diff --git a/stan/math/prim/core/init_threadpool_tbb.hpp b/stan/math/prim/core/init_threadpool_tbb.hpp
index 26c8915f387..ca96dc3a8b2 100644
--- a/stan/math/prim/core/init_threadpool_tbb.hpp
+++ b/stan/math/prim/core/init_threadpool_tbb.hpp
@@ -3,8 +3,6 @@
 
 #include <stan/math/prim/err/invalid_argument.hpp>
 
-#include <boost/lexical_cast.hpp>
-
 #ifndef TBB_INTERFACE_NEW
 #include <tbb/tbb_stddef.h>
 
@@ -20,7 +18,9 @@
 #include <tbb/task_scheduler_init.h>
 #endif
 
+#include <charconv>
 #include <cstdlib>
+#include <string_view>
 #include <thread>
 
 namespace stan {
@@ -44,32 +44,28 @@ namespace internal {
  * is invalid
  */
 inline int get_num_threads() {
-  int num_threads = 1;
 #ifdef STAN_THREADS
   const char* env_stan_num_threads = std::getenv("STAN_NUM_THREADS");
-  if (env_stan_num_threads != nullptr) {
-    try {
-      const int env_num_threads
-          = boost::lexical_cast<int>(env_stan_num_threads);
-      if (env_num_threads > 0) {
-        num_threads = env_num_threads;
-      } else if (env_num_threads == -1) {
-        num_threads = std::thread::hardware_concurrency();
-      } else {
-        invalid_argument("get_num_threads(int)", "STAN_NUM_THREADS",
-                         env_stan_num_threads,
-                         "The STAN_NUM_THREADS environment variable is '",
-                         "' but it must be positive or -1");
-      }
-    } catch (const boost::bad_lexical_cast&) {
-      invalid_argument("get_num_threads(int)", "STAN_NUM_THREADS",
-                       env_stan_num_threads,
-                       "The STAN_NUM_THREADS environment variable is '",
-                       "' but it must be a positive number or -1");
-    }
+  if (env_stan_num_threads == nullptr) {
+    return 1;
+  }
+
+  const std::string_view value(env_stan_num_threads);
+  int num_threads;
+  const auto [end, error]
+      = std::from_chars(value.begin(), value.end(), num_threads);
+  if (error != std::errc() || end != value.end()
+      || (num_threads < 1 && num_threads != -1)) {
+    invalid_argument("get_num_threads(int)", "STAN_NUM_THREADS",
+                     env_stan_num_threads,
+                     "The STAN_NUM_THREADS environment variable is '",
+                     "' but it must be a positive number or -1");
   }
+
+  return num_threads == -1 ? std::thread::hardware_concurrency() : num_threads;
+#else
+  return 1;
 #endif
-  return num_threads;
 }
 
 }  // namespace internal
diff --git a/stan/math/prim/fun/grad_2F1.hpp b/stan/math/prim/fun/grad_2F1.hpp
index 42d5d2a50dd..8731c6d30b7 100644
--- a/stan/math/prim/fun/grad_2F1.hpp
+++ b/stan/math/prim/fun/grad_2F1.hpp
@@ -13,7 +13,6 @@
 #include <stan/math/prim/fun/sign.hpp>
 #include <stan/math/prim/fun/hypergeometric_2F1.hpp>
 #include <cmath>
-#include <boost/optional.hpp>
 
 namespace stan {
 namespace math {
diff --git a/stan/math/prim/fun/hypergeometric_2F1.hpp b/stan/math/prim/fun/hypergeometric_2F1.hpp
index ae327e033f1..fc33f7062d0 100644
--- a/stan/math/prim/fun/hypergeometric_2F1.hpp
+++ b/stan/math/prim/fun/hypergeometric_2F1.hpp
@@ -17,7 +17,7 @@
 #include <stan/math/prim/fun/sqrt.hpp>
 #include <stan/math/prim/fun/square.hpp>
 #include <stan/math/prim/fun/hypergeometric_pFq.hpp>
-#include <boost/optional.hpp>
+#include <optional>
 
 namespace stan {
 namespace math {
@@ -29,7 +29,7 @@ namespace internal {
  * more background (and other possible special-cases), see:
  * https://functions.wolfram.com/HypergeometricFunctions/Hypergeometric2F1/03/
  *
- * The return value is wrapped in a boost::optional<> type so that a void
+ * The return value is wrapped in a std::optional<> type so that a void
  * return is possible if no special-case rules are applicable
  *
  * @tparam Ta1 Type of scalar first 'a' argument
@@ -43,7 +43,7 @@ namespace internal {
  * @return Gauss hypergeometric function
  */
 template <typename Ta1, typename Ta2, typename Tb, typename Tz,
-          typename RtnT = boost::optional<return_type_t<Ta1, Ta2, Tb, Tz>>,
+          typename RtnT = std::optional<return_type_t<Ta1, Ta2, Tb, Tz>>,
           require_all_arithmetic_t<Ta1, Ta2, Tb, Tz>* = nullptr>
 inline RtnT hyper_2F1_special_cases(const Ta1& a1, const Ta2& a2, const Tb& b,
                                     const Tz& z) {
@@ -149,7 +149,7 @@ inline RtnT hyper_2F1_special_cases(const Ta1& a1, const Ta2& a2, const Tb& b,
  */
 template <typename Ta1, typename Ta2, typename Tb, typename Tz,
           typename ScalarT = return_type_t<Ta1, Ta2, Tb, Tz>,
-          typename OptT = boost::optional<ScalarT>,
+          typename OptT = std::optional<ScalarT>,
           require_all_arithmetic_t<Ta1, Ta2, Tb, Tz>* = nullptr>
 inline return_type_t<Ta1, Ta2, Tb, Tz> hypergeometric_2F1(const Ta1& a1,
                                                           const Ta2& a2,
@@ -168,15 +168,15 @@ inline return_type_t<Ta1, Ta2, Tb, Tz> hypergeometric_2F1(const Ta1& a1,
   // Check whether value can be calculated by any special-case rules
   // before estimating infinite sum
   OptT special_case_a1a2 = internal::hyper_2F1_special_cases(a1, a2, b, z);
-  if (special_case_a1a2.is_initialized()) {
-    return special_case_a1a2.get();
+  if (special_case_a1a2.has_value()) {
+    return special_case_a1a2.value();
   }
 
   // Check whether any special case rules apply with 'a' arguments reversed
   // as 2F1(a1, a2, b, z) = 2F1(a2, a1, b, z)
   OptT special_case_a2a1 = internal::hyper_2F1_special_cases(a2, a1, b, z);
-  if (special_case_a2a1.is_initialized()) {
-    return special_case_a2a1.get();
+  if (special_case_a2a1.has_value()) {
+    return special_case_a2a1.value();
   }
 
   Eigen::Matrix<double, 2, 1> a_args(2);
diff --git a/test/unit/math/prim/core/get_num_threads_test.cpp b/test/unit/math/prim/core/get_num_threads_test.cpp
index 3a91eba9f67..5b86e308c89 100644
--- a/test/unit/math/prim/core/get_num_threads_test.cpp
+++ b/test/unit/math/prim/core/get_num_threads_test.cpp
@@ -27,11 +27,11 @@ TEST(get_num_threads, incorrect_values) {
 
   set_n_threads("-2");
   EXPECT_THROW_MSG(stan::math::internal::get_num_threads(),
-                   std::invalid_argument, "must be positive or -1");
+                   std::invalid_argument, "positive number or -1");
 
   set_n_threads("0");
   EXPECT_THROW_MSG(stan::math::internal::get_num_threads(),
-                   std::invalid_argument, "must be positive or -1");
+                   std::invalid_argument, "positive number or -1");
 }
 #else
 TEST(get_num_threads, correct_values_no_stan_threads) {