diff --git a/Lib/test/test_capi/test_long.py b/Lib/test/test_capi/test_long.py
index 7e8d571ae234d1f..903f86bdea15765 100644
--- a/Lib/test/test_capi/test_long.py
+++ b/Lib/test/test_capi/test_long.py
@@ -453,6 +453,18 @@ def test_long_aspid(self):
     def test_long_aspid_limited(self):
         self._test_long_aspid(_testlimitedcapi.pylong_aspid)
 
+    #@support.bigmemtest(2**29, memuse=2.7, dry_run=False)
+    def test_long_asnativebytes_large(self, size=2**29):
+        asnativebytes = _testcapi.pylong_asnativebytes
+        v = 1 << (size * 8)
+        buffer = bytearray(size * 16 // 15 + 10)
+        r = asnativebytes(v, buffer, 0, -1)
+        self.assertEqual(r, size + 1)
+        self.assertEqual(buffer.count(0), len(buffer))
+        r = asnativebytes(v, buffer, len(buffer), -1)
+        self.assertEqual(r, size + 1)
+        self.assertEqual(buffer.count(0), len(buffer) - 1)
+
     def test_long_asnativebytes(self):
         import math
         from _testcapi import (
diff --git a/Lib/test/test_long.py b/Lib/test/test_long.py
index 3b2e7c4e71d10d8..9faac8a8a5b5cbc 100644
--- a/Lib/test/test_long.py
+++ b/Lib/test/test_long.py
@@ -473,6 +473,13 @@ def test_float_conversion(self):
             self.check_float_conversion(value)
             self.check_float_conversion(-value)
 
+    @support.requires_IEEE_754
+    #@support.bigmemtest(2**29, memuse=1.6, dry_run=False)
+    def test_float_conversion_large(self, size=2**29):
+        bits = size * 8
+        v = 1 << bits
+        self.assertRaises(OverflowError, float, v)
+
     def test_float_overflow(self):
         for x in -2.0, -1.0, 0.0, 1.0, 2.0:
             self.assertEqual(float(int(x)), x)
@@ -614,6 +621,57 @@ def __lt__(self, other):
                     eq(x > y, Rcmp > 0)
                     eq(x >= y, Rcmp >= 0)
 
+    @support.requires_IEEE_754
+    #@support.bigmemtest(2**29, memuse=3.2, dry_run=False)
+    def test_mixed_compares_large_integer(self, size=2**29):
+        bits = size * 8
+        v = 1 << bits
+        f = sys.float_info.max
+        self.assertIs(f == v, False)
+        self.assertIs(f != v, True)
+        self.assertIs(f < v, True)
+        self.assertIs(f <= v, True)
+        self.assertIs(f > v, False)
+        self.assertIs(f >= v, False)
+        f = float('inf')
+        self.assertIs(f == v, False)
+        self.assertIs(f != v, True)
+        self.assertIs(f < v, False)
+        self.assertIs(f <= v, False)
+        self.assertIs(f > v, True)
+        self.assertIs(f >= v, True)
+        f = float('nan')
+        self.assertIs(f == v, False)
+        self.assertIs(f != v, True)
+        self.assertIs(f < v, False)
+        self.assertIs(f <= v, False)
+        self.assertIs(f > v, False)
+        self.assertIs(f >= v, False)
+
+        del v
+        v = (-1) << bits
+        f = -sys.float_info.max
+        self.assertIs(f == v, False)
+        self.assertIs(f != v, True)
+        self.assertIs(f < v, False)
+        self.assertIs(f <= v, False)
+        self.assertIs(f > v, True)
+        self.assertIs(f >= v, True)
+        f = float('-inf')
+        self.assertIs(f == v, False)
+        self.assertIs(f != v, True)
+        self.assertIs(f < v, True)
+        self.assertIs(f <= v, True)
+        self.assertIs(f > v, False)
+        self.assertIs(f >= v, False)
+        f = float('nan')
+        self.assertIs(f == v, False)
+        self.assertIs(f != v, True)
+        self.assertIs(f < v, False)
+        self.assertIs(f <= v, False)
+        self.assertIs(f > v, False)
+        self.assertIs(f >= v, False)
+
     def test__format__(self):
         self.assertEqual(format(123456789, 'd'), '123456789')
         self.assertEqual(format(123456789, 'd'), '123456789')
diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index b68c442013c09f0..9a36875aa1e9d10 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -1120,6 +1120,14 @@ def __index__(self):
                 with self.assertRaises(TypeError):
                     math.isqrt(value)
 
+    #@support.bigmemtest(2**29, memuse=7, dry_run=False)
+    def test_isqrt_large(self, size=2**29):
+        bits = size * 8
+        v = 1 << bits
+        w = math.isqrt(v)
+        self.assertEqual(w.bit_length(), bits // 2 + 1)
+        self.assertEqual(w.bit_count(), 1)
+
     def test_lcm(self):
         lcm = math.lcm
         self.assertEqual(lcm(0, 0), 0)
@@ -1261,6 +1269,14 @@ def testLog10(self):
         self.assertEqual(math.log(INF), INF)
         self.assertTrue(math.isnan(math.log10(NAN)))
 
+    #@support.bigmemtest(2**29, memuse=1.6, dry_run=False)
+    def test_log_large_integer(self, size=2**29):
+        bits = size * 8
+        v = 1 << bits
+        self.assertAlmostEqual(math.log2(v), bits)
+        self.assertAlmostEqual(math.log(v), bits * 0.6931471805599453)
+        self.assertAlmostEqual(math.log10(v), bits * 0.3010299956639812)
+
     def testSumProd(self):
         sumprod = math.sumprod
         Decimal = decimal.Decimal