Carol / Kynea Coordinated Search  Reservations
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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 [URL="http://mathworld.wolfram.com/NearSquarePrime.html"]Near Square Primes[/URL]. 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 [URL="http://harvey563.tripod.com/Carol_Kynea.txt"]here[/URL]. 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 [URL="http://www.mersenneforum.org/showthread.php?t=21251"]this thread[/URL]. [B]Please go to the Wiki [URL="https://www.rieselprime.de/ziki/CarolKynea_table"]here[/URL] 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.[/B] 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. 
[STRIKE]Definitely interested in helping, but can't at the moment. I'll keep watching this space for updates so I can jump in later.[/STRIKE]
Screw it, I'll work on base 26 up to n=100,000 
[QUOTE=wombatman;431684][STRIKE]Definitely interested in helping, but can't at the moment. I'll keep watching this space for updates so I can jump in later.[/STRIKE]
Screw it, I'll work on base 26 up to n=100,000[/QUOTE] Thanks for joining. Would you mind starting from n=1? I doubt it would take long to catch up to the range that was searched. 
Is there any mathematical reason why smaller bases (12, 18, 20, 24, etc..) have not been searched?

[QUOTE=axn;431692]Is there any mathematical reason why smaller bases (12, 18, 20, 24, etc..) have not been searched?[/QUOTE]
None that I know of. You can search any even base. I would expect even base 4 to have some primes. 
[QUOTE=rogue;431718]None that I know of. You can search any even base. I would expect even base 4 to have some primes.[/QUOTE]
Base 4 is covered by base 2 (since 4^n = 2^(2n)). Similarly, any perfect power will be covered by its base. So, 4,8,16,32,36,etc... need not be searched. 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. 
[QUOTE=axn;431719]Base 4 is covered by base 2 (since 4^n = 2^(2n)). Similarly, any perfect power will be covered by its base. So, 4,8,16,32,36,etc... need not be searched.[/QUOTE]
Duh! 
I'll run bases 10 and 20 to 100k, and 30 and 40 to 70k for starters.

[QUOTE=rogue;431688]Thanks for joining.
Would you mind starting from n=1? I doubt it would take long to catch up to the range that was searched.[/QUOTE] I'll let the current search (running to P=1e12) finish and then I'll run the range from n=1 up to where I started already. 
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.

hi,
I do like to reserve base=74 n=1 to 100000 
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