Comment by pona-a

I meant fail in the sense that asking a lookup table of first 10,000 primes would pass any tests within this range perfectly, but when you ask it for the 1,001st prime, it would return an error. Mathematically an infinite lookup table of every prime is just a perfectly valid model of a factorization algorithm, unless you're interested in how one actually works, just as an infinite perceptron might be a valid model of any function.