Fermat test base a, $\displaystyle (a,N)=1 , \ \ a^{N-1} = 1 \ \ mod \ N $

problem is, how many values of a are necessary to determine the primality or compositeness of N < 1000000 excluding Carmichael numbers ?

i found, if we test with primes 2,3,5,7,11 and it will find all the primes < 1000000. so i guess we need to test at least 5 values of a?

this is actually a programming problem, and i dont think it is possible to answer without testing