diff --git a/bn_mp_prime_is_prime.c b/bn_mp_prime_is_prime.c
index e3f243618..6f91e1826 100644
--- a/bn_mp_prime_is_prime.c
+++ b/bn_mp_prime_is_prime.c
@@ -25,11 +25,6 @@ mp_err mp_prime_is_prime(const mp_int *a, int t, mp_bool *result)
    /* default to no */
    *result = MP_NO;
 
-   /* valid value of t? */
-   if (t > MP_PRIME_SIZE) {
-      return MP_VAL;
-   }
-
    /* Some shortcuts */
    /* N > 3 */
    if (a->used == 1) {
diff --git a/bn_mp_prime_rabin_miller_trials.c b/bn_mp_prime_rabin_miller_trials.c
index d7613bca3..0b3bab3f5 100644
--- a/bn_mp_prime_rabin_miller_trials.c
+++ b/bn_mp_prime_rabin_miller_trials.c
@@ -19,8 +19,7 @@ static const struct {
    {   768,     5 },
    {   896,     4 },
    {  1024,     4 },
-   {  2048,     2 },
-   {  4096,     1 },
+   {  2048,     2 }  /* For bigger keysizes use always at least 2 Rounds */
 };
 
 /* returns # of RM trials required for a given bit size and max. error of 2^(-96)*/
@@ -35,7 +34,7 @@ int mp_prime_rabin_miller_trials(int size)
          return (x == 0) ? sizes[0].t : sizes[x - 1].t;
       }
    }
-   return sizes[x-1].t + 1;
+   return sizes[x-1].t;
 }
 
 
diff --git a/demo/test.c b/demo/test.c
index cd8025224..7b2abd248 100644
--- a/demo/test.c
+++ b/demo/test.c
@@ -890,7 +890,7 @@ static int test_mp_prime_is_prime(void)
    mp_read_radix(&a,
                  "91xLNF3roobhzgTzoFIG6P13ZqhOVYSN60Fa7Cj2jVR1g0k89zdahO9/kAiRprpfO1VAp1aBHucLFV/qLKLFb+zonV7R2Vxp1K13ClwUXStpV0oxTNQVjwybmFb5NBEHImZ6V7P6+udRJuH8VbMEnS0H8/pSqQrg82OoQQ2fPpAk6G1hkjqoCv5s/Yr",
                  64);
-   mp_prime_is_prime(&a, 8, &cnt);
+   mp_prime_is_prime(&a, mp_prime_rabin_miller_trials(mp_count_bits(&a)), &cnt);
    if (cnt == MP_YES) {
       printf("Arnault's pseudoprime is not prime but mp_prime_is_prime says it is.\n");
       goto LBL_ERR;
@@ -900,7 +900,7 @@ static int test_mp_prime_is_prime(void)
    mp_set(&a, 1uL);
    mp_mul_2d(&a,1119,&a);
    mp_add_d(&a, 53uL, &a);
-   err = mp_prime_is_prime(&a, 8, &cnt);
+   err = mp_prime_is_prime(&a, mp_prime_rabin_miller_trials(mp_count_bits(&a)), &cnt);
    /* small problem */
    if (err != MP_OKAY) {
       printf("\nfailed with error: %s\n", mp_error_to_string(err));
@@ -930,7 +930,7 @@ static int test_mp_prime_is_prime(void)
       /* let's see if it's really a safe prime */
       mp_sub_d(&a, 1uL, &b);
       mp_div_2(&b, &b);
-      err = mp_prime_is_prime(&b, 8, &cnt);
+      err = mp_prime_is_prime(&b, mp_prime_rabin_miller_trials(mp_count_bits(&b)), &cnt);
       /* small problem */
       if (err != MP_OKAY) {
          printf("\nfailed with error: %s\n", mp_error_to_string(err));