Consider integers of the form $(3^n + 1)/4$.
I was able to find some primes.
examples : $n = 13,23,43$ all give primes.
It seems similar to Fermat primes or Mersenne primes.
So how many of $(3^n + 1)/4$ are prime ?
Are there infinitely many ? Or only finite ?
Since this question may be to hard ;
What is the largest known prime of the form $(3^n + 1)/4$ ?
Any sources ?