diff --git a/Lib/test/test_random.py b/Lib/test/test_random.py
index 96f6cc86219a5d..22b097b974c640 100644
--- a/Lib/test/test_random.py
+++ b/Lib/test/test_random.py
@@ -392,6 +392,8 @@ def test_getrandbits(self):
         self.assertRaises(TypeError, self.gen.getrandbits)
         self.assertRaises(TypeError, self.gen.getrandbits, 1, 2)
         self.assertRaises(ValueError, self.gen.getrandbits, -1)
+        self.assertRaises(OverflowError, self.gen.getrandbits, 1<<1000)
+        self.assertRaises(ValueError, self.gen.getrandbits, -1<<1000)
         self.assertRaises(TypeError, self.gen.getrandbits, 10.1)
 
     def test_pickling(self):
@@ -435,6 +437,8 @@ def test_randbytes(self):
         self.assertRaises(TypeError, self.gen.randbytes)
         self.assertRaises(TypeError, self.gen.randbytes, 1, 2)
         self.assertRaises(ValueError, self.gen.randbytes, -1)
+        self.assertRaises(OverflowError, self.gen.randbytes, 1<<1000)
+        self.assertRaises((ValueError, OverflowError), self.gen.randbytes, -1<<1000)
         self.assertRaises(TypeError, self.gen.randbytes, 1.0)
 
     def test_mu_sigma_default_args(self):
@@ -806,6 +810,22 @@ def test_getrandbits(self):
         self.assertEqual(self.gen.getrandbits(100),
                          97904845777343510404718956115)
 
+    def test_getrandbits_2G_bits(self):
+        size = 2**31
+        self.gen.seed(1234567)
+        x = self.gen.getrandbits(size)
+        self.assertEqual(x.bit_length(), size)
+        self.assertEqual(x & (2**100-1), 890186470919986886340158459475)
+        self.assertEqual(x >> (size-100), 1226514312032729439655761284440)
+
+    @support.bigmemtest(size=2**32, memuse=1/8+2/15, dry_run=False)
+    def test_getrandbits_4G_bits(self, size):
+        self.gen.seed(1234568)
+        x = self.gen.getrandbits(size)
+        self.assertEqual(x.bit_length(), size)
+        self.assertEqual(x & (2**100-1), 287241425661104632871036099814)
+        self.assertEqual(x >> (size-100), 739728759900339699429794460738)
+
     def test_randrange_uses_getrandbits(self):
         # Verify use of getrandbits by randrange
         # Use same seed as in the cross-platform repeatability test
@@ -962,6 +982,14 @@ def test_randbytes_getrandbits(self):
             self.assertEqual(self.gen.randbytes(n),
                              gen2.getrandbits(n * 8).to_bytes(n, 'little'))
 
+    @support.bigmemtest(size=2**29, memuse=1+16/15, dry_run=False)
+    def test_randbytes_256M(self, size):
+        self.gen.seed(2849427419)
+        x = self.gen.randbytes(size)
+        self.assertEqual(len(x), size)
+        self.assertEqual(x[:12].hex(), 'f6fd9ae63855ab91ea238b4f')
+        self.assertEqual(x[-12:].hex(), '0e7af69a84ee99bf4a11becc')
+
     def test_sample_counts_equivalence(self):
         # Test the documented strong equivalence to a sample with repeated elements.
         # We run this test on random.Random() which makes deterministic selections
diff --git a/Misc/NEWS.d/next/Library/2025-05-08-13-43-19.gh-issue-133489.9eGS1Z.rst b/Misc/NEWS.d/next/Library/2025-05-08-13-43-19.gh-issue-133489.9eGS1Z.rst
new file mode 100644
index 00000000000000..0c07beb76938f0
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2025-05-08-13-43-19.gh-issue-133489.9eGS1Z.rst
@@ -0,0 +1,2 @@
+:func:`random.getrandbits` can now generate more that 2\ :sup:`31` bits.
+:func:`random.randbytes` can now generate more that 256 MiB.
diff --git a/Modules/_randommodule.c b/Modules/_randommodule.c
index 140640ae8fbf3a..8fb040fb6c5b35 100644
--- a/Modules/_randommodule.c
+++ b/Modules/_randommodule.c
@@ -495,34 +495,32 @@ _random_Random_setstate_impl(RandomObject *self, PyObject *state)
 _random.Random.getrandbits
 
   self: self(type="RandomObject *")
-  k: int
+  k: unsigned_long_long(bitwise=False)
   /
 
 getrandbits(k) -> x.  Generates an int with k random bits.
 [clinic start generated code]*/
 
 static PyObject *
-_random_Random_getrandbits_impl(RandomObject *self, int k)
-/*[clinic end generated code: output=b402f82a2158887f input=87603cd60f79f730]*/
+_random_Random_getrandbits_impl(RandomObject *self, unsigned long long k)
+/*[clinic end generated code: output=25a604fab95885d4 input=88e51091eea2f042]*/
 {
-    int i, words;
+    Py_ssize_t i, words;
     uint32_t r;
     uint32_t *wordarray;
     PyObject *result;
 
-    if (k < 0) {
-        PyErr_SetString(PyExc_ValueError,
-                        "number of bits must be non-negative");
-        return NULL;
-    }
-
     if (k == 0)
         return PyLong_FromLong(0);
 
     if (k <= 32)  /* Fast path */
         return PyLong_FromUnsignedLong(genrand_uint32(self) >> (32 - k));
 
-    words = (k - 1) / 32 + 1;
+    if ((k - 1u) / 32u + 1u > PY_SSIZE_T_MAX / 4u) {
+        PyErr_NoMemory();
+        return NULL;
+    }
+    words = (k - 1u) / 32u + 1u;
     wordarray = (uint32_t *)PyMem_Malloc(words * 4);
     if (wordarray == NULL) {
         PyErr_NoMemory();
diff --git a/Modules/clinic/_randommodule.c.h b/Modules/clinic/_randommodule.c.h
index 6193acac67e7ac..12c845d4c44d00 100644
--- a/Modules/clinic/_randommodule.c.h
+++ b/Modules/clinic/_randommodule.c.h
@@ -3,6 +3,7 @@ preserve
 [clinic start generated code]*/
 
 #include "pycore_critical_section.h"// Py_BEGIN_CRITICAL_SECTION()
+#include "pycore_long.h"          // _PyLong_UnsignedLongLong_Converter()
 #include "pycore_modsupport.h"    // _PyArg_CheckPositional()
 
 PyDoc_STRVAR(_random_Random_random__doc__,
@@ -124,16 +125,15 @@ PyDoc_STRVAR(_random_Random_getrandbits__doc__,
     {"getrandbits", (PyCFunction)_random_Random_getrandbits, METH_O, _random_Random_getrandbits__doc__},
 
 static PyObject *
-_random_Random_getrandbits_impl(RandomObject *self, int k);
+_random_Random_getrandbits_impl(RandomObject *self, unsigned long long k);
 
 static PyObject *
 _random_Random_getrandbits(RandomObject *self, PyObject *arg)
 {
     PyObject *return_value = NULL;
-    int k;
+    unsigned long long k;
 
-    k = PyLong_AsInt(arg);
-    if (k == -1 && PyErr_Occurred()) {
+    if (!_PyLong_UnsignedLongLong_Converter(arg, &k)) {
         goto exit;
     }
     Py_BEGIN_CRITICAL_SECTION(self);
@@ -143,4 +143,4 @@ _random_Random_getrandbits(RandomObject *self, PyObject *arg)
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=bf49ece1d341b1b6 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=e9a5c68295678cff input=a9049054013a1b77]*/
diff --git a/Objects/longobject.c b/Objects/longobject.c
index 03d618aeedcf0a..be5cbf0872b446 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -874,16 +874,9 @@ _PyLong_FromByteArray(const unsigned char* bytes, size_t n,
             ++numsignificantbytes;
     }
 
-    /* How many Python int digits do we need?  We have
-       8*numsignificantbytes bits, and each Python int digit has
-       PyLong_SHIFT bits, so it's the ceiling of the quotient. */
-    /* catch overflow before it happens */
-    if (numsignificantbytes > (PY_SSIZE_T_MAX - PyLong_SHIFT) / 8) {
-        PyErr_SetString(PyExc_OverflowError,
-                        "byte array too long to convert to int");
-        return NULL;
-    }
-    ndigits = (numsignificantbytes * 8 + PyLong_SHIFT - 1) / PyLong_SHIFT;
+    /* avoid integer overflow */
+    ndigits = numsignificantbytes / PyLong_SHIFT * 8
+        + (numsignificantbytes % PyLong_SHIFT * 8 + PyLong_SHIFT - 1) / PyLong_SHIFT;
     v = _PyLong_New(ndigits);
     if (v == NULL)
         return NULL;