diff --git a/PerfectNumbers.Core.Tests/MersenneNumberOrderGpuTesterTests.cs b/PerfectNumbers.Core.Tests/MersenneNumberOrderGpuTesterTests.cs
index 0751886..3af8b5b 100644
--- a/PerfectNumbers.Core.Tests/MersenneNumberOrderGpuTesterTests.cs
+++ b/PerfectNumbers.Core.Tests/MersenneNumberOrderGpuTesterTests.cs
@@ -1,4 +1,9 @@
+using System.Collections.Generic;
+using System.IO;
+using System.Linq;
+using System.Reflection;
 using FluentAssertions;
+using PerfectNumbers.Core;
 using PerfectNumbers.Core.Gpu;
 using Xunit;
 using UInt128 = System.UInt128;
@@ -28,6 +33,60 @@ public class MersenneNumberOrderGpuTesterTests
         RunCase(tester, 127UL, 1_000UL, expectedPrime: true);
     }
 
+    [Fact]
+    [Trait("Category", "Fast")]
+    public void Scan_order_gpu_handles_inaccurate_small_cycle_entries()
+    {
+        const ulong exponent = 23UL;
+        const ulong divisor = 47UL; // 47 | M_23
+
+        string tempPath = Path.GetTempFileName();
+        try
+        {
+            using (var writer = new BinaryWriter(File.Open(tempPath, FileMode.Create, FileAccess.Write, FileShare.Read)))
+            {
+                writer.Write(divisor);
+                writer.Write((ulong)uint.MaxValue);
+            }
+
+            var cycles = MersenneDivisorCycles.Shared;
+            var tableField = typeof(MersenneDivisorCycles).GetField("_table", BindingFlags.NonPublic | BindingFlags.Instance)!;
+            var smallCyclesField = typeof(MersenneDivisorCycles).GetField("_smallCycles", BindingFlags.NonPublic | BindingFlags.Instance)!;
+
+            var originalTable = ((List<(ulong Divisor, ulong Cycle)>)tableField.GetValue(cycles)!).Select(x => x).ToList();
+            var originalSmall = (uint[]?)smallCyclesField.GetValue(cycles);
+            uint[]? backupSmall = originalSmall is null ? null : (uint[])originalSmall.Clone();
+
+            cycles.LoadFrom(tempPath);
+            GpuContextPool.DisposeAll();
+
+            try
+            {
+                var tester = new MersenneNumberOrderGpuTester(GpuKernelType.Pow2Mod, useGpuOrder: false);
+
+                bool isPrime = true;
+                tester.Scan(
+                    exponent,
+                    (UInt128)exponent << 1,
+                    LastDigitIsSeven(exponent),
+                    (UInt128)10UL,
+                    ref isPrime);
+
+                isPrime.Should().BeFalse();
+            }
+            finally
+            {
+                tableField.SetValue(cycles, originalTable);
+                smallCyclesField.SetValue(cycles, backupSmall);
+                GpuContextPool.DisposeAll();
+            }
+        }
+        finally
+        {
+            File.Delete(tempPath);
+        }
+    }
+
     private static void RunCase(MersenneNumberOrderGpuTester tester, ulong exponent, ulong maxK, bool expectedPrime)
     {
         bool isPrime = true;
diff --git a/PerfectNumbers.Core.Tests/MersenneNumberResidueGpuTesterTests.cs b/PerfectNumbers.Core.Tests/MersenneNumberResidueGpuTesterTests.cs
index 8867345..a721d33 100644
--- a/PerfectNumbers.Core.Tests/MersenneNumberResidueGpuTesterTests.cs
+++ b/PerfectNumbers.Core.Tests/MersenneNumberResidueGpuTesterTests.cs
@@ -1,4 +1,8 @@
+using System.IO;
+using System.Linq;
+using System.Reflection;
 using FluentAssertions;
+using PerfectNumbers.Core;
 using PerfectNumbers.Core.Gpu;
 using Xunit;
 using UInt128 = System.UInt128;
@@ -25,6 +29,66 @@ public class MersenneNumberResidueGpuTesterTests
         RunCase(tester, 127UL, 1_001UL, expectedPrime: true);
     }
 
+    [Fact]
+    [Trait("Category", "Fast")]
+    public void Scan_residue_gpu_handles_inaccurate_small_cycle_entries()
+    {
+        const ulong exponent = 23UL;
+        const ulong divisor = 47UL; // 47 | M_23
+
+        string tempPath = Path.GetTempFileName();
+        try
+        {
+            using (var writer = new BinaryWriter(File.Open(tempPath, FileMode.Create, FileAccess.Write, FileShare.Read)))
+            {
+                writer.Write(divisor);
+                writer.Write((ulong)uint.MaxValue);
+            }
+
+            var cycles = MersenneDivisorCycles.Shared;
+            var tableField = typeof(MersenneDivisorCycles).GetField("_table", BindingFlags.NonPublic | BindingFlags.Instance)!;
+            var smallCyclesField = typeof(MersenneDivisorCycles).GetField("_smallCycles", BindingFlags.NonPublic | BindingFlags.Instance)!;
+
+            var originalTable = ((List<(ulong Divisor, ulong Cycle)>)tableField.GetValue(cycles)!).Select(x => x).ToList();
+            var originalSmall = (uint[]?)smallCyclesField.GetValue(cycles);
+            uint[]? backupSmall = originalSmall is null ? null : (uint[])originalSmall.Clone();
+
+            cycles.LoadFrom(tempPath);
+            GpuContextPool.DisposeAll();
+
+            try
+            {
+                var tester = new MersenneNumberResidueGpuTester(useGpuOrder: false);
+
+                bool isPrime = true;
+                bool exhausted = false;
+
+                tester.Scan(
+                    exponent,
+                    (UInt128)exponent << 1,
+                    lastIsSeven: true,
+                    perSetLimit: (UInt128)10UL,
+                    setCount: UInt128.One,
+                    overallLimit: (UInt128)10UL,
+                    ref isPrime,
+                    ref exhausted);
+
+                isPrime.Should().BeFalse();
+                exhausted.Should().BeTrue();
+            }
+            finally
+            {
+                tableField.SetValue(cycles, originalTable);
+                smallCyclesField.SetValue(cycles, backupSmall);
+                GpuContextPool.DisposeAll();
+            }
+        }
+        finally
+        {
+            File.Delete(tempPath);
+        }
+    }
+
     [Theory]
     [InlineData(false)]
     [InlineData(true)]
diff --git a/PerfectNumbers.Core.Tests/MersenneNumberResidueIntegrationTests.cs b/PerfectNumbers.Core.Tests/MersenneNumberResidueIntegrationTests.cs
index 903b04b..e6770b7 100644
--- a/PerfectNumbers.Core.Tests/MersenneNumberResidueIntegrationTests.cs
+++ b/PerfectNumbers.Core.Tests/MersenneNumberResidueIntegrationTests.cs
@@ -51,6 +51,38 @@ public class MersenneNumberResidueIntegrationTests
         }
     }
 
+    [Theory]
+    [InlineData(107UL)]
+    [InlineData(127UL)]
+    [Trait("Category", "Fast")]
+    public void Residue_gpu_mode_matches_cli_limits_for_known_primes(ulong exponent)
+    {
+        var tester = new MersenneNumberTester(
+            useIncremental: true,
+            useOrderCache: false,
+            kernelType: GpuKernelType.Pow2Mod,
+            useModuloWorkaround: false,
+            useOrder: false,
+            useGpuLucas: false,
+            useGpuScan: true,
+            useGpuOrder: true,
+            useResidue: true,
+            maxK: (UInt128)5_000_000UL,
+            residueDivisorSets: (UInt128)1_024UL);
+
+        try
+        {
+            bool isPrime = tester.IsMersennePrime(exponent, out bool divisorsExhausted);
+
+            isPrime.Should().BeTrue();
+            divisorsExhausted.Should().BeTrue();
+        }
+        finally
+        {
+            GpuContextPool.DisposeAll();
+        }
+    }
+
     [Theory]
     [MemberData(nameof(ResidueThreadCounts))]
     [Trait("Category", "Fast")]
diff --git a/PerfectNumbers.Core/Gpu/GpuKernelPool.cs b/PerfectNumbers.Core/Gpu/GpuKernelPool.cs
index 9082f4d..f73a69a 100644
--- a/PerfectNumbers.Core/Gpu/GpuKernelPool.cs
+++ b/PerfectNumbers.Core/Gpu/GpuKernelPool.cs
@@ -246,10 +246,14 @@ public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, Kerne
         if (q.High == 0UL && q.Low < (ulong)smallCycles.Length)
         {
             uint cyc = smallCycles[(int)q.Low];
-            if (cyc != 0U && (exponent % cyc) != 0UL)
+            if (cyc != 0U)
             {
-                orders[index] = 0UL;
-                return;
+                ulong cycle = cyc;
+                if (cycle <= exponent && (exponent % cycle) != 0UL)
+                {
+                    orders[index] = 0UL;
+                    return;
+                }
             }
         }
 
@@ -396,10 +400,14 @@ public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, Kerne
         if (q.High == 0UL && q.Low < (ulong)smallCycles.Length)
         {
             uint cyc = smallCycles[(int)q.Low];
-            if (cyc != 0U && (exponent % cyc) != 0UL)
+            if (cyc != 0U)
             {
-                orders[index] = 0UL;
-                return;
+                ulong cycle = cyc;
+                if (cycle <= exponent && (exponent % cycle) != 0UL)
+                {
+                    orders[index] = 0UL;
+                    return;
+                }
             }
         }
         if (GpuUInt128.Pow2Minus1Mod(exponent, q) != GpuUInt128.Zero)
@@ -524,9 +532,13 @@ public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, Kerne
         if (q.High == 0UL && q.Low < (ulong)smallCycles.Length)
         {
             uint cyc = smallCycles[(int)q.Low];
-            if (cyc != 0U && (exponent % (ulong)cyc) != 0UL)
+            if (cyc != 0U)
             {
-                return;
+                ulong cycle = cyc;
+                if (cycle <= exponent && (exponent % cycle) != 0UL)
+                {
+                    return;
+                }
             }
         }
         GpuUInt128 phi = q - GpuUInt128.One;
@@ -603,9 +615,13 @@ public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, Kerne
         if (q.High == 0UL && q.Low < (ulong)smallCycles.Length)
         {
             uint cyc = smallCycles[(int)q.Low];
-            if (cyc != 0U && (exponent % (ulong)cyc) != 0UL)
+            if (cyc != 0U)
             {
-                return;
+                ulong cycle = cyc;
+                if (cycle <= exponent && (exponent % cycle) != 0UL)
+                {
+                    return;
+                }
             }
         }
         if (GpuUInt128.Pow2Mod(exponent, q) != GpuUInt128.One)