Most primality tests aren't 100% accurate either (eg Miller Rabin), they just are "reasonably accurate" while being very fast to compute. You can use them in conjunction to improve your confidence in the result.
Yes, and we know they are inaccurate and we know that if you find a prime that way you can only use it to reject, not confirm so if you think that something is prime you need to check it.
But now imagine that instead of it being a valid reject 0.3% of the time it would also reject valid primes. Now it would be instantly useless because it fails the test for determinism.
Yes, and we know they are inaccurate and we know that if you find a prime that way you can only use it to reject, not confirm so if you think that something is prime you need to check it.
But now imagine that instead of it being a valid reject 0.3% of the time it would also reject valid primes. Now it would be instantly useless because it fails the test for determinism.