If I gave you a number, 207, how would you go about (dis)proving it's primality? I think most people would have an inner dialogue that goes something like this:

"Well it's not divisible by 2, but it is divisible by 3, so it's composite."

You just keep on going through the numbers until you find a number that divides into it or you reach the square root of the number.3

This works! it's actually fairly easy to program, and it correctly identifies numbers as either prime or composite: