
COMMENTS

Corresponding n are 2^1, 2^2, 2^3. What are the following terms? Cf. A074606 3^n + 5^n.
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?  W. Edwin Clark, Sep 10 2006
Next term, if it exists, is > (3^2500+5^2500)/2.  Hugo Pfoertner, Sep 10 2006
No more terms <= (3^(2^17)+5^(2^17))/2=(3^131072+5^131072)/2. Hence the next term, if it exists, is greater than 10^91616 (so is too large to include).  Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 31 2007


PROG

(PARI) for(n=1, 17, m=(3^(2^n)+5^(2^n))/2; if(isprime(m), print1(m", "))) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 31 2007
