Miller Rabin Primality test accuracy

Question

I know the Miller–Rabin primality test is probabilistic. However I want to use it for a programming task that leaves no room for error.

Can we assume that it is corr

Answer 1

In each iteration of Miller-Rabin you need to choose a random number. If you are unlucky this random number doesn't reveal certain composites. A small example of this is that 2^341 mod 341 = 2, passing the test

But the test guarantees that it only lets a composite pass with probability <1/4. So if you run the test 64 times with different random values, the probability drops below 2^(-128) which is enough in practice.

You should take a look at the Baillie–PSW primality test. While it may have false positives, there are no known examples for this and according to wikipedia has been verified that no composite number below 2^64 passes the test. So it should fit your requirements.