diff --git a/include/mbedtls/bignum.h b/include/mbedtls/bignum.h
index 0ee32dd..40cfab4 100644
--- a/include/mbedtls/bignum.h
+++ b/include/mbedtls/bignum.h
@@ -725,10 +725,19 @@
  */
 int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N );
 
+#if !defined(MBEDTLS_DEPRECATED_REMOVED)
+#if defined(MBEDTLS_DEPRECATED_WARNING)
+#define MBEDTLS_DEPRECATED      __attribute__((deprecated))
+#else
+#define MBEDTLS_DEPRECATED
+#endif
 /**
  * \brief          Miller-Rabin primality test with error probability of
  *                 2<sup>-80</sup>
  *
+ * \deprecated     Superseded by mbedtls_mpi_is_prime_ext() which allows
+ *                 specifying the number of Miller-Rabin rounds.
+ *
  * \param X        MPI to check
  * \param f_rng    RNG function
  * \param p_rng    RNG parameter
@@ -737,11 +746,39 @@
  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
  *                 MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if X is not prime
  */
-int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
-                  int (*f_rng)(void *, unsigned char *, size_t),
-                  void *p_rng );
+MBEDTLS_DEPRECATED int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
+                          int (*f_rng)(void *, unsigned char *, size_t),
+                          void *p_rng );
+#undef MBEDTLS_DEPRECATED
+#endif /* !MBEDTLS_DEPRECATED_REMOVED */
 
 /**
+ * \brief          Miller-Rabin primality test.
+ *
+ * \warning        If \p X is potentially generated by an adversary, for example
+ *                 when validating cryptographic parameters that you didn't
+ *                 generate yourself and that are supposed to be prime, then
+ *                 \p rounds should be at least the half of the security
+ *                 strength of the cryptographic algorithm. On the other hand,
+ *                 if \p X is chosen uniformly or non-adversially (as is the
+ *                 case when mbedtls_mpi_gen_prime calls this function), then
+ *                 \p rounds can be much lower.
+ *
+ * \param X        MPI to check
+ * \param rounds   Number of bases to perform Miller-Rabin primality test for.
+ *                 The probability of returning 0 on a composite is at most
+ *                 2<sup>-2*\p rounds</sup>.
+ * \param f_rng    RNG function
+ * \param p_rng    RNG parameter
+ *
+ * \return         0 if successful (probably prime),
+ *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
+ *                 MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if X is not prime
+ */
+int mbedtls_mpi_is_prime_ext( const mbedtls_mpi *X, int rounds,
+                              int (*f_rng)(void *, unsigned char *, size_t),
+                              void *p_rng );
+/**
  * \brief Flags for mbedtls_mpi_gen_prime()
  *
  * Each of these flags is a constraint on the result X returned by
diff --git a/library/bignum.c b/library/bignum.c
index 6d166c6..9dc4e4d 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -2145,9 +2145,9 @@
 /*
  * Pseudo-primality test: small factors, then Miller-Rabin
  */
-int mpi_is_prime_internal( const mbedtls_mpi *X, int rounds,
-                  int (*f_rng)(void *, unsigned char *, size_t),
-                  void *p_rng )
+int mbedtls_mpi_is_prime_ext( const mbedtls_mpi *X, int rounds,
+                              int (*f_rng)(void *, unsigned char *, size_t),
+                              void *p_rng )
 {
     int ret;
     mbedtls_mpi XX;
@@ -2174,6 +2174,7 @@
     return( mpi_miller_rabin( &XX, rounds, f_rng, p_rng ) );
 }
 
+#if !defined(MBEDTLS_DEPRECATED_REMOVED)
 /*
  * Pseudo-primality test, error probability 2^-80
  */
@@ -2181,8 +2182,14 @@
                   int (*f_rng)(void *, unsigned char *, size_t),
                   void *p_rng )
 {
-    return mpi_is_prime_internal( X, 40, f_rng, p_rng );
+    /*
+     * In the past our key generation aimed for an error rate of at most
+     * 2^-80. Since this function is deprecated, aim for the same certainty
+     * here as well.
+     */
+    return mbedtls_mpi_is_prime_ext( X, 40, f_rng, p_rng );
 }
+#endif
 
 /*
  * Prime number generation
@@ -2248,7 +2255,7 @@
 
         if( ( flags & MBEDTLS_MPI_GEN_PRIME_FLAG_DH ) == 0 )
         {
-            ret = mpi_is_prime_internal( X, rounds, f_rng, p_rng );
+            ret = mbedtls_mpi_is_prime_ext( X, rounds, f_rng, p_rng );
 
             if( ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
                 goto cleanup;
diff --git a/library/rsa_internal.c b/library/rsa_internal.c
index 507009f..9a42d47 100644
--- a/library/rsa_internal.c
+++ b/library/rsa_internal.c
@@ -351,15 +351,20 @@
      */
 
 #if defined(MBEDTLS_GENPRIME)
+    /*
+     * When generating keys, the strongest security we support aims for an error
+     * rate of at most 2^-100 and we are aiming for the same certainty here as
+     * well.
+     */
     if( f_rng != NULL && P != NULL &&
-        ( ret = mbedtls_mpi_is_prime( P, f_rng, p_rng ) ) != 0 )
+        ( ret = mbedtls_mpi_is_prime_ext( P, 50, f_rng, p_rng ) ) != 0 )
     {
         ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
         goto cleanup;
     }
 
     if( f_rng != NULL && Q != NULL &&
-        ( ret = mbedtls_mpi_is_prime( Q, f_rng, p_rng ) ) != 0 )
+        ( ret = mbedtls_mpi_is_prime_ext( Q, 50, f_rng, p_rng ) ) != 0 )
     {
         ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
         goto cleanup;
diff --git a/programs/pkey/dh_genprime.c b/programs/pkey/dh_genprime.c
index dbe9153..360e355 100644
--- a/programs/pkey/dh_genprime.c
+++ b/programs/pkey/dh_genprime.c
@@ -156,7 +156,7 @@
         goto exit;
     }
 
-    if( ( ret = mbedtls_mpi_is_prime( &Q, mbedtls_ctr_drbg_random, &ctr_drbg ) ) != 0 )
+    if( ( ret = mbedtls_mpi_is_prime_ext( &Q, 50, mbedtls_ctr_drbg_random, &ctr_drbg ) ) != 0 )
     {
         mbedtls_printf( " failed\n  ! mbedtls_mpi_is_prime returned %d\n\n", ret );
         goto exit;
diff --git a/tests/suites/test_suite_mpi.data b/tests/suites/test_suite_mpi.data
index b046be7..b8b7b9e 100644
--- a/tests/suites/test_suite_mpi.data
+++ b/tests/suites/test_suite_mpi.data
@@ -682,11 +682,11 @@
 
 Test mbedtls_mpi_is_prime_det (4 non-witnesses)
 depends_on:MBEDTLS_GENPRIME
-mbedtls_mpi_is_prime_det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
+mbedtls_mpi_is_prime_det:"043BD64BA10B11DA83FBD296B04BCA9E0552FAF6E09CAC74E2D7E735ED0DB09FC47ED76145644203EE0C826013BC602F560BCDAAED557D04683859A65D659FF828A245A2C5B1AC41E01E4669A525A45E23AF":"040EA852F7935ACCECC0E87B845281F047D10DC9AAFEF990AF9D3D66770DA30B0C5B5E03EEA8C0CB79B936FE0BB8EE5389EC1D34EB16C58AA3F2E11AF084160CDF6400BE1CC179867AB074866952D9F34EE7042D27F960E715A97FCB93F3182247D0A6AE51BD21CC2F6B0651F9E572C5FB86F3137053FA85FD7A51816D69B3A53A5A438C17754836D04E98CA240B901F828332F2D72D88C497DA45F533F99A6E53EDEA6B0424EC8951B048FA9A80134B37D0A67014597934E3CFC52C5A4DD4751ADF8D66FC79E84E2A3148C4B15C17E12CB659390FD275F39A331FFC80EC699BC3F6FAB868E30E9B14575FCDAB6FAED01E00112DD28704177E09C335AD43A696FEA761E8DF3B0663277A5C3637F9060CB5E5654F72E9A6B0F369E660AD4CF7ABF4195493545B367BD55271CD4BB7D9C15D3F508FE8F7409C2126FC8E73B43A67CD4EFB21E9F15DBF040A2A8D5F5ED75CEAC12B595C0051F3EC9D5A58ACE82A9506E64F780E9836728260FFE1BFD73E8A9869E3D46A35A856D3028F7FEAB9F4F1A04449AEDC80017EE1014080D87F0B50C8EF255324CD89F7D039":82:5:MBEDTLS_ERR_MPI_NOT_ACCEPTABLE
 
 Test mbedtls_mpi_is_prime_det (39 non-witnesses)
 depends_on:MBEDTLS_GENPRIME
-mbedtls_mpi_is_prime_det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
+mbedtls_mpi_is_prime_det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
 
 Test mbedtls_mpi_gen_prime (Too small)
 depends_on:MBEDTLS_GENPRIME
diff --git a/tests/suites/test_suite_mpi.function b/tests/suites/test_suite_mpi.function
index c6548b1..95fe99c 100644
--- a/tests/suites/test_suite_mpi.function
+++ b/tests/suites/test_suite_mpi.function
@@ -843,7 +843,7 @@
     mbedtls_mpi_init( &X );
 
     TEST_ASSERT( mbedtls_mpi_read_string( &X, radix_X, input_X ) == 0 );
-    res = mbedtls_mpi_is_prime( &X, rnd_std_rand, NULL );
+    res = mbedtls_mpi_is_prime_ext( &X, 40, rnd_std_rand, NULL );
     TEST_ASSERT( res == div_result );
 
 exit:
@@ -853,7 +853,7 @@
 
 /* BEGIN_CASE depends_on:MBEDTLS_GENPRIME */
 void mbedtls_mpi_is_prime_det( data_t * input_X, data_t * witnesses,
-                               int chunk_len, int div_result )
+                               int chunk_len, int rounds, int div_result )
 {
     mbedtls_mpi X;
     int res;
@@ -865,7 +865,8 @@
     rand.chunk_len = chunk_len;
 
     TEST_ASSERT( mbedtls_mpi_read_binary( &X, input_X->x, input_X->len ) == 0 );
-    res = mbedtls_mpi_is_prime( &X, mbedtls_test_mpi_miller_rabin_determinizer,
+    res = mbedtls_mpi_is_prime_ext( &X, rounds,
+                                    mbedtls_test_mpi_miller_rabin_determinizer,
                                     &rand );
     TEST_ASSERT( res == div_result );
 
@@ -892,12 +893,14 @@
         TEST_ASSERT( actual_bits >= (size_t) bits );
         TEST_ASSERT( actual_bits <= (size_t) bits + 1 );
 
-        TEST_ASSERT( mbedtls_mpi_is_prime( &X, rnd_std_rand, NULL ) == 0 );
+        TEST_ASSERT( mbedtls_mpi_is_prime_ext( &X, 40, rnd_std_rand, NULL )
+                     == 0 );
         if( flags & MBEDTLS_MPI_GEN_PRIME_FLAG_DH )
         {
             /* X = ( X - 1 ) / 2 */
             TEST_ASSERT( mbedtls_mpi_shift_r( &X, 1 ) == 0 );
-            TEST_ASSERT( mbedtls_mpi_is_prime( &X, rnd_std_rand, NULL ) == 0 );
+            TEST_ASSERT( mbedtls_mpi_is_prime_ext( &X, 40, rnd_std_rand, NULL )
+                         == 0 );
         }
     }