First you can set up something like the following...
So that might make you wonder if there is some function that does a better job than this one, like it has peaks of 1 at all the prime numbers and is 0 elsewhere... In the frequency domain a function like that would look like:
This is where the Heisenburg uncertainty principle comes in, it says the narrower these bands are in the frequency domain the less certain the function is in the time domain. Meaning there couldn't be a function with information about every prime in the frequency domain that gave any information at all in the time domain. Eventually the uncertainty results in so much error as to showing which number is prime that it becomes useless.
So there can't really be a prime number function that does something like taking on a 1 value for primes and 0 otherwise.