Looking for UUID collisions in Java

UUIDTest.java

import java.util.HashSet;
import java.util.LinkedList;
import java.util.UUID;

public class UUIDTest {

    public static void main(String[] args) throws InterruptedException {
        HashSet<UUID> set = new HashSet<UUID>(1000);
        LinkedList<Thread> threads = new LinkedList<Thread>();
        for(int i=0; i<128; ++i) {
            Thread t = new UUIDGenThread(set, 100000);
            t.start();
            threads.push(t);
        }
        for(Thread t: threads) t.join();

        System.out.println("Set size: " + set.size());

    }

    static class UUIDGenThread extends Thread {

        private HashSet<UUID> set;
        private int numUUIDS;

        public UUIDGenThread(HashSet<UUID> set, int numUUIDS) {
            this.set = set;
            this.numUUIDS = numUUIDS;
        }

        public void run() {
            for(int i=0; i<numUUIDS; ++i) {
                synchronized (set) {
                    UUID uuid = UUID.randomUUID();
                    if(set.contains(uuid)) System.out.println("Collision: " + uuid);
                    else set.add(uuid);
                }
            }
        }

    }

}