[quote=Batalov;225985]Now, after that spline, I like more
[COLOR=#0000ff]f[sub]luck[/sub](b,CK) = b*sqrt(CK) >= 9000 [/COLOR]

[COLOR=#0000ff][COLOR=black]Outliers are[/COLOR] [COLOR=darkred]S36 (f = 11316)[/COLOR][/COLOR][COLOR=black], S337, S580, S589, S903 (these four are almost equal) ...and S57 comes close.[/COLOR][/quote]

In looking this over, the formula appears to favor larger bases. For example, if we were able to prove Riesel base 6, it would score 6*sqrt(84687)=1746. That's pretty low for what would be a relatively difficult proof. The even more difficult Sierp base 6 would only score 6*sqrt(174308)=2505. It has 19 k's remaining at n=327K and is unlikely to be proven in most of our lifetimes without new mathematical methods being discovered.

I wonder if taking the log of the base would work better. OK, let's try log(b)*sqrt(CK) and see what we get:

S36 = 67.58
S57 = 60.52
S337 = 58.41
S589 = 56.36
S580 = 56.23
S903 = 54.34

S57 would be in 2nd place. This all seems reasonable.

Now...if these were to be proven:
R6 = 226.45
S6 = 324.88


That seems to more accurately reflect the difficulty in proving base 6 on both sides. Would you agree? If so, can you plot that function? That would be interesting to see.


Gary

This looks something like below (log is log[sub]10[/sub] but this is just a question of scale).

This concept is somewhere between difficulty and luck. This measure is a tongue-in-cheek, anyway. Luck is involved to a certain degree. For example, one may have tested a conjecture to 100K, but the prime is waiting at 100.5K and the conjecture remains a 1ker...

Riesel 668
 

Riesel 668, the last k, tested n=25K-100K. Nothing found.

Results emailed. Base released

Riesel 684
 

Riesel 684, the last k, tested n=25K-100K. Nothing found.

Results emailed. Base released

Reserving S706. To 100K.

6*692^45446-1 is prime. Conjecture proven - Results emailed

Reserving the following 1ker's to n=100K:
R702 R724 R730 R743 R759
S836 S866 S879 S893 S934

R552 R638 R710 R995 are all complete to 25k unreserving
prpnet results: [URL]http://www.sendspace.com/file/q5erw1[/URL]
edit: just realized i didn't update pl_prime and pl_remain with the primes from prpnet this time

[quote=henryzz;226470]R552 R638 R710 R995 are all complete to 25k unreserving
prpnet results: [URL]http://www.sendspace.com/file/q5erw1[/URL]
edit: just realized i didn't update pl_prime and pl_remain with the primes from prpnet this time[/quote]

Please Email me the primes (separated from the results) and k's remaining on each base to:
gbarnes017 at gmail dot com

This is only results and I have to navigate through a bunch of popups and ads to get to it.

Thanks.

Extending the project slightly, which I plan to do no more:

Both with CK=104:

R1029 is complete to n=25K; only k=26 & 36 remain; highest prime 98*1029^859-1; base released.
S1029 is complete to n=25K; only k=34 remains; highest prime 54*1029^459+1; base released.

[quote=henryzz;226470]R552 R638 R710 R995 are all complete to 25k unreserving
prpnet results: [URL]http://www.sendspace.com/file/q5erw1[/URL]
edit: just realized i didn't update pl_prime and pl_remain with the primes from prpnet this time[/quote]
Got the results--I'll process them as soon as I get the chance.

[quote=gd_barnes;226476]Please Email me the primes (separated from the results) and k's remaining on each base to:
gbarnes017 at gmail dot com

This is only results and I have to navigate through a bunch of popups and ads to get to it.

Thanks.[/quote]
Sent.
I didn't realise that sendspace had popups. I thought that people elsewhere on the forum had verified it as clean and have only uploaded to it not downloaded from it. You don't have to wait on this one to download which is why others use that upload site.
I dislike the fuss of searching for the correct email address etc. I have just added you to contacts so that shouldn't be a problem in future. Shouldn't these be Ian's to process as they are all CKs<200?