See

here for a list of exceptions to multiple Rabin-Miller tests. From the GMP-ECM source:

Code:

if (SP_NUMB_BITS <= 32)
{
/* 32-bit primality test
* See http://primes.utm.edu/prove/prove2_3.html */
if (!sp_spp (2, x, d) || !sp_spp (7, x, d) || !sp_spp (61, x, d))
return 0;
}
else
{
ASSERT (SP_NUMB_BITS <= 64);
/* 64-bit primality test
* follows from results by Jaeschke, "On strong pseudoprimes to several
* bases" Math. Comp. 61 (1993) p916 */
if (!sp_spp (2, x, d) || !sp_spp (3, x, d) || !sp_spp (5, x, d)
|| !sp_spp (7, x, d) || !sp_spp (11, x, d) || !sp_spp (13, x, d)
|| !sp_spp (17, x, d) || ! sp_spp (19, x, d) || !sp_spp (23, x, d)
|| !sp_spp (29, x, d))
return 0;
}

There is no Rabin-Miller version of Carmichael numbers; the asymptotic probability of failure is the same for any input. This makes R-M nice for cryptographic applications that need large random primes in a fixed time with fixed chance of an error.