diff --git a/library/bignum.c b/library/bignum.c
index 9289d1fbc..af523fcd3 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -2043,12 +2043,12 @@ cleanup:
 /*
  * Miller-Rabin pseudo-primality test  (HAC 4.24)
  */
-static int mpi_miller_rabin( const mbedtls_mpi *X,
+static int mpi_miller_rabin( const mbedtls_mpi *X, size_t rounds,
                              int (*f_rng)(void *, unsigned char *, size_t),
                              void *p_rng )
 {
     int ret, count;
-    size_t i, j, k, n, s;
+    size_t i, j, k, s;
     mbedtls_mpi W, R, T, A, RR;
 
     mbedtls_mpi_init( &W ); mbedtls_mpi_init( &R ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &A );
@@ -2064,14 +2064,8 @@ static int mpi_miller_rabin( const mbedtls_mpi *X,
     MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &R, s ) );
 
     i = mbedtls_mpi_bitlen( X );
-    /*
-     * HAC, table 4.4
-     */
-    n = ( ( i >= 1300 ) ?  2 : ( i >=  850 ) ?  3 :
-          ( i >=  650 ) ?  4 : ( i >=  350 ) ?  8 :
-          ( i >=  250 ) ? 12 : ( i >=  150 ) ? 18 : 27 );
 
-    for( i = 0; i < n; i++ )
+    for( i = 0; i < rounds; i++ )
     {
         /*
          * pick a random A, 1 < A < |X| - 1
@@ -2138,7 +2132,7 @@ cleanup:
 /*
  * Pseudo-primality test: small factors, then Miller-Rabin
  */
-int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
+int mpi_is_prime_internal( const mbedtls_mpi *X, int rounds,
                   int (*f_rng)(void *, unsigned char *, size_t),
                   void *p_rng )
 {
@@ -2164,7 +2158,17 @@ int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
         return( ret );
     }
 
-    return( mpi_miller_rabin( &XX, f_rng, p_rng ) );
+    return( mpi_miller_rabin( &XX, rounds, f_rng, p_rng ) );
+}
+
+/*
+ * Pseudo-primality test, error probability 2^-80
+ */
+int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
+                  int (*f_rng)(void *, unsigned char *, size_t),
+                  void *p_rng )
+{
+    return mpi_is_prime_internal( X, 40, f_rng, p_rng );
 }
 
 /*
@@ -2176,6 +2180,7 @@ int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int dh_flag,
 {
     int ret;
     size_t k, n;
+    int rounds;
     mbedtls_mpi_uint r;
     mbedtls_mpi Y;
 
@@ -2186,6 +2191,13 @@ int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int dh_flag,
 
     n = BITS_TO_LIMBS( nbits );
 
+    /*
+     * 2^-80 error probability, number of rounds chosen per HAC, table 4.4
+     */
+    rounds = ( ( nbits >= 1300 ) ?  2 : ( nbits >=  850 ) ?  3 :
+               ( nbits >=  650 ) ?  4 : ( nbits >=  350 ) ?  8 :
+               ( nbits >=  250 ) ? 12 : ( nbits >=  150 ) ? 18 : 27 );
+
     MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( X, n * ciL, f_rng, p_rng ) );
 
     k = mbedtls_mpi_bitlen( X );
@@ -2197,7 +2209,7 @@ int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int dh_flag,
 
     if( dh_flag == 0 )
     {
-        while( ( ret = mbedtls_mpi_is_prime( X, f_rng, p_rng ) ) != 0 )
+        while( ( ret = mpi_is_prime_internal( X, rounds, f_rng, p_rng ) ) != 0 )
         {
             if( ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
                 goto cleanup;
@@ -2233,8 +2245,10 @@ int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int dh_flag,
              */
             if( ( ret = mpi_check_small_factors(  X         ) ) == 0 &&
                 ( ret = mpi_check_small_factors( &Y         ) ) == 0 &&
-                ( ret = mpi_miller_rabin(  X, f_rng, p_rng  ) ) == 0 &&
-                ( ret = mpi_miller_rabin( &Y, f_rng, p_rng  ) ) == 0 )
+                ( ret = mpi_miller_rabin(  X, rounds, f_rng, p_rng  ) )
+                                                                == 0 &&
+                ( ret = mpi_miller_rabin( &Y, rounds, f_rng, p_rng  ) )
+                                                                == 0 )
             {
                 break;
             }