Let 
be an odd integer, and
assume there exists a Lucas sequence 
with associated Sylvester
cyclotomic numbers 
such that there is an 
(with 
and 
relatively prime) for
which 
divides 
. Then 
is a prime unless it has one
of the following two forms:
1. 
, with 
prime and 
, or
2. 
, with 
and 
prime.
