Fermat prime

A Fermat prime is a prime number of the formFor $k\ge 1$, it is congruent to $1$ modulo $4$ and to $2$ modulo $3$.

For a Fermat prime $p=2^{2^k}+1$, the multiplicative group modulo $p$ has order $2^{2^k}$. Its $\phi (p-1)=(p-1)/2$ primitive roots are all quadratic nonresidues; since there are also $(p-1)/2$ nonresidues, the two sets coincide.