diff --git a/src/cmd/compile/internal/ssa/prove.go b/src/cmd/compile/internal/ssa/prove.go
index d1d851be91..9fedbdbbc9 100644
--- a/src/cmd/compile/internal/ssa/prove.go
+++ b/src/cmd/compile/internal/ssa/prove.go
@@ -1645,13 +1645,13 @@ func initLimit(v *Value) limit {
 		lim = lim.signedMinMax(math.MinInt32, math.MaxInt32)
 
 	// math/bits intrinsics
-	case OpCtz64, OpBitLen64:
+	case OpCtz64, OpBitLen64, OpPopCount64:
 		lim = lim.unsignedMax(64)
-	case OpCtz32, OpBitLen32:
+	case OpCtz32, OpBitLen32, OpPopCount32:
 		lim = lim.unsignedMax(32)
-	case OpCtz16, OpBitLen16:
+	case OpCtz16, OpBitLen16, OpPopCount16:
 		lim = lim.unsignedMax(16)
-	case OpCtz8, OpBitLen8:
+	case OpCtz8, OpBitLen8, OpPopCount8:
 		lim = lim.unsignedMax(8)
 
 	// bool to uint8 conversion
diff --git a/test/prove_popcount.go b/test/prove_popcount.go
new file mode 100644
index 0000000000..430df01ec3
--- /dev/null
+++ b/test/prove_popcount.go
@@ -0,0 +1,37 @@
+// errorcheck -0 -d=ssa/prove/debug=1
+
+//go:build amd64.v3 || arm64
+
+// Copyright 2025 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// FIXME(@Jorropo): this file exists because I havn't yet bothered to
+// make prove work on the pure go function call fallback.
+// My idea was to wait until CL 637936 is merged, then we can always emit
+// the PopCount SSA operation and translate them to pure function calls
+// in late-opt.
+
+package main
+
+import "math/bits"
+
+func onesCountsBounds(x uint64, ensureAllBranchesCouldHappen func() bool) int {
+	z := bits.OnesCount64(x)
+	if ensureAllBranchesCouldHappen() && z > 64 { // ERROR "Disproved Less64$"
+		return 42
+	}
+	if ensureAllBranchesCouldHappen() && z <= 64 { // ERROR "Proved Leq64$"
+		return 4242
+	}
+	if ensureAllBranchesCouldHappen() && z < 0 { // ERROR "Disproved Less64$"
+		return 424242
+	}
+	if ensureAllBranchesCouldHappen() && z >= 0 { // ERROR "Proved Leq64$"
+		return 42424242
+	}
+	return z
+}
+
+func main() {
+}