How to Generate Twin Primes and Implement Basic Sorting in Java

Prime generation via recursive filtering

The algorithm builds a list of integers up to a given limit (e.g., 10,000) and then recursively removes any element that is divisible by the current prime candidate. After each pass the next element in the list becomes the new divisor, and the process repeats until the end of the list is reached, leaving only prime numbers.

static void get(List<Integer> list, int tt) {
    int num = list.get(tt);
    for (int i = tt + 1; i < list.size(); i++) {
        if (list.get(i) % num == 0) {
            list.remove(i--);
        }
    }
    if (list.size() > ++tt) {
        get(list, tt);
    }
}

Twin‑prime detection

After the sieve finishes, the program scans the resulting list of primes. Adjacent entries whose difference equals 2 constitute a twin‑prime pair and are printed.

List<Integer> list = new ArrayList<>();
for (int i = 2; i < 10000; i += 2) {
    list.add(i);
}
get(list, 0);
for (int i = 0; i < list.size() - 1; i++) {
    int a = list.get(i);
    int b = list.get(i + 1);
    if (b - a == 2) {
        System.out.println("Twin prime: " + a + "\t" + b);
    }
}

Sorting examples for practice

Two classic elementary sorting algorithms are provided as additional exercises: insertion sort (implemented as a stable in‑place sort) and bubble sort.

public static void insertionSort(int[] data) {
    for (int i = 0; i < data.length; i++) {
        for (int j = i; j > 0; j--) {
            if (data[j] < data[j - 1]) {
                int tmp = data[j];
                data[j] = data[j - 1];
                data[j - 1] = tmp;
            }
        }
    }
}

public static void bubbleSort(int[] data) {
    for (int i = 0; i < data.length; i++) {
        for (int j = 0; j < data.length - i - 1; j++) {
            if (data[j] > data[j + 1]) {
                int tmp = data[j];
                data[j] = data[j + 1];
                data[j + 1] = tmp;
            }
        }
    }
}