Miller had found a set of equations (expressed in terms of two numbers, n and x) that are always true if n is prime, regardless of what values you plug in for x. If they come out false even for a single value of x, then there’s no way n can be prime—in these cases, x is called a “witness” against primality. The problem, though, is false positives: even when n is not prime, the equations will still come out true some of the time.
