diff --git a/specs/phase0/beacon-chain.md b/specs/phase0/beacon-chain.md
index 536bba336..572f46246 100644
--- a/specs/phase0/beacon-chain.md
+++ b/specs/phase0/beacon-chain.md
@@ -178,7 +178,7 @@ The following values are (non-configurable) constants used throughout the specif
 
 | Name | Value |
 | - | - |
-| `MAX_UINT_64` | `uint64(2**64 - 1)` |
+| `UINT64_MAX` | `uint64(2**64 - 1)` |
 | `GENESIS_SLOT` | `Slot(0)` |
 | `GENESIS_EPOCH` | `Epoch(0)` |
 | `FAR_FUTURE_EPOCH` | `Epoch(2**64 - 1)` |
@@ -600,7 +600,7 @@ def integer_squareroot(n: uint64) -> uint64:
     """
     Return the largest integer ``x`` such that ``x**2 <= n``.
     """
-    if n == MAX_UINT_64:
+    if n == UINT64_MAX:
         return uint64(4294967295)
     x = n
     y = (x + 1) // 2
diff --git a/tests/core/pyspec/eth2spec/test/helpers/constants.py b/tests/core/pyspec/eth2spec/test/helpers/constants.py
index fc939ce09..a51201906 100644
--- a/tests/core/pyspec/eth2spec/test/helpers/constants.py
+++ b/tests/core/pyspec/eth2spec/test/helpers/constants.py
@@ -89,4 +89,4 @@ ALL_PRESETS = (MINIMAL, MAINNET)
 #
 # Number
 #
-MAX_UINT_64 = 2**64 - 1
+UINT64_MAX = 2**64 - 1
diff --git a/tests/core/pyspec/eth2spec/test/phase0/unittests/test_config_invariants.py b/tests/core/pyspec/eth2spec/test/phase0/unittests/test_config_invariants.py
index 6216ea2f0..c58f817f7 100644
--- a/tests/core/pyspec/eth2spec/test/phase0/unittests/test_config_invariants.py
+++ b/tests/core/pyspec/eth2spec/test/phase0/unittests/test_config_invariants.py
@@ -2,7 +2,7 @@ from eth2spec.test.context import (
     spec_state_test,
     with_all_phases,
 )
-from eth2spec.test.helpers.constants import MAX_UINT_64
+from eth2spec.test.helpers.constants import UINT64_MAX
 from eth2spec.test.helpers.forks import (
     is_post_altair, is_post_bellatrix,
 )
@@ -16,9 +16,9 @@ def check_bound(value, lower_bound, upper_bound):
 @with_all_phases
 @spec_state_test
 def test_validators(spec, state):
-    check_bound(spec.VALIDATOR_REGISTRY_LIMIT, 1, MAX_UINT_64)
-    check_bound(spec.MAX_COMMITTEES_PER_SLOT, 1, MAX_UINT_64)
-    check_bound(spec.TARGET_COMMITTEE_SIZE, 1, MAX_UINT_64)
+    check_bound(spec.VALIDATOR_REGISTRY_LIMIT, 1, UINT64_MAX)
+    check_bound(spec.MAX_COMMITTEES_PER_SLOT, 1, UINT64_MAX)
+    check_bound(spec.TARGET_COMMITTEE_SIZE, 1, UINT64_MAX)
 
     # Note: can be less if you assume stricters bounds on validator set based on total ETH supply
     maximum_validators_per_committee = (
@@ -30,24 +30,24 @@ def test_validators(spec, state):
     check_bound(spec.config.MIN_PER_EPOCH_CHURN_LIMIT, 1, spec.VALIDATOR_REGISTRY_LIMIT)
     check_bound(spec.config.CHURN_LIMIT_QUOTIENT, 1, spec.VALIDATOR_REGISTRY_LIMIT)
 
-    check_bound(spec.config.MIN_GENESIS_ACTIVE_VALIDATOR_COUNT, spec.TARGET_COMMITTEE_SIZE, MAX_UINT_64)
+    check_bound(spec.config.MIN_GENESIS_ACTIVE_VALIDATOR_COUNT, spec.TARGET_COMMITTEE_SIZE, UINT64_MAX)
 
 
 @with_all_phases
 @spec_state_test
 def test_balances(spec, state):
     assert spec.MAX_EFFECTIVE_BALANCE % spec.EFFECTIVE_BALANCE_INCREMENT == 0
-    check_bound(spec.MIN_DEPOSIT_AMOUNT, 1, MAX_UINT_64)
-    check_bound(spec.MAX_EFFECTIVE_BALANCE, spec.MIN_DEPOSIT_AMOUNT, MAX_UINT_64)
-    check_bound(spec.MAX_EFFECTIVE_BALANCE, spec.EFFECTIVE_BALANCE_INCREMENT, MAX_UINT_64)
+    check_bound(spec.MIN_DEPOSIT_AMOUNT, 1, UINT64_MAX)
+    check_bound(spec.MAX_EFFECTIVE_BALANCE, spec.MIN_DEPOSIT_AMOUNT, UINT64_MAX)
+    check_bound(spec.MAX_EFFECTIVE_BALANCE, spec.EFFECTIVE_BALANCE_INCREMENT, UINT64_MAX)
 
 
 @with_all_phases
 @spec_state_test
 def test_hysteresis_quotient(spec, state):
-    check_bound(spec.HYSTERESIS_QUOTIENT, 1, MAX_UINT_64)
+    check_bound(spec.HYSTERESIS_QUOTIENT, 1, UINT64_MAX)
     check_bound(spec.HYSTERESIS_DOWNWARD_MULTIPLIER, 1, spec.HYSTERESIS_QUOTIENT)
-    check_bound(spec.HYSTERESIS_UPWARD_MULTIPLIER, spec.HYSTERESIS_QUOTIENT, MAX_UINT_64)
+    check_bound(spec.HYSTERESIS_UPWARD_MULTIPLIER, spec.HYSTERESIS_QUOTIENT, UINT64_MAX)
 
 
 @with_all_phases
@@ -68,7 +68,7 @@ def test_time(spec, state):
     assert spec.SLOTS_PER_EPOCH <= spec.SLOTS_PER_HISTORICAL_ROOT
     assert spec.MIN_SEED_LOOKAHEAD < spec.MAX_SEED_LOOKAHEAD
     assert spec.SLOTS_PER_HISTORICAL_ROOT % spec.SLOTS_PER_EPOCH == 0
-    check_bound(spec.SLOTS_PER_HISTORICAL_ROOT, spec.SLOTS_PER_EPOCH, MAX_UINT_64)
+    check_bound(spec.SLOTS_PER_HISTORICAL_ROOT, spec.SLOTS_PER_EPOCH, UINT64_MAX)
     check_bound(spec.MIN_ATTESTATION_INCLUSION_DELAY, 1, spec.SLOTS_PER_EPOCH)