diff --git a/src/core/include/mp-units/ext/prime.h b/src/core/include/mp-units/ext/prime.h
index 3c3dc22d..2b03a5ec 100644
--- a/src/core/include/mp-units/ext/prime.h
+++ b/src/core/include/mp-units/ext/prime.h
@@ -379,6 +379,28 @@ struct LucasSequenceElement {
   return false;
 }
 
+// The Baillie-PSW test is technically a "probable prime" test.  However, it is known to be correct for all
+// 64-bit integers, and no counterexample of any size has ever been found.  Thus, for this library's purposes,
+// we can treat it as deterministic... probably.
+[[nodiscard]] consteval bool baillie_psw_probable_prime(uint64_t n)
+{
+  if (n < 2u) {
+    return false;
+  }
+  if (n < 4u) {
+    return true;
+  }
+  if (n % 2u == 0u) {
+    return false;
+  }
+
+  if (!miller_rabin_probable_prime(2u, n)) {
+    return false;
+  }
+
+  return strong_lucas_probable_prime(n);
+}
+
 [[nodiscard]] consteval bool is_prime_by_trial_division(std::uintmax_t n)
 {
   for (std::uintmax_t f = 2; f * f <= n; f += 1 + (f % 2)) {
diff --git a/test/static/prime_test.cpp b/test/static/prime_test.cpp
index 5378e211..c7c317fa 100644
--- a/test/static/prime_test.cpp
+++ b/test/static/prime_test.cpp
@@ -197,4 +197,28 @@ static_assert(strong_lucas_probable_prime(9'007'199'254'740'881u), "Large known
 
 static_assert(strong_lucas_probable_prime(18'446'744'073'709'551'557u), "Largest 64-bit prime");
 
+// Tests for Baillie-PSW, which is known to be correct for all 64-bit integers.
+static_assert(baillie_psw_probable_prime(3u), "Known small prime");
+static_assert(baillie_psw_probable_prime(5u), "Known small prime");
+static_assert(baillie_psw_probable_prime(7u), "Known small prime");
+static_assert(!baillie_psw_probable_prime(9u), "Known small composite");
+
+// Test some Miller-Rabin pseudoprimes (https://oeis.org/A001262), which should NOT be marked prime.
+static_assert(!baillie_psw_probable_prime(2047u), "Miller-Rabin pseudoprime");
+static_assert(!baillie_psw_probable_prime(3277u), "Miller-Rabin pseudoprime");
+static_assert(!baillie_psw_probable_prime(486737u), "Miller-Rabin pseudoprime");
+
+// Test some Strong Lucas pseudoprimes (https://oeis.org/A217255), which should NOT be marked prime.
+static_assert(!baillie_psw_probable_prime(5459u), "Strong Lucas pseudoprime");
+static_assert(!baillie_psw_probable_prime(5777u), "Strong Lucas pseudoprime");
+static_assert(!baillie_psw_probable_prime(10877u), "Strong Lucas pseudoprime");
+static_assert(!baillie_psw_probable_prime(324899u), "Strong Lucas pseudoprime");
+
+// Test some actual primes
+static_assert(baillie_psw_probable_prime(225'653'407'801u), "Large known prime");
+static_assert(baillie_psw_probable_prime(334'524'384'739u), "Large known prime");
+static_assert(baillie_psw_probable_prime(9'007'199'254'740'881u), "Large known prime");
+
+static_assert(baillie_psw_probable_prime(18'446'744'073'709'551'557u), "Largest 64-bit prime");
+
 }  // namespace