Java -- Prime number algorithm returns 16

Question

I want this Java program to stream 10001 prime numbers, but it inexplicably decides to label 16 as a prime number.

The algorithm here is just keeping a running count of prime numbers, and checking each new number to see if it is divisible by any of the primes less than it. If it isn't, then it is added to the array primes[ ], the number is displayed on the console, and the process continues, until primes[ ] is full.

public static void main(String[] args){
    int[] primes = new int[10001];
    int primeCount = 1;
    int testNumber = 3;
    primes[0] = 2;
    while(primeCount < 10001){
        for (int i = 0; i < primeCount; i++){
            if (testNumber % primes[i] == 0){
                i = 0;
                testNumber++;
            }
        }
        primes[primeCount] = testNumber;
        System.out.println(testNumber);
        primeCount++;
        testNumber++;

    }
}

Console readout:

   
3
5
7
11
13
16
17
19
.
.
.

Everything else looks to be in order except for the 16... any ideas?

Answer 1

You should set i = -1 instead of i = 0 since you are immediately increasing the value of i after setting it to zero.

I recommend you to fresh up your mind with how for loop works.

Answer 2

For software programming perspective you should not use a for loop inside that while loop. You should loop until if you see that it is not a prime number or you check all of possibilities and consider that it is a prime cos of you could not find any divider. So you should have a while loop inside the bigger while. I mean:

public static void main(String[] args) {
    int[] primes = new int[10001];
    int primeCount = 1;
    int testNumber = 3;
    primes[0] = 2;
    while (primeCount < 10001) {
        boolean isPrime = true;
        int i = 0;
        while (isPrime && i < primeCount) {
            if (testNumber % primes[i] == 0) {
                i = 0;
                testNumber++;
                isPrime = false;
            } else {
                i++;
            }
        }
        if (isPrime) {
            primes[primeCount] = testNumber;
            System.out.println(testNumber);
            primeCount++;
            testNumber++;
        }

    }
}