Sierp 758
 

Sierp 758, the last k, tested n=50K-100K. Nothing found.

Results emailed. Base released

32*670^79644-1 (225081 digits, give or take) proves R670.

Sierpinski base 928 is complete to n=15K. Ten primes found. I believe this makes it 607 k-values remaining.

[CODE]5140*928^14126+1
26836*928^14180+1
27109*928^14325+1
412*928^14594+1
6378*928^14750+1
16071*928^14756+1
14581*928^14805+1
12477*928^14829+1
21727*928^14876+1
7957*928^14976+1
[/CODE]

Results emailed to Gary.

Continuing.

Progress of R603: at n= ~21,600. Continuing to 25K. Achingly slow.

R790 is complete to n=25K; only k=20 & 48 remain; largest prime 146*790^400-1; base released.
S649 is complete to n=25K; only k=64 remains; largest prime 66*649^10970+1; base released.
S778 is complete to n=25K; only k=163 remains; largest prime 18*778^19927+1; base released.
S853 is complete to n=25K; only k=42 & 106 remain; largest prime 34*853^267+1; base released.

Hope I haven't messed anyone up, but I just finished 12 bases with a ck > 500 that I didn't reserve. :blush:

R667 - 265 primes - 5 remaining - ck = 834
S567 - 457 primes - 2 remaining - ck = 924
S577 - 212 primes - 8 remaining - ck = 664
S617 - 189 primes - 10 remaining - ck = 514
S703 - 159 primes - 5 remaining - ck = 538
S712 - 331 primes - 15 remaining - ck = 528
S805 - 231 primes - 3 remaining - ck = 714
S814 - 416 primes - 14 remaining - ck = 651
S889 - 200 primes - 2 remaining - ck = 624
S964 - 485 primes - 22 remaining - ck = 771
S985 - 287 primes - 5 remaining - ck = 900
S1006 - 271 primes - 6 remaining - ck = 531

All pages will be sent to Gary.

[quote=gd_barnes;224663]NICE!!

Along with S589 that also has CK=414, it is the largest conjecture proven on both sides for bases > 165!

Does anyone care to test some 1/2/3 k'ers for bases > 165 with CK>414 that are only at n=25K to try to beat the record?
[/quote]
Thanks! Followed your advice. Now CK=534 is the one to beat.
__________

[COLOR=blue]P.S. I wonder if a simple plot of proven conjectures and a bit of splining will find an easy to remember function that would bring both b and CK together in an ad hoc measure of unusual luck. (Because there are some proven conjectures with low b and much higher CK. It would be nice for the function to be flat with occasional spikes.)[/COLOR]
[COLOR=blue][/COLOR]
[COLOR=blue]Off the top of my head f[sub]luck[/sub](b,CK) = b*CK , for example? [/COLOR]

[quote=Batalov;225969]Thanks! Followed your advice. Now CK=534 is the one to beat.[/quote]

VERY nice!

CK414 is still the one to beat for bases > 350. :smile:

Reserving the following bases to n=25K:

R573
R828
S533
S573
S588
S638
S766
S774
S790
S832
S833
S949
S987

Time for the Sierp side to do a little catch up.

[quote=Batalov;225969][COLOR=blue]Off the top of my head f[sub]luck[/sub](b,CK) = b*CK , for example? [/COLOR][/quote]
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]

Riesel 665
 

Riesel 665, the last k, tested n=25K-100K. Nothing found.

Results emailed. Base released

[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]

It took me a few mins. to understand what you were getting at here.

It's interesting that you call it luck, implying bases that have been the most "lucky" score the highest. I think that in most cases, it's not luck. It's that the bases are heavier weight, i.e. many of their k's have fewer small factors, than normal. Clearly there is an element of luck but the absence of small factors on most/all k's is the biggest contributor to proven bases scoring high.

Note that none of the bases are b==(2 mod 3). Bases that are (2 mod 3) have been notoriously difficult to prove. That brings up another question: What proven base that is b==(2 mod 3) scores the highest using your formula?