diff --git a/stan/math/prim/prob/yule_simon_lccdf.hpp b/stan/math/prim/prob/yule_simon_lccdf.hpp
new file mode 100644
index 00000000000..bee197415b9
--- /dev/null
+++ b/stan/math/prim/prob/yule_simon_lccdf.hpp
@@ -0,0 +1,84 @@
+#ifndef STAN_MATH_PRIM_PROB_YULE_SIMON_LCCDF_HPP
+#define STAN_MATH_PRIM_PROB_YULE_SIMON_LCCDF_HPP
+
+#include <stan/math/prim/meta.hpp>
+#include <stan/math/prim/err.hpp>
+#include <stan/math/prim/fun/constants.hpp>
+#include <stan/math/prim/fun/digamma.hpp>
+#include <stan/math/prim/fun/beta.hpp>
+#include <stan/math/prim/fun/lgamma.hpp>
+#include <stan/math/prim/fun/max_size.hpp>
+#include <stan/math/prim/fun/scalar_seq_view.hpp>
+#include <stan/math/prim/fun/size.hpp>
+#include <stan/math/prim/fun/size_zero.hpp>
+#include <stan/math/prim/fun/value_of.hpp>
+#include <stan/math/prim/functor/partials_propagator.hpp>
+
+namespace stan {
+namespace math {
+
+/** \ingroup prob_dists
+ * Returns the log CCDF of the Yule-Simon distribution with shape parameter.
+ * Given containers of matching sizes, returns the log sum of probabilities.
+ *
+ * @tparam T_n type of outcome parameter
+ * @tparam T_alpha type of shape parameter
+ *
+ * @param n outcome variable
+ * @param alpha shape parameter
+ * @return log probability or log sum of probabilities
+ * @throw std::domain_error if alpha fails to be positive
+ * @throw std::invalid_argument if container sizes mismatch
+ */
+template <typename T_n, typename T_alpha>
+inline return_type_t<T_alpha> yule_simon_lccdf(const T_n& n,
+                                               const T_alpha& alpha) {
+  using T_partials_return = partials_return_t<T_n, T_alpha>;
+  using T_n_ref = ref_type_t<T_n>;
+  using T_alpha_ref = ref_type_t<T_alpha>;
+  static constexpr const char* function = "yule_simon_lccdf";
+
+  check_consistent_sizes(function, "Outcome variable", n, "Shape parameter",
+                         alpha);
+  if (size_zero(n, alpha)) {
+    return 0.0;
+  }
+
+  T_n_ref n_ref = n;
+  T_alpha_ref alpha_ref = alpha;
+  check_positive_finite(function, "Shape parameter", alpha_ref);
+
+  scalar_seq_view<T_n> n_vec(n);
+  scalar_seq_view<T_alpha_ref> alpha_vec(alpha_ref);
+  const size_t max_size_seq_view = max_size(n_ref, alpha_ref);
+
+  // Explicit return for invalid or extreme values
+  // The gradients are technically ill-defined, but treated as zero
+  for (int i = 0; i < stan::math::size(n); i++) {
+    if (n_vec.val(i) < 1.0) {
+      return 0.0;
+    }
+    if (n_vec.val(i) == std::numeric_limits<int>::max()) {
+      return negative_infinity();
+    }
+  }
+
+  T_partials_return log_ccdf(0.0);
+  auto ops_partials = make_partials_propagator(alpha_ref);
+  for (size_t i = 0; i < max_size_seq_view; i++) {
+    auto np1 = n_vec.val(i) + 1.0;
+    auto ap1 = alpha_vec.val(i) + 1.0;
+    auto nap1 = n_vec.val(i) + ap1;
+    log_ccdf += lgamma(ap1) + lgamma(np1) - lgamma(nap1);
+
+    if constexpr (!is_constant<T_alpha>::value) {
+      partials<0>(ops_partials)[i] += digamma(ap1) - digamma(nap1);
+    }
+  }
+
+  return ops_partials.build(log_ccdf);
+}
+
+}  // namespace math
+}  // namespace stan
+#endif
diff --git a/test/prob/yule_simon/yule_simon_ccdf_log_test.hpp b/test/prob/yule_simon/yule_simon_ccdf_log_test.hpp
new file mode 100644
index 00000000000..d5dbe5521b3
--- /dev/null
+++ b/test/prob/yule_simon/yule_simon_ccdf_log_test.hpp
@@ -0,0 +1,65 @@
+// Arguments: Ints, Doubles
+#include <stan/math/prim/prob/yule_simon_lccdf.hpp>
+#include <stan/math/prim/fun/lgamma.hpp>
+
+using std::numeric_limits;
+using std::vector;
+
+class AgradCcdfLogYuleSimon : public AgradCcdfLogTest {
+ public:
+  void valid_values(vector<vector<double>>& parameters,
+                    vector<double>& cdf_log) {
+    vector<double> param(2);
+
+    param[0] = 5;     // n
+    param[1] = 20.0;  // alpha
+    parameters.push_back(param);
+    cdf_log.push_back(std::log(1.0 - 0.9999811782420478));  // expected ccdf_log
+
+    param[0] = 10;   // n
+    param[1] = 5.5;  // alpha
+    parameters.push_back(param);
+    cdf_log.push_back(std::log(1.0 - 0.9997987132162779));  // expected ccdf_log
+  }
+
+  void invalid_values(vector<size_t>& index, vector<double>& value) {
+    // n
+
+    // alpha
+    index.push_back(1U);
+    value.push_back(0.0);
+
+    index.push_back(1U);
+    value.push_back(-1.0);
+
+    index.push_back(1U);
+    value.push_back(std::numeric_limits<double>::infinity());
+  }
+
+  // BOUND INCLUDED IN ORDER FOR TEST TO PASS WITH CURRENT FRAMEWORK
+  bool has_lower_bound() { return false; }
+
+  bool has_upper_bound() { return false; }
+
+  template <class T_n, class T_alpha, typename T2, typename T3, typename T4,
+            typename T5>
+  stan::return_type_t<T_n, T_alpha> ccdf_log(const T_n& n, const T_alpha& alpha,
+                                             const T2&, const T3&, const T4&,
+                                             const T5&) {
+    return stan::math::yule_simon_lccdf(n, alpha);
+  }
+
+  template <class T_n, class T_alpha, typename T2, typename T3, typename T4,
+            typename T5>
+  stan::return_type_t<T_n, T_alpha> ccdf_log_function(const T_n& n,
+                                                      const T_alpha& alpha,
+                                                      const T2&, const T3&,
+                                                      const T4&, const T5&) {
+    using stan::math::lgamma;
+
+    auto log_ccdf
+        = lgamma(alpha + 1.0) + lgamma(n + 1.0) - lgamma(n + alpha + 1.0);
+
+    return log_ccdf;
+  }
+};