Task: Strange unique prime triplets
C#: using System; using System.Collections.Generic; using static System.Console; using System.Linq; using DT = System.DateTime;

class Program { static void Main(string[] args) { string s;
  foreach (int lmt in new int[]{ 90, 300, 3000, 30000, 111000 }) {
    var pr = PG.Primes(lmt).Skip(1).ToList(); DT st = DT.Now;
    int d, f = 0; var r = new List<string>();
    int i = -1, m, h = (m = lmt / 3), j, k, pra, prab;
    while (i < 0) i = pr.IndexOf(h--); k = (j = i - 1) - 1;
    for (int a = 0; a <= k; a++) { pra = pr[a];
    for (int b = a + 1; b <= j; b++) { prab = pra + pr[b]; 
    for (int c = b + 1; c <= i; c++) {
      if (PG.flags[d = prab + pr[c]]) continue; f++;
      if (lmt < 100) r.Add(string.Format("{3,5} = {0,2} + {1,2} + {2,2}", pra, pr[b], pr[c], d)); } } }
    s = "s.u.p.t.s under "; r.Sort(); if (r.Count > 0) WriteLine("{0}{1}:\n{2}", s, m, string.Join("\n", r));
    if (lmt > 100) WriteLine("Count of {0}{1,6:n0}: {2,13:n0}  {3} sec", s, m, f, (DT.Now - st).ToString().Substring(6)); } } }

class PG { public static bool[] flags;
  public static IEnumerable<int> Primes(int lim) {
  flags = new bool[lim + 1]; int j = 2;
  for (int d = 3, sq = 4; sq <= lim; j++, sq += d += 2)
    if (!flags[j]) { yield return j;
      for (int k = sq; k <= lim; k += j) flags[k] = true; }
  for (; j <= lim; j++) if (!flags[j]) yield return j; } }

Java: import java.util.*;

public class StrangeUniquePrimeTriplets {
    public static void main(String[] args) {
        strangeUniquePrimeTriplets(30, true);
        strangeUniquePrimeTriplets(1000, false);
    }

    private static void strangeUniquePrimeTriplets(int limit, boolean verbose) {
        boolean[] sieve = primeSieve(limit * 3);
        List<Integer> primeList = new ArrayList<>();
        for (int p = 3; p < limit; p += 2) {
            if (sieve[p])
                primeList.add(p);
        }
        int n = primeList.size();
        
        int[] primes = new int[n];
        for (int i = 0; i < n; ++i)
            primes[i] = primeList.get(i);
        int count = 0;
        if (verbose)
            System.out.printf("Strange unique prime triplets < %d:\n", limit);
        for (int i = 0; i + 2 < n; ++i) {
            for (int j = i + 1; j + 1 < n; ++j) {
                int s = primes[i] + primes[j];
                for (int k = j + 1; k < n; ++k) {
                    int sum = s + primes[k];
                    if (sieve[sum]) {
                        ++count;
                        if (verbose)
                            System.out.printf("%2d + %2d + %2d = %2d\n", primes[i], primes[j], primes[k], sum);
                    }
                }
            }
        }
        System.out.printf("\nCount of strange unique prime triplets < %d is %d.\n", limit, count);
    }

    private static boolean[] primeSieve(int limit) {
        boolean[] sieve = new boolean[limit];
        Arrays.fill(sieve, true);
        if (limit > 0)
            sieve[0] = false;
        if (limit > 1)
            sieve[1] = false;
        for (int i = 4; i < limit; i += 2)
            sieve[i] = false;
        for (int p = 3; ; p += 2) {
            int q = p * p;
            if (q >= limit)
                break;
            if (sieve[p]) {
                int inc = 2 * p;
                for (; q < limit; q += inc)
                    sieve[q] = false;
            }
        }
        return sieve;
    }
}