Primality testing (deterministic vs. non-deterministic) I noticed that non-deterministic primality testing algorithms are more commonly used in practice while there is a deterministic algorithm e.g., AKS which runs in polynomial time? I am right? if so, then why? is there any drawbacks of using AKS?

Thanks,
The simple answer is that AKS horribly inefficient in the real world.
Even the asymptotic complexity is orders of magnitudes higher than the one of probabilistic algorithms. Here is a comparison of AKS with Rabin-Miller and other probabilistic algorithms.
The following table illustrates the problem nicely (The tested number was $10^{
100}
+ 267$: