In C. McMullen's [Uniformly Diophantine numbers in a fixed real quadratic field](http://www.math.harvard.edu/~ctm/papers/home/text/papers/cf/cf.pdf) 
generalized Fibonacci sequence are defined as follows:


$f\_0=0,f\_1=1,f\_m=tf\_{m-1}-nf\_{m-2}$ where some fixed $t\in \mathbb Z$ and $n$ is $+1$ or $-1$ and $t^2-4n>0$.
For example, for $t=1,n=-1$ we get the usual Fibonacci sequence.


My question: Does there exist $t,n$ such that the resulting Fibonacci sequence has infinitely primes in it?
I think that it is conjectured to hold for the usual Fibonacci sequence.
A weaker assertion: Does there exist $t,n$ such that the resulting Fibonacci has infinitely many elements with a large prime divisor, e.g., infinitely many $m$'s such that $p\_m|f\_m$, $p\_m$ prime and $\frac{p\_m}{f\_m}>C$ for some C>0?


A related paper (which does not contain any answer to the above questions) is 
(By Y. Bugeaud F. Luca, M. Mignotte et S. Siksek) [On Fibonacci numbers with few prime divisors](http://www-irma.u-strasbg.fr/~bugeaud/travaux/OmegaDef.pdf). 


I'll be happy to know about any reference that deal with these generalized sequences.



Primes in generalized fibonacci sequences
These are Lucas Sequences (<http://en.wikipedia.org/wiki/Lucas_sequence>), of which the Fibonacci Sequence is a specific case, and they share with the usual Fibonacci Sequence the following characteristics which, unless there are further reasons preventing what I'm about to say from being true, would allow the same sort of heuristic analysis for primes in these sequences as that appearing for Fibonacci Primes in Section 5 of the paper by Bugeaud, Luca, Mignotte and Siksek you mentioned.


a)Binet-type formula, which, apart from special cases like $t=2, n=1$ mentioned by Robert Israel, give exponential growth.


b)According to Wikipedia, the $m$-th term divides the $mk$-th term, so only those with prime indices have a chance to be prime.


