The largest three primes it can show are

  3317044064679887385961783
  3317044064679887385961801
  3317044064679887385961813

So essentially it can test all 81-bit integers and some 82-bit integers for primality. It does so using the Miller-Rabin primality test with prime bases derived from https://oeis.org/A014233 (OEIS A014233). The algorithm is implemented in about 80 lines of plain JavaScript. If you view the source, look for the function isPrimeByMR.

The Miller-Rabin test is inherently probabilistic. It tests whether a number is a probable prime by checking whether certain number theoretic congruence relations hold for a given base a. The test can yield false positives, that is, a composite number may pass the test. But it cannot have false negatives, so a number that fails the test is definitely composite. The more bases for which the test holds, the more likely it is that the tested number is prime. It has been computationally verified that there are no false positives below 3317044064679887385961981 when tested with prime bases 2, 3, 5, ..., 41. So although the algorithm is probabilistic, it functions as a deterministic test for all numbers below this bound when tested with these 13 bases.

I use this algorithm here https://surenenfiajyan.github.io/prime-explorer/

64266330917908644872330635228106713310880186591609208114244758680898150367880703152525200743234420230

This would require 334 bits.

    n = 1000000 # must be even
    sieve = [True] * (n/2)
    for i in range(3,int(n**0.5)+1,2):
        if sieve[i/2]: sieve[i*i/2::i] = [False] * ((n-i*i-1)/(2*i)+1)
    …
    # x is prime if x%2 and sieve[x/2]

It makes the trade-offs much clearer than jumping straight to a complex sieve.