20160415, 17:28  #1 
"Mark"
Apr 2003
Between here and the
2^{2}×5×17×19 Posts 
Carol / Kynea Coordinated Search  Reservations
I've decided to start a new thread for a coordinated Carol / Kynea search. Carol and Kynea primes are a subset of what is known as Near Square Primes. These primes have the form of (b^n1)^22 (Carol) and (b^n+1)^22 (Kynea). Steven Harvey has coordinated the search in the past and still coordinates the base 2 search here. This thread is for those who want to search other bases. Although his page has some other bases on it, the page is incomplete and it is unknown to me if there are any gaps or if bugs might have causes previous searches to miss some primes.
I am already working on base 2 in another thread of the subforum and am coordinating that effort with Steven directly. Odd bases can be skipped because the Carol/Kynea number is always even. I could modify the sieve to test (b^n+/2)^2+/1 for odd b, but that is for a different project somewhere down the road. pfgw (for base 2) is about 15% faster than llr, so pfgw is recommended for testing this form at this time. This form is supported by PRPNet, so you can find that elsewhere if you want to use it to distribute PRP testing. Please post primes in this thread. Please go to the Wiki here to see a list of bases, primes, and current reservations. Karsten (kar_bon) is doing most of the updates. You may also create an account at the Wiki and make updates yourself. Please continue to use this thread to submit and complete your reservations. Attached are some sieving files available for testing. You may want to verify that they have been sufficiently sieved before beginning testing. Last fiddled with by gd_barnes on 20210521 at 19:45 Reason: update info 
20160416, 02:08  #2 
I moo ablest echo power!
May 2013
11011111001_{2} Posts 
Screw it, I'll work on base 26 up to n=100,000 Last fiddled with by wombatman on 20160416 at 02:12 
20160416, 03:44  #3  
"Mark"
Apr 2003
Between here and the
2^{2}·5·17·19 Posts 
Quote:
Would you mind starting from n=1? I doubt it would take long to catch up to the range that was searched. 

20160416, 06:23  #4 
Jun 2003
5,179 Posts 
Is there any mathematical reason why smaller bases (12, 18, 20, 24, etc..) have not been searched?

20160416, 14:19  #5 
"Mark"
Apr 2003
Between here and the
2^{2}×5×17×19 Posts 

20160416, 14:56  #6  
Jun 2003
5,179 Posts 
Quote:
EDIT: I'll work on base12 to 50,000. I'll sieve base18 to 100,000 but not sure how far I'm willing to test. Will know further once I'm done with base12. Last fiddled with by axn on 20160416 at 15:02 

20160416, 15:30  #7 
"Mark"
Apr 2003
Between here and the
14474_{8} Posts 

20160416, 18:04  #8 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{3}·1,201 Posts 
I'll run bases 10 and 20 to 100k, and 30 and 40 to 70k for starters.

20160416, 20:35  #9 
I moo ablest echo power!
May 2013
3×5×7×17 Posts 

20160416, 22:55  #10 
"Mark"
Apr 2003
Between here and the
2^{2}·5·17·19 Posts 
Make sure you sieve deeply enough. For base 2, I'm continuing to sieve up to 1e13 and it is still removing factors at more than one an hour. Granted higher bases won't need to be sieved as deeply to find prime with the same number of bits for lower bases, but I wouldn't be surprised if most bases need to be sieved to at least 1e12.

20160417, 15:10  #11 
Jul 2003
2·307 Posts 
hi,
I do like to reserve base=74 n=1 to 100000 
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