No. Numbers need to be proven prime. I can go on about how special primes are and stuff, but it doesn't really matter.
But it comes down to a simple truthtable problem  the one that few people seem to grasp:
p := function returns that n is prime
q := n really is prime
r := answers the question: "Is n prime?"
++++
 p  q  p>q  Does (function result) imply (n is prime)?
++++
 T  T  T  A prime number is prime.
 F  F  T  A not prime number is not prime.
++++
 F  T  T  case 1
 T  F  F  case 2
++++

The first two items are obvious. A prime number is prime, a not prime number is not. However, a single, simplistic primality test cannot possibly guarantee either of these truth implications.
So the trick is now which of the remaining truth implications we want our function to have.
In
case 1, we have asked the question: "Is this (truly prime) number prime?" and received the response "no". I may not be able to trust the function when it says "no", but I can still trust the function when it says "yes". (That is the meaning of the implication.)
In
case 2, we have asked the question: "Is this (not prime) number prime?" and received the (useless) response "yes".
I cannot trust the function.
Get it? If the question is, "is this number prime?" I must be able to trust that the response is valid for all truly prime numbers.
Hope this helps.
[edit]
It is actually possible to prove a number prime using just two or three simple functions, though...