20170915, 20:46  #111 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
2^{4}·211 Posts 
I searched least Carol/Kynea primes (i.e. least k such that (b^k+1)^22 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". Last fiddled with by sweety439 on 20170915 at 20:47 
20170928, 23:28  #112 
"Dylan"
Mar 2017
2^{4}·37 Posts 
For base 228, 1 <= n <= 10000, the following primes were found:
Code:
(228^3+1)^22 (228^48+1)^22 (228^150+1)^22 (228^21231)^22 Code:
(278^1+1)^22 (278^3+1)^22 (278^7+1)^22 (278^174+1)^22 (278^8261)^22 (278^2025+1)^22 Code:
(290^31)^22 (290^33861)^22 Code:
(326^2881)^22 (326^2901)^22 (326^8941+1)^22 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. Last fiddled with by Dylan14 on 20170928 at 23:35 
20170929, 01:52  #113 
"Mark"
Apr 2003
Between here and the
3×13^{3} Posts 
Yes, a multithreaded 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. 
20171118, 07:32  #114 
"Vasiliy"
Apr 2017
Ukraine
3^{2}×7 Posts 
Base 34 from n= 1000 to 10000
Three primes (34^2901+1)^22 (34^6501+1)^22 (34^8093+1)^22 
20171119, 08:48  #115 
"Vasiliy"
Apr 2017
Ukraine
3^{2}·7 Posts 
Base 42 from n=1000 to 10000
Seven primes (42^2046+1)^22 (42^2466+1)^22 (42^25261)^22 (42^4020+1)^22 (42^48521)^22 (42^7907+1)^22 (42^8424+1)^22 
20171126, 15:43  #116 
"Mark"
Apr 2003
Between here and the
3×13^{3} Posts 
I have made the updates. Please let me know if I missed anything or made any mistakes.

20171126, 20:28  #117  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
2^{4}×211 Posts 
Quote:
See http://mersenneforum.org/showpost.ph...5&postcount=87, base 290 (both sides) is searched up to n=20000. 

20171126, 21:43  #118 
"Dylan"
Mar 2017
2^{4}×37 Posts 
Found a mistake on the web page: (204^17521)^22 is composite (it has 79 as a factor), but (204^175221)^22 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? 
20171127, 02:06  #119  
"Mark"
Apr 2003
Between here and the
3×13^{3} Posts 
Quote:


20171129, 17:09  #120 
"Vasiliy"
Apr 2017
Ukraine
3^{2}·7 Posts 
base 46
Base 46 from n=1000 to n=10000
Three primes (46^13041)^22 (46^2040+1)^22 (46^51721)^22 
20171129, 22:21  #121 
"Mark"
Apr 2003
Between here and the
3×13^{3} Posts 
I've made the updates to my webpage

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