Find prime numbers under N
This doesn't look like a Sieve of Eratosthenes.  This sure looks like trial division:


  while(numbersIterator.hasNext()){
      int number = numbersIterator.next();
      if(number % prime == 0){ //Remove all multiples of the number.
          numbersIterator.remove();
      }
  }



Unless I'm misunderstanding what your iterators are doing.  A simple SoE will have something that looks like:

for i from 2 to sqrt(n):          /* Loop from 2 to square root of max */
  if A[i]:                        /* If this location indicates prime, */
    for j from i*i to n step i:   /* then for each multiple of i,      */
      A[j] = false;               /* mark composite                    */


See the examples at RosettaCode or Wikipedia for example.  For comparison, RosettaCode's Trial Division task has a loop like your function.

So the immediate performance issue is that a sieve will be much faster than trial division.