diff --git a/runtime/stdlib/random_test.go b/runtime/stdlib/random_test.go
new file mode 100644
index 0000000000..56f42e88bc
--- /dev/null
+++ b/runtime/stdlib/random_test.go
@@ -0,0 +1,109 @@
+/*
+ * Cadence - The resource-oriented smart contract programming language
+ *
+ * Copyright Dapper Labs, Inc.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *   http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package stdlib
+
+import (
+	"crypto/rand"
+	"strconv"
+	"testing"
+
+	"github.com/onflow/crypto/random"
+	"github.com/stretchr/testify/require"
+
+	"github.com/onflow/cadence/runtime/interpreter"
+	"github.com/onflow/cadence/runtime/sema"
+)
+
+type testCryptRandomGenerator struct{}
+
+var _ RandomGenerator = testCryptRandomGenerator{}
+
+func (t testCryptRandomGenerator) ReadRandom(buffer []byte) error {
+	_, err := rand.Read(buffer)
+	return err
+}
+
+// TestRandomBasicUniformityWithModulo is a sanity statistical test
+// to make sure the random numbers less than modulo are uniform in [0,modulo-1].
+// The test requires the original random source (here `crypto/rand`) to be uniform.
+// The test uses the same small values for all types:
+// one is a power of 2 and the other is not.
+func TestRandomBasicUniformityWithModulo(t *testing.T) {
+
+	t.Parallel()
+
+	if testing.Short() {
+		// skipped because the test is slow
+		t.Skip()
+	}
+
+	testTypes := func(t *testing.T, testType func(*testing.T, sema.Type), allTypes bool) {
+		for _, ty := range sema.AllFixedSizeUnsignedIntegerTypes {
+			tyCopy := ty
+			t.Run(ty.String(), func(t *testing.T) {
+				t.Parallel()
+
+				testType(t, tyCopy)
+			})
+		}
+	}
+
+	// dummy interpreter, just use for ConvertAndBox
+	inter := newInterpreter(t, ``)
+
+	runStatisticsWithModulo := func(modulo int) func(*testing.T, sema.Type) {
+		return func(t *testing.T, ty sema.Type) {
+			// make sure modulo fits in 8 bits
+			require.Less(t, modulo, 1<<8)
+
+			f := func() (uint64, error) {
+
+				moduloValue := inter.ConvertAndBox(
+					interpreter.EmptyLocationRange,
+					interpreter.NewUnmeteredUIntValueFromUint64(uint64(modulo)),
+					sema.UIntType,
+					ty,
+				)
+
+				value := RevertibleRandom(
+					testCryptRandomGenerator{},
+					nil,
+					ty,
+					moduloValue,
+				)
+
+				return strconv.ParseUint(value.String(), 10, 8)
+			}
+
+			random.BasicDistributionTest(t, uint64(modulo), 1, f)
+		}
+	}
+
+	t.Run("power of 2 (that fits in 8 bits)", func(t *testing.T) {
+		t.Parallel()
+
+		testTypes(t, runStatisticsWithModulo(64), false)
+	})
+
+	t.Run("non-power of 2", func(t *testing.T) {
+		t.Parallel()
+
+		testTypes(t, runStatisticsWithModulo(71), false)
+	})
+}