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2017-09-15, 20:46   #111
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

24·211 Posts

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".
Attached Files
 least n such that (n^k-1)^2-2 is prime.txt (1.2 KB, 144 views) least n such that (n^k+1)^2-2 is prime.txt (1.2 KB, 144 views)

Last fiddled with by sweety439 on 2017-09-15 at 20:47

 2017-09-28, 23:28 #112 Dylan14     "Dylan" Mar 2017 24·37 Posts For base 228, 1 <= n <= 10000, the following primes were found: Code:  (228^3+1)^2-2 (228^48+1)^2-2 (228^150+1)^2-2 (228^2123-1)^2-2 For base 278, 1 <= n <= 10000, the following primes were found: Code:  (278^1+1)^2-2 (278^3+1)^2-2 (278^7+1)^2-2 (278^174+1)^2-2 (278^826-1)^2-2 (278^2025+1)^2-2 For base 290, 1 <= n <= 10000, the following primes were found: Code:  (290^3-1)^2-2 (290^3386-1)^2-2 For base 326, 1 <= n <= 10000, the following primes were found: Code:  (326^288-1)^2-2 (326^290-1)^2-2 (326^8941+1)^2-2 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. Last fiddled with by Dylan14 on 2017-09-28 at 23:35
 2017-09-29, 01:52 #113 rogue     "Mark" Apr 2003 Between here and the 3×133 Posts 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.
 2017-11-18, 07:32 #114 vasyannyasha     "Vasiliy" Apr 2017 Ukraine 32×7 Posts Base 34 from n= 1000 to 10000 Three primes (34^2901+1)^2-2 (34^6501+1)^2-2 (34^8093+1)^2-2
 2017-11-19, 08:48 #115 vasyannyasha     "Vasiliy" Apr 2017 Ukraine 32·7 Posts 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
 2017-11-26, 15:43 #116 rogue     "Mark" Apr 2003 Between here and the 3×133 Posts I have made the updates. Please let me know if I missed anything or made any mistakes.
2017-11-26, 20:28   #117
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

24×211 Posts

Quote:

See http://mersenneforum.org/showpost.ph...5&postcount=87, base 290 (both sides) is searched up to n=20000.

 2017-11-26, 21:43 #118 Dylan14     "Dylan" Mar 2017 24×37 Posts 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?
2017-11-27, 02:06   #119
rogue

"Mark"
Apr 2003
Between here and the

3×133 Posts

Quote:
 Originally Posted by Dylan14 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?
Thanks. I'll take care of it.

 2017-11-29, 17:09 #120 vasyannyasha     "Vasiliy" Apr 2017 Ukraine 32·7 Posts 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
 2017-11-29, 22:21 #121 rogue     "Mark" Apr 2003 Between here and the 3×133 Posts I've made the updates to my webpage

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