- Hello, Group.

Let n= 1, 2, 3, etc. and Nn= 3^n -2.

Does the sequence 1, 7, 25, 79, 241, 727, 1185, etc. have a test for

verifying the primality of Nn similar to the LL test for Mersenne Mp=

2^p -1?

I tried for several weeks to find one and couldn't.

Bill >

No.

> Let n= 1, 2, 3, etc. and Nn= 3^n -2.

>

> Does the sequence 1, 7, 25, 79, 241, 727, 1185, etc. have a test for

> verifying the primality of Nn similar to the LL test for Mersenne Mp=

> 2^p -1?

>

Note N+1 == 3^n-2+1 == 3^n-1

and N-1 == 3^n-2-1 == 3*(3^(n-1)-1

So given enough factors of N+-1 the combined "classical tests" can be

used:

http://primes.utm.edu/prove/index.html

These have been implemented in PFGW:

http://groups.yahoo.com/group/primeform/

At the cutting edge, a less than 33.33 % factored percentage could

lead to a proof: "Konyagin-Pomerance" (KP) or "Coppersmith

Howgrave-Graham" (CHG).

If the number is sub-gigantic (<10,000 digits) it can be proven with

Marcel Martin's ECCP implementation, Primo:

http://www.ellipsa.net/

Wojciech Florek has some good pages covering 3^n-2:

http://perta.fizyka.amu.edu.pl/pnq/

> I tried for several weeks to find one and couldn't.

You aren't the first to try ;-)

>

Paul