Task: Partition an integer x into n primes
C#: using System;
using System.Collections;
using System.Collections.Generic;
using static System.Linq.Enumerable;

public static class Rosetta
{
    static void Main()
    {
        foreach ((int x, int n) in new [] {
            (99809, 1),
            (18, 2),
            (19, 3),
            (20, 4),
            (2017, 24),
            (22699, 1),
            (22699, 2),
            (22699, 3),
            (22699, 4),
            (40355, 3)
        }) {
            Console.WriteLine(Partition(x, n));
        }
    }

    public static string Partition(int x, int n) {
        if (x < 1 || n < 1) throw new ArgumentOutOfRangeException("Parameters must be positive.");
        string header = $"{x} with {n} {(n == 1 ? "prime" : "primes")}: ";
        int[] primes = SievePrimes(x).ToArray();
        if (primes.Length < n) return header + "not enough primes";
        int[] solution = CombinationsOf(n, primes).FirstOrDefault(c => c.Sum() == x);
        return header + (solution == null ? "not possible" : string.Join("+", solution);
    }

    static IEnumerable<int> SievePrimes(int bound) {
        if (bound < 2) yield break;
        yield return 2;

        BitArray composite = new BitArray((bound - 1) / 2);
        int limit = ((int)(Math.Sqrt(bound)) - 1) / 2;
        for (int i = 0; i < limit; i++) {
            if (composite[i]) continue;
            int prime = 2 * i + 3;
            yield return prime;
            for (int j = (prime * prime - 2) / 2; j < composite.Count; j += prime) composite[j] = true;
        }
        for (int i = limit; i < composite.Count; i++) {
            if (!composite[i]) yield return 2 * i + 3;
        }
    }

    static IEnumerable<int[]> CombinationsOf(int count, int[] input) {
        T[] result = new T[count];
        foreach (int[] indices in Combinations(input.Length, count)) {
            for (int i = 0; i < count; i++) result[i] = input[indices[i]];
            yield return result;
        }
    }

    static IEnumerable<int[]> Combinations(int n, int k) {
        var result = new int[k];
        var stack = new Stack<int>();
        stack.Push(0);
        while (stack.Count > 0) {
            int index = stack.Count - 1;
            int value = stack.Pop();
            while (value < n) {
                result[index++] = value++;
                stack.Push(value);
                if (index == k) {
                    yield return result;
                    break;
                }
            }
        }
    }

}

Java: import java.util.Arrays;
import java.util.stream.IntStream;

public class PartitionInteger {
    private static final int[] primes = IntStream.concat(IntStream.of(2), IntStream.iterate(3, n -> n + 2))
        .filter(PartitionInteger::isPrime)
        .limit(50_000)
        .toArray();

    private static boolean isPrime(int n) {
        if (n < 2) return false;
        if (n % 2 == 0) return n == 2;
        if (n % 3 == 0) return n == 3;
        int d = 5;
        while (d * d <= n) {
            if (n % d == 0) return false;
            d += 2;
            if (n % d == 0) return false;
            d += 4;
        }
        return true;
    }

    private static boolean findCombo(int k, int x, int m, int n, int[] combo) {
        boolean foundCombo = false;
        if (k >= m) {
            if (Arrays.stream(combo).map(i -> primes[i]).sum() == x) {
                String s = m > 1 ? "s" : "";
                System.out.printf("Partitioned %5d with %2d prime%s: ", x, m, s);
                for (int i = 0; i < m; ++i) {
                    System.out.print(primes[combo[i]]);
                    if (i < m - 1) System.out.print('+');
                    else System.out.println();
                }
                foundCombo = true;
            }
        } else {
            for (int j = 0; j < n; ++j) {
                if (k == 0 || j > combo[k - 1]) {
                    combo[k] = j;
                    if (!foundCombo) {
                        foundCombo = findCombo(k + 1, x, m, n, combo);
                    }
                }
            }
        }
        return foundCombo;
    }

    private static void partition(int x, int m) {
        if (x < 2 || m < 1 || m >= x) {
            throw new IllegalArgumentException();
        }
        int[] filteredPrimes = Arrays.stream(primes).filter(it -> it <= x).toArray();
        int n = filteredPrimes.length;
        if (n < m) throw new IllegalArgumentException("Not enough primes");
        int[] combo = new int[m];
        boolean foundCombo = findCombo(0, x, m, n, combo);
        if (!foundCombo) {
            String s = m > 1 ? "s" : " ";
            System.out.printf("Partitioned %5d with %2d prime%s: (not possible)\n", x, m, s);
        }
    }

    public static void main(String[] args) {
        partition(99809, 1);
        partition(18, 2);
        partition(19, 3);
        partition(20, 4);
        partition(2017, 24);
        partition(22699, 1);
        partition(22699, 2);
        partition(22699, 3);
        partition(22699, 4);
        partition(40355, 3);
    }
}