FKS hashing lemma states.
Given a set of $n-$bit numbers $\{x_1,x_2,\dots,x_k\}$ there exist a prime $p$ of $O(\log n + \log k)$-bit such that $x_i$ mod $p \neq $ $x_j$ mod $p$ if $x_i \neq x_j$.
This follows from prime number theorem. But finding such a prime takes a lot of time. Are there more efficient hashing schemes which achieve the similar results?