hard to find primes for in a team effort because the base is so high, leaving few candidates to test within any specific numerical length range.


Gary

[gd_barnes]

Originally Posted by mdettweiler

Reserving Sierp. base 33 for sieving to n=100K.

I was thinking that this would be an interesting base to run through PRPnet--we'd probably have it done in a very short time, and with only 3 k's remaining, there is a very good chance of proving this base in a short amount of time. What does everyone think about this?

(Note: even if we don't do it through PRPnet, I still plan to complete the sieving, which I started earlier today and is proceeding to finish probably sometime today or tomorrow. )

I rate the odds at < 5% that this base will be proven in a "short" amount of time. By short, I mean < 1 year running a full quad 24x7. If we can focus 5-10 total quads from the team 24x7, we might have a 50-50 shot at proving it in < 1 year, but that's just a guess. I'd have to look at the specific weights of the k's to get a better estimate. If you can post your sieve file here or let me know how many testing candidates remain for each k, I can get a better estimate.

I sense that the tremendous difficulty in finding the final primes on these bases is still lost on many people here. Base 33 is a very high base compared to bases < 10.

A few questions: What do you mean by we'll have it "done" in a short amount of time? Do you mean proven or just the sieved n-range completely tested? Proven?...highly unlikely. Sieved n-range completely primality tested?...sure.

I think that sieving n=25K-100K is a good range to start with and can probably be sieved to an optimal depth within 3 days. But the final prime on this base is likely to be far greater than n=100K so will probably need a lot more work.

This base would fall in #3 of the 'initial process' that I spoke of in the last post. In other words, let's get it tested to n=100K and then we can consider putting the k's that remain in the 'group 1' team PRPnet server for higher n-ranges after getting those sieved. Group 1 will be the "> 50% chance provable in the next 10 years" bases.

Be careful about thinking that a base can be proven in a "short" amount of time when testing has already reached n=25K with multiple k's remaining, even with just 2 or 3. Sometimes it happens but far more often then not, it does not.


Gary

[mdettweiler]

@Gary regarding the overall plan you presented: okay, that sounds good. One thing I'm sort of confused about, though: are you saying that we should only put them into PRPnet for n>100K? Because PRPnet can handle stuff much lower than that, and it would be a waste to not utilize it for lower stuff because of an arbitrary limit.

Regarding Sierp. base 33: Ah, I see what you mean. Yeah, I guess you're right about it not being likely to be proven any time soon--I guess I just saw the three k's remaining at n=25K for a somewhat low base and figured "hey, looky, we can prove this one!" Anyway, regardless of when it's likely to be proven, I'll still continue the sieving and will probably reserve it to PRP to n=100K myself. Who knows--maybe I'll hit the jackpot and knock out all three k's before 100K.

Max

[Flatlander]

Riesel base 52 has been tested to n=1k. 664 ks left.
I'm sieving to n=10k.

[mdettweiler]

Sierp. base 33 has now completed sieving for n=25K-100K. I'll now reserve this base to PRP test for the same range.

[gd_barnes]

Originally Posted by mdettweiler

@Gary regarding the overall plan you presented: okay, that sounds good. One thing I'm sort of confused about, though: are you saying that we should only put them into PRPnet for n>100K? Because PRPnet can handle stuff much lower than that, and it would be a waste to not utilize it for lower stuff because of an arbitrary limit.

Max

No, not at all. Check out group 3. We'll have plenty of n>=10K and n>=25K tests for the PRPnet servers for bases where there are up to 35 k's remaining. What I'm saying is that for the bases that are close to being proven, we should individually test them to n=100K before putting them into a team "proving" server, i.e. the group 1 server.

What I brought up there was just a brain dump that keeps us from getting overly complex with the servers. Imagine if you ran a team server for base 33 and then someone else wanted to do one for base 37 because it only has 4 k's remaining at n=25K, and then another because it has only 2 k's remaining, etc. We'd have servers all over the place. The idea of the group 1 server is to put some LONG tests in it for perhaps a total of ~40 k's on ~20 bases, i.e. bases with 1-3 k's remaining at n=100K or higher. (Actually by the time we get it going, many bases < 32 that have 1-3 k's remaining will be at n=250K or higher so we may want a special 4th group server for them.)

Regardless, as a brain dump, nothing is set in stone there. It was just me throwing out some generalities about how to load the servers without going too overboard with them. Keep in mind that as an admin here, I can't stop anyone from doing anything. I can only attempt to coordinate efforts and keep them from being overly complex. If people strongly prefer having one server for each base for n>=10K or 25K, then who am I to stop them? If that is the case, I'll do my best to make things the least complex that they can be.

Everyone, please give your opinions on how to divide up the bases for loading into a limited # of PRPnet servers; perhaps 2-5 of them. In asking for the opinions, please note that existing team drives are completely separate then the aforementioned "group" servers.

Good luck with base 33! I have this funny feeling that you'll find 2 k's with primes for n=25K-100K and that we'll have, yet again, a base with one k remaining. Personally, I was glad when k=36 fell at n=~23.6K. k's that are perfect squares are frequently problem children and it gave me hope that the base could be proven in a reasonable amount of time.

Edit: Feel free to set up personal PRPnet servers for yourself or others on my machines. If that one machine has enough servers on it right now, go ahead and use another. I don't count those as "official CRUS" team or group servers because they are only a temporary way to help automate one's personal reservations.


Gary

[mdettweiler]

Originally Posted by gd_barnes

No, not at all. Check out group 3. We'll have plenty of n>=10K and n>=25K tests for the PRPnet servers for bases where there are up to 35 k's remaining. What I'm saying is that for the bases that are close to being proven, we should individually test them to n=100K before putting them into a team "proving" server, i.e. the group 1 server.

What I brought up there was just a brain dump that keeps us from getting overly complex with the servers. Imagine if you ran a team server for base 33 and then someone else wanted to do one for base 37 because it only has 4 k's remaining at n=25K, and then another because it has only 2 k's remaining, etc. We'd have servers all over the place. The idea of the group 1 server is to put some LONG tests in it for perhaps a total of ~40 k's on ~20 bases, i.e. bases with 1-3 k's remaining at n=100K or higher. (Actually by the time we get it going, many bases < 32 that have 1-3 k's remaining will be at n=250K or higher so we may want a special 4th group server for them.)

Regardless, as a brain dump, nothing is set in stone there. It was just me throwing out some generalities about how to load the servers without going too overboard with them. Keep in mind that as an admin here, I can't stop anyone from doing anything. I can only attempt to coordinate efforts and keep them from being overly complex. If people strongly prefer having one server for each base for n>=10K or 25K, then who am I to stop them? If that is the case, I'll do my best to make things the least complex that they can be.

Everyone, please give your opinions on how to divide up the bases for loading into a limited # of PRPnet servers; perhaps 2-5 of them. In asking for the opinions, please note that existing team drives are completely separate then the aforementioned "group" servers.

Good luck with base 33! I have this funny feeling that you'll find 2 k's with primes for n=25K-100K and that we'll have, yet again, a base with one k remaining. Personally, I was glad when k=36 fell at n=~23.6K. k's that are perfect squares are frequently problem children and it gave me hope that the base could be proven in a reasonable amount of time.

Edit: Feel free to set up personal PRPnet servers for yourself or others on my machines. If that one machine has enough servers on it right now, go ahead and use another. I don't count those as "official CRUS" team or group servers because they are only a temporary way to help automate one's personal reservations.


Gary

Ah, okay, that makes sense now--sounds like a pretty good plan to me.

[Flatlander]

I've have no way of knowing if this is easy, hard or something in between and I probably won't understand the maths anyway but:

While fiddling with Riesel base 39, I found lots of ks that have algebraic/trivial/whatever factors for odd and even n and can be removed. These form a pattern. Who can tell me that pattern and show me why it exists? (No cheating to get the pattern like I had to!)

edit:
I don't mean k = = 1 mod 2 and k = = 1 mod 19. These weren't tested. (Some ks in the pattern above were excluded because of this.)

[gd_barnes]

Originally Posted by Flatlander

I've have no way of knowing if this is easy, hard or something in between and I probably won't understand the maths anyway but:

While fiddling with Riesel base 39, I found lots of ks that have algebraic/trivial/whatever factors for odd and even n and can be removed. These form a pattern. Who can tell me that pattern and show me why it exists? (No cheating to get the pattern like I had to!)

edit:
I don't mean k = = 1 mod 2 and k = = 1 mod 19. These weren't tested. (Some ks in the pattern above were excluded because of this.)

I've done no factoring using Alpertron's site nor testing on this base but if you look at this thread by me, it states the following for all b == 4 mod 5 on the Riesel side:

algebraic factors on even-n combine with a numeric factor on odd-n in the following scenario:

k=m^2 and m==(2 or 3 mod 5)

Factors to:

for even-n, let n=2q:
(m*b^q-1)*(m*b^q+1)
-and-
odd-n: factor of 5

Therefore, I suspect that the following k's have algebraic factors on even-n that combine with a factor of 5 on odd-n to eliminate them:

k=2^2 = 4
k=8^2 = 64
k=12^2 = 144
(note k=18^2 = 324 is not considered because k == 1 mod 19 and so all n-values have a trivial factor of 19)
k=22^2 = 484
k= 28^2 = 784
(etc. if k not == 1 mod 19)

Note that we don't include k=3^2, 7^2, 13^2, 17^2, etc. in this algebraic factor analysis because they are odd-k with a trivial factor of 2 on all n-values. But if you look closely at them and discount the factor of 2, you'll see that they still have the same pattern of algebraic factors on even-n and a factor of 5 on odd-n.

This situation is why I posted that thread. If the above is correct here, it will show that I have generallized the factors correctly (for this case anyway) in the other thread.


Gary

[Flatlander]

Originally Posted by gd_barnes

...
k=2^2 = 4
k=8^2 = 64
k=12^2 = 144
(note k=18^2 = 324 is not considered because k == 1 mod 19 and so all n-values have a trivial factor of 19)
k=22^2 = 484
k= 28^2 = 784
(etc. if k not == 1 mod 19)

Gary

Perfecto!!!