eratosthenes.js

const nthPrime = (n) => {
    
    // conservative upper bound for nth prime is n log(n log n)
    // works for all n >= 6
    const max = Math.floor(n * Math.log(n * Math.log(n)));

    // allocate sieve
    const sieve = new Uint8Array(Math.ceil(max / 8)).fill(0);

    // we need to keep track of how many primes we've encountered so far because the upper bound probably includes more than `n` primes
    let maxPrime, nth = 0;
    for(let i = 2; i < max; i++) {
    
        // if i is not marked...
        if((sieve[Math.floor(i / 8)] & (1 << i % 8)) == 0) {

            maxPrime = i;
            nth++;

            if(nth == n) return maxPrime;

            // mark all
            for(let j = i; j < max; j += i) {
                sieve[Math.floor(j / 8)] |= (1 << (j % 8));
            }

        }

    }

    return maxPrime;

};