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^n-1)^2-2 (Carol) and (b^n+1)^2-2 (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 sub-forum 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.