Theorem :
Let $k$ be positive integer such that : $k \in [1,\lfloor \sqrt p \rfloor ]$
$\binom{p}{k} \equiv 0 \pmod p$ for all $k$ iff $p$ is a prime number .
Test written in Maple :
Test is general , unconditional , deterministic but it runs in exponential time .
Can it be optimized to runs in polynomial time ?