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.

New Largest Known Prime Number Discovered

Martin Nowak, an eye surgeon in Germany, and a long-time volunteer in the Great Internet Mersenne Prime Search (GIMPS) distributed computing project (http://www.mersenne.org/prime.htm), has discovered the largest known prime number. Nowak used one of his business PCs and free software by George Woltman and Scott Kurowski. His computer is a part of a wordwide array of tens of thousands of computers working together to make this discovery. The formula for the new prime number is 2^25,964,951-1. The number belongs to a special class of rare prime numbers called "Mersenne primes." This is only the 42nd Mersenne prime found since Marin Mersenne, a 17th century French monk, first studied these numbers over 350 years ago. Written out, the number has 7,816,230 digits, over half a million digits larger than the previous largest known prime number. It was discovered after more than 50 days of calculations on a 2.4-GHz Pentium 4 computer.