Quote:
Originally Posted by bur
Not really related to this specific question, but also a question about 2^n + 1:
Why aren't they researched in regard to being prime? It is basically a Proth number with k = 1. I just checked for n <= 200 and got primes only for n = 1, 2, 4, 8, 16  or F(0) to F(4).
Is this sequence similar to Fermat and there are no known primes for 2^n + 1 other than those I mentioned above? If so, is it proven?
Googling didn't yield any results surprisingly, but looking up formulas can be hard.

For 2^n+1 to be prime n must be a power of 2
https://mathworld.wolfram.com/FermatNumber.html has a proof of this.