import java.io.*;
import java.util.*;

public class Crab2Slower {
	private static final int LMAX = 100000;
	private static final Scanner cin = new Scanner(System.in);

	public static void main(String[] args) {
		boolean[] isPrime;
		{
			isPrime = new boolean[LMAX+1];

			Arrays.fill(isPrime, true);
			isPrime[0] = false;
			isPrime[1] = false;

			for(int i = 2; i <= LMAX; i++) {
				if(isPrime[i]) {
					for(int j = i + i; j <= LMAX; j += i) {
						isPrime[j] = false;
					}
				}
			}
		}

		for(int l; (l = cin.nextInt()) != 0; ) {
			int count = 0;

			for(int a = 1; a <= l; a++) {
				if(!isPrime[a]) continue;
				for(int b = a; b <= l; b++) {
					int c = l - a - b;
					if(b > c) break;
					if(!isPrime[b]) continue;
					if(!isPrime[c]) continue;
					if( a + b <= c) continue;
					if( b + c <= a) continue;
					if( c + a <= b) continue;
					count++;
				}
			}

			System.out.println(count);
		}
	}
}