diff --git a/src/gmpy2.c b/src/gmpy2.c
index 3652cdc5..8f0326e0 100644
--- a/src/gmpy2.c
+++ b/src/gmpy2.c
@@ -754,7 +754,7 @@ static PyMethodDef Pygmpy_methods [] =
     { "is_lucas_prp", GMPY_mpz_is_lucas_prp, METH_VARARGS, doc_mpz_is_lucas_prp },
     { "is_odd", GMPy_MPZ_Function_IsOdd, METH_O, GMPy_doc_mpz_function_is_odd },
     { "is_power", GMPy_MPZ_Function_IsPower, METH_O, GMPy_doc_mpz_function_is_power },
-    { "is_prime", GMPy_MPZ_Function_IsPrime, METH_VARARGS, GMPy_doc_mpz_function_is_prime },
+    { "is_prime", (PyCFunction)GMPy_MPZ_Function_IsPrime, METH_FASTCALL, GMPy_doc_mpz_function_is_prime },
     { "is_probab_prime", (PyCFunction)GMPy_MPZ_Function_IsProbabPrime, METH_FASTCALL, GMPy_doc_mpz_function_is_probab_prime },
     { "is_selfridge_prp", GMPY_mpz_is_selfridge_prp, METH_VARARGS, doc_mpz_is_selfridge_prp },
     { "is_square", GMPy_MPZ_Function_IsSquare, METH_O, GMPy_doc_mpz_function_is_square },
@@ -762,10 +762,10 @@ static PyMethodDef Pygmpy_methods [] =
     { "is_strong_bpsw_prp", GMPY_mpz_is_strongbpsw_prp, METH_VARARGS, doc_mpz_is_strongbpsw_prp },
     { "is_strong_lucas_prp", GMPY_mpz_is_stronglucas_prp, METH_VARARGS, doc_mpz_is_stronglucas_prp },
     { "is_strong_selfridge_prp", GMPY_mpz_is_strongselfridge_prp, METH_VARARGS, doc_mpz_is_strongselfridge_prp },
-    { "jacobi", GMPy_MPZ_Function_Jacobi, METH_VARARGS, GMPy_doc_mpz_function_jacobi },
-    { "kronecker", GMPy_MPZ_Function_Kronecker, METH_VARARGS, GMPy_doc_mpz_function_kronecker },
+    { "jacobi", (PyCFunction)GMPy_MPZ_Function_Jacobi, METH_FASTCALL, GMPy_doc_mpz_function_jacobi },
+    { "kronecker", (PyCFunction)GMPy_MPZ_Function_Kronecker, METH_FASTCALL, GMPy_doc_mpz_function_kronecker },
     { "lcm", (PyCFunction)GMPy_MPZ_Function_LCM, METH_FASTCALL, GMPy_doc_mpz_function_lcm },
-    { "legendre", GMPy_MPZ_Function_Legendre, METH_VARARGS, GMPy_doc_mpz_function_legendre },
+    { "legendre", (PyCFunction)GMPy_MPZ_Function_Legendre, METH_FASTCALL, GMPy_doc_mpz_function_legendre },
     { "license", GMPy_get_license, METH_NOARGS, GMPy_doc_license },
     { "lucas", GMPy_MPZ_Function_Lucas, METH_O, GMPy_doc_mpz_function_lucas },
     { "lucasu", GMPY_mpz_lucasu, METH_VARARGS, doc_mpz_lucasu },
diff --git a/src/gmpy2_mpz.c b/src/gmpy2_mpz.c
index fa289b4f..ab4a0c92 100644
--- a/src/gmpy2_mpz.c
+++ b/src/gmpy2_mpz.c
@@ -106,7 +106,7 @@ static PyMethodDef GMPy_MPZ_methods[] = {
     { "is_even", GMPy_MPZ_Method_IsEven, METH_NOARGS, GMPy_doc_mpz_method_is_even },
     { "is_odd", GMPy_MPZ_Method_IsOdd, METH_NOARGS, GMPy_doc_mpz_method_is_odd },
     { "is_power", GMPy_MPZ_Method_IsPower, METH_NOARGS, GMPy_doc_mpz_method_is_power },
-    { "is_prime", GMPy_MPZ_Method_IsPrime, METH_VARARGS, GMPy_doc_mpz_method_is_prime },
+    { "is_prime", (PyCFunction)GMPy_MPZ_Method_IsPrime, METH_FASTCALL, GMPy_doc_mpz_method_is_prime },
     { "is_probab_prime", (PyCFunction)GMPy_MPZ_Method_IsProbabPrime, METH_FASTCALL, GMPy_doc_mpz_method_is_probab_prime },
     { "is_square", GMPy_MPZ_Method_IsSquare, METH_NOARGS, GMPy_doc_mpz_method_is_square },
     { "num_digits", (PyCFunction)GMPy_MPZ_Method_NumDigits, METH_FASTCALL, GMPy_doc_mpz_method_num_digits },
diff --git a/src/gmpy2_mpz_misc.c b/src/gmpy2_mpz_misc.c
index 28781310..d38fed4a 100644
--- a/src/gmpy2_mpz_misc.c
+++ b/src/gmpy2_mpz_misc.c
@@ -1321,22 +1321,20 @@ PyDoc_STRVAR(GMPy_doc_mpz_function_is_prime,
 "to n Miller-Rabin tests are performed.");
 
 static PyObject *
-GMPy_MPZ_Function_IsPrime(PyObject *self, PyObject *args)
+GMPy_MPZ_Function_IsPrime(PyObject *self, PyObject * const *args,
+                          Py_ssize_t nargs)
 {
     int i;
     unsigned long reps = 25;
     MPZ_Object* tempx;
-    Py_ssize_t argc;
-
-    argc = PyTuple_GET_SIZE(args);
 
-    if (argc == 0 || argc > 2) {
+    if (nargs == 0 || nargs > 2) {
         TYPE_ERROR("is_prime() requires 'mpz'[,'int'] arguments");
         return NULL;
     }
 
-    if (PyTuple_GET_SIZE(args) == 2) {
-        reps = GMPy_Integer_AsUnsignedLong(PyTuple_GET_ITEM(args, 1));
+    if (nargs == 2) {
+        reps = GMPy_Integer_AsUnsignedLong(args[1]);
         if (reps == (unsigned long)(-1) && PyErr_Occurred()) {
             return NULL;
         }
@@ -1346,7 +1344,7 @@ GMPy_MPZ_Function_IsPrime(PyObject *self, PyObject *args)
         }
     }
 
-    if (!(tempx = GMPy_MPZ_From_Integer(PyTuple_GET_ITEM(args, 0), NULL))) {
+    if (!(tempx = GMPy_MPZ_From_Integer(args[0], NULL))) {
         return NULL;
     }
 
@@ -1371,21 +1369,19 @@ PyDoc_STRVAR(GMPy_doc_mpz_method_is_prime,
 "to n Miller-Rabin tests are performed.");
 
 static PyObject *
-GMPy_MPZ_Method_IsPrime(PyObject *self, PyObject *args)
+GMPy_MPZ_Method_IsPrime(PyObject *self, PyObject * const *args,
+                        Py_ssize_t nargs)
 {
     int i;
     unsigned long reps = 25;
-    Py_ssize_t argc;
-
-    argc = PyTuple_GET_SIZE(args);
 
-    if (argc > 1) {
+    if (nargs > 1) {
         TYPE_ERROR("is_prime() takes at most 1 argument");
         return NULL;
     }
 
-    if (PyTuple_GET_SIZE(args) == 1) {
-        reps = GMPy_Integer_AsUnsignedLong(PyTuple_GET_ITEM(args, 0));
+    if (nargs == 1) {
+        reps = GMPy_Integer_AsUnsignedLong(args[0]);
         if (reps == (unsigned long)(-1) && PyErr_Occurred()) {
             return NULL;
         }
@@ -1559,18 +1555,19 @@ PyDoc_STRVAR(GMPy_doc_mpz_function_jacobi,
 "Return the Jacobi symbol (x|y). y must be odd and >0.");
 
 static PyObject *
-GMPy_MPZ_Function_Jacobi(PyObject *self, PyObject *args)
+GMPy_MPZ_Function_Jacobi(PyObject *self, PyObject *const *args,
+                         Py_ssize_t nargs)
 {
     MPZ_Object *tempx = NULL, *tempy = NULL;
     long res;
 
-    if (PyTuple_GET_SIZE(args) != 2) {
+    if (nargs != 2) {
         TYPE_ERROR("jacobi() requires 'mpz','mpz' arguments");
         return NULL;
     }
 
-    if (!(tempx = GMPy_MPZ_From_Integer(PyTuple_GET_ITEM(args, 0), NULL)) ||
-        !(tempy = GMPy_MPZ_From_Integer(PyTuple_GET_ITEM(args, 1), NULL))) {
+    if (!(tempx = GMPy_MPZ_From_Integer(args[0], NULL)) ||
+        !(tempy = GMPy_MPZ_From_Integer(args[1], NULL))) {
 
         Py_XDECREF((PyObject*)tempx);
         Py_XDECREF((PyObject*)tempy);
@@ -1595,18 +1592,19 @@ PyDoc_STRVAR(GMPy_doc_mpz_function_legendre,
 "Return the Legendre symbol (x|y). y is assumed to be an odd prime.");
 
 static PyObject *
-GMPy_MPZ_Function_Legendre(PyObject *self, PyObject *args)
+GMPy_MPZ_Function_Legendre(PyObject *self, PyObject * const *args,
+                           Py_ssize_t nargs)
 {
     MPZ_Object *tempx = NULL, *tempy = NULL;
     long res;
 
-    if (PyTuple_GET_SIZE(args) != 2) {
+    if (nargs != 2) {
         TYPE_ERROR("legendre() requires 'mpz','mpz' arguments");
         return NULL;
     }
 
-    if (!(tempx = GMPy_MPZ_From_Integer(PyTuple_GET_ITEM(args, 0), NULL)) ||
-        !(tempy = GMPy_MPZ_From_Integer(PyTuple_GET_ITEM(args, 1), NULL))) {
+    if (!(tempx = GMPy_MPZ_From_Integer(args[0], NULL)) ||
+        !(tempy = GMPy_MPZ_From_Integer(args[1], NULL))) {
 
         Py_XDECREF((PyObject*)tempx);
         Py_XDECREF((PyObject*)tempy);
@@ -1631,18 +1629,19 @@ PyDoc_STRVAR(GMPy_doc_mpz_function_kronecker,
 "Return the Kronecker-Jacobi symbol (x|y).");
 
 static PyObject *
-GMPy_MPZ_Function_Kronecker(PyObject *self, PyObject *args)
+GMPy_MPZ_Function_Kronecker(PyObject *self, PyObject * const *args,
+                            Py_ssize_t nargs)
 {
     MPZ_Object *tempx = NULL, *tempy = NULL;
     long res;
 
-    if (PyTuple_GET_SIZE(args) != 2) {
+    if (nargs != 2) {
         TYPE_ERROR("kronecker() requires 'mpz','mpz' arguments");
         return NULL;
     }
 
-    if (!(tempx = GMPy_MPZ_From_Integer(PyTuple_GET_ITEM(args, 0), NULL)) ||
-        !(tempy = GMPy_MPZ_From_Integer(PyTuple_GET_ITEM(args, 1), NULL))) {
+    if (!(tempx = GMPy_MPZ_From_Integer(args[0], NULL)) ||
+        !(tempy = GMPy_MPZ_From_Integer(args[1], NULL))) {
 
         Py_XDECREF((PyObject*)tempx);
         Py_XDECREF((PyObject*)tempy);
diff --git a/src/gmpy2_mpz_misc.h b/src/gmpy2_mpz_misc.h
index 2a15c653..a4b388ff 100644
--- a/src/gmpy2_mpz_misc.h
+++ b/src/gmpy2_mpz_misc.h
@@ -54,7 +54,7 @@ static PyObject * GMPy_MPZ_Method_IsSquare(PyObject *self, PyObject *other);
 static PyObject * GMPy_MPZ_Method_IsDivisible(PyObject *self, PyObject *other);
 static PyObject * GMPy_MPZ_Method_IsCongruent(PyObject *self, PyObject *const *args, Py_ssize_t nargs);
 static PyObject * GMPy_MPZ_Method_IsPower(PyObject *self, PyObject *other);
-static PyObject * GMPy_MPZ_Method_IsPrime(PyObject *self, PyObject *args);
+static PyObject * GMPy_MPZ_Method_IsPrime(PyObject *self, PyObject *const *args, Py_ssize_t nargs);
 static PyObject * GMPy_MPZ_Method_IsProbabPrime(PyObject *self, PyObject *const *args, Py_ssize_t nargs);
 static PyObject * GMPy_MPZ_Method_IsEven(PyObject *self, PyObject *other);
 static PyObject * GMPy_MPZ_Method_IsOdd(PyObject *self, PyObject *other);
@@ -85,15 +85,15 @@ static PyObject * GMPy_MPZ_Function_IsSquare(PyObject *self, PyObject *other);
 static PyObject * GMPy_MPZ_Function_IsDivisible(PyObject *self, PyObject * const *args, Py_ssize_t nargs);
 static PyObject * GMPy_MPZ_Function_IsCongruent(PyObject *self, PyObject * const *args, Py_ssize_t nargs);
 static PyObject * GMPy_MPZ_Function_IsPower(PyObject *self, PyObject *other);
-static PyObject * GMPy_MPZ_Function_IsPrime(PyObject *self, PyObject *args);
+static PyObject * GMPy_MPZ_Function_IsPrime(PyObject *self, PyObject * const *args, Py_ssize_t nargs);
 static PyObject * GMPy_MPZ_Function_IsProbabPrime(PyObject *self, PyObject *const *args, Py_ssize_t nargs);
 static PyObject * GMPy_MPZ_Function_NextPrime(PyObject *self, PyObject *other);
 #if (__GNU_MP_VERSION > 6) || (__GNU_MP_VERSION == 6 &&  __GNU_MP_VERSION_MINOR >= 3)
 static PyObject * GMPy_MPZ_Function_PrevPrime(PyObject *self, PyObject *other);
 #endif
-static PyObject * GMPy_MPZ_Function_Jacobi(PyObject *self, PyObject *args);
-static PyObject * GMPy_MPZ_Function_Legendre(PyObject *self, PyObject *args);
-static PyObject * GMPy_MPZ_Function_Kronecker(PyObject *self, PyObject *args);
+static PyObject * GMPy_MPZ_Function_Jacobi(PyObject *self, PyObject * const *args, Py_ssize_t nargs);
+static PyObject * GMPy_MPZ_Function_Legendre(PyObject *self, PyObject * const *args, Py_ssize_t nargs);
+static PyObject * GMPy_MPZ_Function_Kronecker(PyObject *self, PyObject * const *args, Py_ssize_t nargs);
 static PyObject * GMPy_MPZ_Function_IsEven(PyObject *self, PyObject *other);
 static PyObject * GMPy_MPZ_Function_IsOdd(PyObject *self, PyObject *other);