What are primes in the form of $2^n+1$ called?

Question

What are primes in the form of $2^n+1$ called? I know that those of form $2^n-1$ are Mersenne primes, but I'm not sure about the other ones.

Answer 1

For $n\ge 1$, they are called the Fermat primes.

It turns out that in order for $2^n+1$ to be prime, where $n$ is a positive integer, $n$ has to be of the shape $n=2^k$. So the Fermat primes are usually described as being the primes of the shape $2^{(2^k)}+1$.

There are only $5$ Fermat primes known.