At that time, no practical deterministic algorithm for primality was known.

Most of the practical algorithms have one fundamental problem: there is no way to prove that they really are secure.

Several problems seem to be intractable (no practical algorithm).

Computational learning theory has led to several practical algorithms.

For examples of practical super-recursive algorithms, see the book of Burgin.

Neither of the methods mentioned previously leads to practical algorithms to calculate the Mertens function.

A running time of .00001 seconds is reasonable, and that's why this is called a practical algorithm.

This is a well-studied problem in computer science for which many practical algorithms have emerged, many taking advantage of novel data structures.

Therefore, whether a practical God's algorithm for this problem exists remains unknown, but appears unlikely.

No practical algorithms for computing the minimum core are known.