prime number generator

[JeffK31]

Hi all,

I am attempting to teach myself java from a tutorial webpage. One of the exercises is to write a program to calculate the first 100 prime numbers. Here's what I came up with:

class Prime {
	public static void main(String[] arguments) {
		int number = 2;
		int primes = 1;
		System.out.println("Prime #" + primes + " is " + number);
		number++;
		primes++;

		// keep a count of prime numbers
		while (primes <= 100) {
		
		// test each number for primeness
		for (int divisor = 2; divisor < number; divisor++) {
			if (number % divisor == 0) {
				number++; 
				continue;}
			
		}

		// print prime numbers
		System.out.println("Prime #" + primes + " is " + number);
		number++;
		primes++;}
	}
}

The program compiles just fine. When I ran it, it appeared to run just fine... until I realized that not all the numbers it's returning as prime actually are. It lists 2, 3, 5, 7, 11, 13, 17, 19, 23 (so far so good), 27(?), 29, 31, 35(?), 37, 41, and so on. Every once in a while a composite number sneaks into the list and I have no idea why. Browsing other threads, it's clear from other people who have worked on similar programs that there are more efficient ways of doing it (for instance, since 2 is the only even prime, I only really need to test odd numbers) but it still seems like my program should work. Can anyone help?

Jeff