diff --git a/lib/prime.rb b/lib/prime.rb
index b2b55f1..27fe193 100644
--- a/lib/prime.rb
+++ b/lib/prime.rb
@@ -289,7 +289,16 @@ class Prime
     end
 
     # see +Enumerator+#with_index.
-    alias with_index each_with_index
+    def with_index(offset = 0)
+      return enum_for(:with_index) unless block_given?
+      # if offset == 0, use each_with_index, which is faster because of C implementation.
+      return each_with_index(&proc) if offset == 0
+
+      each do |prime|
+        yield prime, offset
+        offset += 1
+      end
+    end
 
     # see +Enumerator+#with_object.
     def with_object(obj)
diff --git a/test/test_prime.rb b/test/test_prime.rb
index 885406f..0cbe512 100644
--- a/test/test_prime.rb
+++ b/test/test_prime.rb
@@ -92,6 +92,17 @@ class TestPrime < Test::Unit::TestCase
     end
   end
 
+  def test_enumerator_with_index_with_offset
+    enum = Prime.each
+    last = 5-1
+    enum.with_index(5) do |p,i|
+      break if i >= 100+5
+      assert_equal last+1, i
+      assert_equal PRIMES[i-5], p
+      last = i
+    end
+  end
+
   def test_default_instance_does_not_have_compatibility_methods
     assert !Prime.instance.respond_to?(:succ)
     assert !Prime.instance.respond_to?(:next)