Prime Numbers

Is there any real good formula(s) for finding out if a number is prime? I've managed to devise a formula on my own, but it doesn't work when you plug in something that has a multiple of three. The formula would yield either a whole or a fraction. A fraction means that the number you plugged in is a composite number, whereas a whole number meant you got yourself a genuine prime number. But, when I plug in a multiple of 3, I get a whole number and that's no good.

So, if anyone has a favorite formula or if there's just one good formula right now, please do share. Thanks.

>>25
2^2^2^2^2^2+1 = 2^32+1 = 4,294,967,297 = (641)*(6,700,417)