Quote:
Originally Posted by kijinSeija
Thanks for your reply :)
Unfortunately, I'm not a mathematician so I think it could be impossible for me to prove it. I try to understand the proof of the LucasLehmer test and trying to transpose it with Wagstaff primes but I don't understand completly the LucasLehmer test. So trying to find a proof for Wagstaff primes is not possible for me I guess.

Wagstaff numbers are pretty special cyclotomic numbers, these are polcyclo(2*p,2)=(2^p+1)/3.
There is no known fast tests (at speed of LL test), though there could be! Note that here for example polcyclo(p,2)=2^p1 and we have the LL test for these.
This is a same/similar problem to find a test for repunits, (10^p1)/9 because those are polcyclo(p,10).