Bases 501-1030 reservations/statuses/primes

[gd_barnes]

Originally Posted by rogue

I'm only doing two today and the other will be for tomorrow (if someone doesn't beat me to it). I don't want to break the rules.

The rules state that you can do as many as you want each day for bases with a conjectured k of <= 200. That's why I enlisted Ian.

[rogue]

Originally Posted by gd_barnes

The rules state that you can do as many as you want each day for bases with a conjectured k of <= 200. That's why I enlisted Ian.

For some odd reason I was thinking bases <= 200.

In that case I will take Sierpinski base 740 too.

[rogue]

All of these have a conjectured k of 16. I'm reserving them.

[rogue]

Reserving.

[rogue]

Reserving

[rogue]

Reserving

[Mathew]

rogue,

Hilarious.

[gd_barnes]

Originally Posted by Mathew Steine

rogue,

Hilarious.

Hum, well...I think he is serious. (unless there is some inside joke that I am missing)

He's doing a bunch of the small ones.

[gd_barnes]

Here we go with some more from my former k=2 effort. There are a total of 9 but 2 are in the bases 251-500 thread. These are most of the bases from the k=2 search that had from 2 to 5 k's remaining at n=5K when I originally did the search a couple of years ago.

The following bases have been searched to n=25K and are released. None were proven but we have 3 more for the 1k remaining thread (including one with only k=2 remaining) and 3 more with k=2 remaining. Details to be shown on the pages.

R551; CK=22; k=10 & 14 remain; highest prime 2*551^2718-1
R662; CK=14; only k=7 remains; highest prime 2*662^16590-1
R785; CK=130; k=16 & 28 remain; highest prime 94*785^23033-1

S635 CK=52; only k=28 remains; highest prime 32*635^17309+1
S836 CK=32; only k=2 remains; highest prime 7*836^5700+1
S878 CK=23; k=2, 11, 13, & 17 remain; highest prime 10*878^972+1
S947 CK=80; k=2, 34, & 68 remain; highest prime 22*947^870+1


Collective primes for n=5K-25K:
11*662^13306-1
2*662^16590-1
2*785^9670-1
94*785^23033-1
4*635^11722+1
32*635^17309+1
7*836^5700+1


I checked others recent and older reservations and saw that just one overlapped with these: S878. I'll let Mark know separately.

Ian, all of these (plus the 2 for bases <= 500) have CK<=200 but I'll show these on the pages myself like before so that we aren't sending files back and forth.


Gary

[Mathew]

Gary,

I know he is serious about the reservations.

How does a low CK help in the time it takes? R596 with a CK=200 took me <24 hrs to prove whereas R332 with a CK=38 (started only seconds apart, on the same machine) took me almost 2 weeks to get to n=25K. Is there some foresight that I am unaware of?

Also the joke (not inside) is that rogue thought the policy was 2 bases a day. After realizing this was not the case his mindset changed. Which, I find hilarious.

[gd_barnes]

Originally Posted by Mathew Steine

Gary,

I know he is serious about the reservations.

How does a low CK help in the time it takes? R596 with a CK=200 took me <24 hrs to prove whereas R332 with a CK=38 (started only seconds apart, on the same machine) took me almost 2 weeks to get to n=25K. Is there some foresight that I am unaware of?

Also the joke (not inside) is that rogue thought the policy was 2 bases a day. After realizing this was not the case his mindset changed. Which, I find hilarious.

I admit it is a bit funny. But I can say that since Ian is doing the HTML for them all as well as updating the untested and 1k threads.

As a general rule, the lower conjectures will take less time. Of course as you found, there are exceptions. But the fact is, if you choose a base with a CK of 10,000 and one with a CK of 10 or 100, the latter is likely to take much less time but there can be a wide variance in that time. S36 is the most glaring example of this. With a CK of 1886, it was proven almost instantly with a highest prime of n=1571. It is the highest conjecture proven at CRUS but what was the most amazing thing is that it was proven at such a low n. The second highest is S11 with CK=1490 but it did not fall until n=300544 so is not nearly as remarkable as S36!

So...if you choose a base with a CK of > 2000, it's highly unlikely that you will prove it. We do have one base with a CK of 9175 (S10) that has only one k remaining and is being searched at n=470K right now. But S10, S11, and S36 are all fairly small bases relative to the project as a whole. With the bases that are remaining untested now, it's unlikely that any one person will prove any one of those with a CK of > 1000.

I can offer up little in the way of telling ahead-of-time what base will be easy to prove. I know that bases where b==(1 mod 30) and where b=2^q-1 are relatively prime for their size but all of the smaller CK's from those have been searched already. The best thing to do is simply search a base to n=1000 or n=2500 and see what remains relative to the size of the conjecture. I say that because 3 k's remaining for a conjecture of k=1000 is much better than for a conjecture of k=100. The former likely has k's that are much heavier weight than the latter and so will likely be proven more easily.

Reference the weight of individual k's: If you have a k that has < 2% of its candidates remaining on a sieve to P=1G, that would be low weight. One with > 4% would be decent and with > 5% would definitely be high weight. If you have a k with > 5% of candidates remaining and it has been unlucky enough to not have a prime at n=2500 or n=10K or whatever, the chances are pretty good that a prime can be found with a continued search.


Gary