[QUOTE=VBCurtis;451013]One core of my laptop took 10 days to reach 5000, with exactly 750 k's remaining.
A single core of desktop is approaching 6000 now, with 50 more primes found.[/QUOTE]
550 k's remaining for R2017 at n= 10650. Continuing.

500 k's remain at n = 13500 for R2017. Continuing.

S2017 has hit n=10000 (after repeating n=5k-10k b/c I used the wrong base :mad:)

There are 1011 k remaining. I'll take it to n=15000 and then decide whether to continue. :smile:

Anyone interested in S/R 2018? I´ve booth tested to n=10K and like to stop.
I´ve stored the information´s at my PC at home, I´ll upload them in the middle of February.

I was just thinking about this! Sure, I'll take R2018 from 10k to 15k, and then pass it along to the next person.

I'll also post k's remaining for R2017 at 20k sometime soon.

Back in 2011 I posted lists of conjectured ks for bases 1031 to 2048 in this thread. Since then I found smaller ks for a few very difficult bases, so here are some updated lists. I know it's likely that no-one will ever work on these bases, but I thought it would be good to put the lists up in any case for the sake of correctness - if they even are correct, as these are all just conjectures, and maybe some of the ks can still be improved.

Looking at the CKs for 2018 on both sides I am surprised one isn't proven.

The base is b==(2 mod 3), which makes it low weight. That combined with the fact that it is a huge base and has no k's with trivial factors makes it tougher.

k=2 remains on both sides at n=2500.

[QUOTE=gd_barnes;478707]The base is b==(2 mod 3), which makes it low weight. That combined with the fact that it is a huge base and has no k's with trivial factors makes it tougher.

k=2 remains on both sides at n=2500.[/QUOTE]

They are both alive at n=10K.
Will upload the found primes and remaining k´s mid February.

There you go, all you need is in the .zip.
Tested up to 2,5K with pfgw-script. (pfgw 3.8.3) and than tested up to n=10K with cllr.
No primes between n=2,5K-10K found, on booth sides.

I have done some experimenting with numbers of the form k*b!^n+1 and found for b=11! the following ck:

5632536606457830

Well, at first i guessed I found the largest ck, but. It´s not that easy because n=1 and n=14 are prime; so the guessed number is not the ck.
Well, where are we now? I´ve found some other ck´s.

[CODE]
And their orders: 3,6,8,9,9,9,12,18,24,36,36,72,72
**************** Solution found ****************
3280323810310732029 (primed)
**************** Solution found ****************
2778419435096714989 (primed)
**************** Solution found ****************
2301476499057487007 (primed)
**************** Solution found ****************
51656689484884092 (primed)
**************** Solution found ****************
24201424107893047 (primed, tooo)
**************** Solution found ****************
20936636839733734 (primed)
**************** Solution found ****************
18509009541806713 (now primed)
**************** Solution found ****************
15868137785229282 (primed)
**************** Solution found ****************
11552808260600936 (primed)
**************** Solution found ****************
5632536606457830 (primed)

[/CODE]I´ve only tryed exponent 144 (above is seen using 72; for sure. :P ). Is there any other exponents that I might try?
(It seems that the other ck´s are not getting a full covering set; I´m just searching for a prime n<10K. ;) )


more edits:
18509009541806713*39916800^367+1 is prime!
24201424107893047*39916800^180+1 is prime!
2778419435096414989*39916800^148+1 is prime!
(not very surprising.)