From f49963c4f69475dcbf8bc2b5427c7cb737ff84d8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Marek=20Lema=C5=84czyk?= <marek@lemanczyk.eu>
Date: Wed, 29 Oct 2025 01:43:12 +0100
Subject: [PATCH] Restore Math.Sqrt heuristic bound

---
 .../HeuristicCombinedPrimeTester.cs           | 34 +++++++------------
 PerfectNumbers.Core/HeuristicPrimeTester.cs   | 34 +++++++------------
 2 files changed, 26 insertions(+), 42 deletions(-)

diff --git a/PerfectNumbers.Core/HeuristicCombinedPrimeTester.cs b/PerfectNumbers.Core/HeuristicCombinedPrimeTester.cs
index 05c22a8..1ae2880 100644
--- a/PerfectNumbers.Core/HeuristicCombinedPrimeTester.cs
+++ b/PerfectNumbers.Core/HeuristicCombinedPrimeTester.cs
@@ -306,33 +306,25 @@ Cleanup:
 
     internal static ulong ComputeHeuristicSqrt(ulong n)
     {
-        if (n < 2UL)
+        ulong sqrt = (ulong)Math.Sqrt(n);
+        UInt128 square = (UInt128)sqrt * sqrt;
+
+        while (square > n)
         {
-            return n;
+            sqrt--;
+            square = (UInt128)sqrt * sqrt;
         }
 
-        int log2 = BitOperations.Log2(n);
-        ulong estimate = 1UL << ((log2 + 1) >> 1);
-        ulong quotient = n / estimate;
-
-        while (estimate > quotient)
+        ulong next = sqrt + 1UL;
+        UInt128 nextSquare = (UInt128)next * next;
+        while (nextSquare <= n)
         {
-            estimate = (estimate + quotient) >> 1;
-            quotient = n / estimate;
+            sqrt = next;
+            next++;
+            nextSquare = (UInt128)next * next;
         }
 
-        while (true)
-        {
-            ulong nextEstimate = estimate + 1UL;
-            if (nextEstimate > n / nextEstimate)
-            {
-                break;
-            }
-
-            estimate = nextEstimate;
-        }
-
-        return estimate;
+        return sqrt;
     }
 
     private static ReadOnlySpan<uint> GetCombinedDivisors(byte nMod10)
diff --git a/PerfectNumbers.Core/HeuristicPrimeTester.cs b/PerfectNumbers.Core/HeuristicPrimeTester.cs
index d752147..c3983a1 100644
--- a/PerfectNumbers.Core/HeuristicPrimeTester.cs
+++ b/PerfectNumbers.Core/HeuristicPrimeTester.cs
@@ -431,33 +431,25 @@ Cleanup:
 
     internal static ulong ComputeHeuristicSqrt(ulong n)
     {
-        if (n < 2UL)
+        ulong sqrt = (ulong)Math.Sqrt(n);
+        UInt128 square = (UInt128)sqrt * sqrt;
+
+        while (square > n)
         {
-            return n;
+            sqrt--;
+            square = (UInt128)sqrt * sqrt;
         }
 
-        int log2 = BitOperations.Log2(n);
-        ulong estimate = 1UL << ((log2 + 1) >> 1);
-        ulong quotient = n / estimate;
-
-        while (estimate > quotient)
+        ulong next = sqrt + 1UL;
+        UInt128 nextSquare = (UInt128)next * next;
+        while (nextSquare <= n)
         {
-            estimate = (estimate + quotient) >> 1;
-            quotient = n / estimate;
+            sqrt = next;
+            next++;
+            nextSquare = (UInt128)next * next;
         }
 
-        while (true)
-        {
-            ulong nextEstimate = estimate + 1UL;
-            if (nextEstimate > n / nextEstimate)
-            {
-                break;
-            }
-
-            estimate = nextEstimate;
-        }
-
-        return estimate;
+        return sqrt;
     }
 
     private static ReadOnlySpan<byte> GetGroupBEndingOrder(byte nMod10) => nMod10 switch