the above conditions to several bases, one gets somewhat more powerful primality tests than by using one base alone. For example, there are only 13 numbers less than 25·109 that are strong pseudoprimes to bases 2, 3, and 5 simultaneously. They are listed in Table 7 of. The smallest such number is 25326001. This means that, if n is less than 25326001 and n is a strong probable prime to bases 2, 3, and 5, then n is prime. Carrying this further, 3825123056546413051 is the smallest number that is a strong pseudoprime to the 9 bases 2, 3, 5, 7, 11, 13, 17, 19, and 23. So, if n is less than 3825123056546413051 and n is a strong probable prime to these 9 bases, then n is prime. By judicious choice of bases that are not necessarily prime, even better tests can be constructed. For example, there is no composite that is a strong pseudoprime to all of the seven bases 2, 325, 9375, 28178, 450775, 9780504, and 1795265022. Smallest strong pseudoprime to base a References Pseudoprimes