I searched least Carol/Kynea primes (i.e. least k such that (b^k+-1)^2-2 is prime) for all even bases b up to 360. In the Carol (-1) side, there are only 2 bases remain: 228 and 278 (the primes for bases 110, 124, 144 and 256 are given using link). In the Kynea (+1) side, there are also only 2 bases remain: 290 and 326 (the primes for bases 158 and 192 are given using link).

I did not search very far, will someone search these bases?

Note: The name of the files are not right, it should be "least k", not "least n".

For base 228, 1 <= n <= 10000, the following primes were found:

[CODE] [FONT=Times New Roman, serif](228^3+1)^2-2[/FONT]
[FONT=Times New Roman, serif](228^48+1)^2-2[/FONT]
[FONT=Times New Roman, serif](228^150+1)^2-2[/FONT]
[FONT=Times New Roman, serif](228^2123-1)^2-2[/FONT]
[/CODE]For base 278, 1 <= n <= 10000, the following primes were found:

[CODE] [FONT=Times New Roman, serif](278^1+1)^2-2[/FONT]
[FONT=Times New Roman, serif](278^3+1)^2-2[/FONT]
[FONT=Times New Roman, serif](278^7+1)^2-2[/FONT]
[FONT=Times New Roman, serif](278^174+1)^2-2[/FONT]
[FONT=Times New Roman, serif](278^826-1)^2-2[/FONT]
[FONT=Times New Roman, serif](278^2025+1)^2-2[/FONT]
[/CODE]For base 290, 1 <= n <= 10000, the following primes were found:

[CODE] [FONT=Times New Roman, serif](290^3-1)^2-2[/FONT]
[FONT=Times New Roman, serif](290^3386-1)^2-2[/FONT]
[/CODE]For base 326, 1 <= n <= 10000, the following primes were found:

[CODE] [FONT=Times New Roman, serif](326^288-1)^2-2[/FONT]
[FONT=Times New Roman, serif](326^290-1)^2-2[/FONT]
[FONT=Times New Roman, serif](326^8941+1)^2-2[/FONT]
[/CODE]This shows that all bases <= 360 have a Carol prime. Base 290 still needs a Kynea prime. (*)
While searching for these primes, a question popped up: would be possible to make a OpenCL version of cksieve so that GPU's can run it? Or at least a multithreaded version of the sieve?
(*) At least, according to sweety's lists. Not all bases <= 360 have been searched according to the website.

Yes, a multi-threaded version is possible. I don't know when I will have time to work on it.

An OpenCL version will be much harder due to various reasons, such as memory needs and the varying time to do a discrete log for each p.

Base 34 from n= 1000 to 10000
Three primes
(34^2901+1)^2-2
(34^6501+1)^2-2
(34^8093+1)^2-2

Base 42 from n=1000 to 10000
Seven primes
(42^2046+1)^2-2
(42^2466+1)^2-2
(42^2526-1)^2-2
(42^4020+1)^2-2
(42^4852-1)^2-2
(42^7907+1)^2-2
(42^8424+1)^2-2

I have made the updates. Please let me know if I missed anything or made any mistakes.

[QUOTE=rogue;472459]I have made the updates. Please let me know if I missed anything or made any mistakes.[/QUOTE]


See [URL="http://mersenneforum.org/showpost.php?p=471065&postcount=87"]http://mersenneforum.org/showpost.php?p=471065&postcount=87[/URL], base 290 (both sides) is searched up to n=20000.

Found a mistake on the web page: (204^1752-1)^2-2 is composite (it has 79 as a factor), but (204^17522-1)^2-2 is prime.
I also noticed that there are reservations by Serge, wombatman and Norb Schneider that have not been updated in over a year. I wonder if they are still working on those reservations?

[QUOTE=Dylan14;472479]Found a mistake on the web page: (204^1752-1)^2-2 is composite (it has 79 as a factor), but (204^17522-1)^2-2 is prime.
I also noticed that there are reservations by Serge, wombatman and Norb Schneider that have not been updated in over a year. I wonder if they are still working on those reservations?[/QUOTE]

Thanks. I'll take care of it.

base 46
 

Base 46 from n=1000 to n=10000
Three primes
(46^1304-1)^2-2
(46^2040+1)^2-2
(46^5172-1)^2-2

I've made the updates to my webpage