“very prime has a succinct certificate”
\begin{equation} \text{PRIMES} : \left\{A \mid A\text{ is prime}\right\} \end{equation}
The certificate?
\begin{equation} A \text{ prime} \Leftrightarrow \exists 1 < b < A : B, B^{2}, \dots, B^{A*2} \not \cong \ \text{mod}\ A \end{equation}
So \text{PRIMES} \in \text{NP} But actually PRIMES is in P