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 truth-table 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.
It is actually possible to prove a number prime using just two or three simple functions, though...