Rob,

In 1995, I did check Carol\Kynea for powers of 3 and greater, but found that they were not poppulated enough as far as I was concern. They may be of good interest, because they are more easily proven prime compared to powers of 4 and greater. I felt that K= (2^n+1)^4 - 2 was more interesting that C/K = (2^n +/- 1)^3 - 2. Although the former is more easily proven prime, I had a greater interest in the latter, as a result I found the largest known PRP.

Just like we've found (6^n-1)^2 - 2 to be interesting, So is (2^n-1)^6 - 2. If one wants to beat my record PRP, I suggest that they search using (2^n-1)^6 - 2. I've toyed Carol/Kynea Numbers in severall generalized ways, but abondoned a lot of the results because I didn't think that a particular form was dense enough for me. Again, once I can prove my conjecture then most of these numbers will be of great importance because they would be readily proven prime if they pass a PRP test.

----Cletus Emmanuel

Rob Binnekamp <

robdine@...> wrote:

Steven et al.,

I propose to introduce the Carol-rel. form (2^k-1)^3+2

and the Kynea-rel. form (2^k+1)^3-2.

These forms produce provable primes, powers > 3 prp's.

I tested both forms nearly up to k=50000 and will send you the results.

Rob

[Non-text portions of this message have been removed]

Unsubscribe by an email to:

primenumbers-unsubscribe@yahoogroups.com
The Prime Pages :

http://www.primepages.org/
---------------------------------

Yahoo! Groups Links

To visit your group on the web, go to:

http://groups.yahoo.com/group/primenumbers/
To unsubscribe from this group, send an email to:

primenumbers-unsubscribe@yahoogroups.com
Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.

---------------------------------

Do you Yahoo!?

Yahoo! Mail SpamGuard - Read only the mail you want.

[Non-text portions of this message have been removed]