diff --git a/bayes_opt/parameter.py b/bayes_opt/parameter.py
index 2eaa7a44..bbb0a4e5 100644
--- a/bayes_opt/parameter.py
+++ b/bayes_opt/parameter.py
@@ -278,7 +278,9 @@ def random_sample(
             The samples.
         """
         random_state = ensure_rng(random_state)
-        return random_state.randint(self.bounds[0], self.bounds[1] + 1, n_samples).astype(float)
+        return random_state.randint(self.bounds[0], self.bounds[1] + 1, n_samples, dtype=np.int64).astype(
+            float
+        )
 
     def to_float(self, value: int | float) -> float:
         """Convert a parameter value to a float.
diff --git a/tests/test_parameter.py b/tests/test_parameter.py
index 5e7b6eed..44c0bc66 100644
--- a/tests/test_parameter.py
+++ b/tests/test_parameter.py
@@ -87,6 +87,20 @@ def target_func(**kwargs):
     assert p1.kernel_transform(np.array([1.3, 3.6, 7.2])) == pytest.approx(np.array([1, 4, 7]))
 
 
+@pytest.mark.parametrize("bounds", [(3_000_000_000, 3_000_000_010), (-3_000_000_010, -3_000_000_000), (0, 5)])
+def test_int_random_sample_large_bounds(bounds):
+    parameter = IntParameter("x", bounds)
+    samples = parameter.random_sample(100, random_state=np.random.RandomState(42))
+    repeated = parameter.random_sample(100, random_state=np.random.RandomState(42))
+    assert samples.dtype == np.dtype(float)
+    np.testing.assert_array_equal(samples, repeated)
+    assert np.all(samples >= bounds[0])
+    assert np.all(samples <= bounds[1])
+    assert np.all(samples == np.floor(samples))
+    assert bounds[0] in samples
+    assert bounds[1] in samples
+
+
 def test_categorical_kernel_transform_preserves_batch_rows():
     parameter = CategoricalParameter("x", ["a", "b", "c"])
     values = np.array([[0.2, 0.8, 0.1], [0.9, 0.1, 0.2], [0.1, 0.2, 0.7], [0.2, 0.8, 0.1]])