Essentially they’re 2, 3, 5, 7, 11, 13, 17, 19 and more.
1 is debatable.
First few are:
One thing to notice is that prime numbers (with the exception of 2) are all odd. So if you see an even number, you can say straight away it is not prime because it has a divisor (namely 2) that is neither 1 nor the number itself.
Secondly, every odd number (with the exception of 5) is not prime. So numbers like 15, 25, 35, ... are not primes (they are divisible by 5)
Thirdly, if the sum of the digits of your number is a multiple of 3, then your number is not prime.
A common way to test whether an odd number is prime or not is to take its square root, and see whether your number is divisible by any prime up to this square root. If not, then your number is prime.
With small numbers it's easy enough to verify it by brute force, That is, trying to divide by each number up to , rounded down. Obviously, if is a whole number, is not prime, since it is a square number. If it's even, you know that it's not prime right off the bat.
For larger numbers it is far harder to find out whether a number is prime. How best to do so would depend on the problem at hand. (I'm not sure if you'll be interested in this bit, I think the first line would have you covered)
If you're interesting in programming a solution, look up the sieve of sieve of eratosthenes to generate a list of the first primes.