I was reading somewhere that it's hard to determine if a number is prime or not if it gets too large.
If I understand correctly, all numbers can be broken into prime factors. And numbers which can't be broken down to any factors beside $1$ and themselves are prime.
So to check if $N$ is prime, you need to
calculate prime numbers upto $N/2$, (as any number bigger than $N/2$ can't be a factor for $N$ since multiplying it with the minimum number that will have effect, which is $2$, will make it more than $N$).
and check if any of these are factors of $N$.
I want to know if I am right, and what I am missing in terms of it being hard to compute.