Primes of the form (3^n + 5^n)/2.

[Edwin Clark]

On Sun, 10 Sep 2006, Hugo Pfoertner wrote:

> zak seidov wrote:
> > 
> > Not appeared in OEIS:
> > 
> > %S A000001 17, 353, 198593
> > %N A000001 Primes of the form (3^n + 5^n)/2.
> > %C A000001 Corresponding n's are 2^1, 2^2, and 2^3.
> > What are next terms?
> > Cf. A074606 3^n + 5^n.
> > %A A000001 Zak Seidov, Aug 27 2006
> > 
> > My kind request to gurus:
> > What are next terms?
> > Thanks, Zak
> 
> If any more should exist, they are > (3^2500+5^2500)/2
> 
> Hugo
> 

Since x^n + y^n has x+y as a factor if n is odd, we can assume
that n is a power of 2. Maple shows that up to n = 2^15, there
are no more primes of the form (3^n + 5^n)/2. 

This raises the question:
Is it true that x^n + (x+2)^n is irreducible over Q for n a power
of 2? 

--Edwin