Lucas-Lehmer like test
- 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=
I tried for several weeks to find one and couldn't.
> 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
These have been implemented in PFGW:
At the cutting edge, a less than 33.33 % factored percentage could
lead to a proof: "Konyagin-Pomerance" (KP) or "Coppersmith
If the number is sub-gigantic (<10,000 digits) it can be proven with
Marcel Martin's ECCP implementation, Primo:
Wojciech Florek has some good pages covering 3^n-2:
> I tried for several weeks to find one and couldn't.You aren't the first to try ;-)