Prime Number Generator Logic

Question

I am supposed to make a class PrimeNumberGenerator which has a method nextPrime that will print out all prime numbers up to a number the user input

Answer 1

I wrote this function which lists the first n prime numbers:

static void primes(int n) {
    int[] prime = new int[n];
    prime[0] = 2;
    int pp = 0;

    int i = 2;
    while(pp < n - 1) {
        int g = 1;
        for(int p = 0; p <= pp; p++) {
            if(i % prime[p] == 0) {
                g = prime[p];
                break;
            }
        }
        if(g == 1) {
            pp += 1;
            prime[pp] = i;
        }
        i += 1;
    }
    
    for(int z = 0; z < n; z++) {
        System.out.println(prime[z]);
    }
}

It also should be relatively fast because it checks the lowest amount of divsors necessary. (i think)