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Oh, what a happy little question! Prime numbers are like the stars in the night sky, shining brightly on their own - they can only be divided by 1 and themselves. Numbers like 2, 3, 5, and 7 are prime. Composite numbers are a bit more social, as they can be divided by more than just 1 and themselves. Numbers like 4, 6, 8, 9, and 10 are composite, but each one is special in its own way.
Prime numbers are numbers greater than 1 that are only divisible by 1 and themselves. The prime numbers up to 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. Composite numbers are numbers that have more than two factors, including 1 and themselves. All other numbers up to 100 that are not prime are composite.
Oh, dude, prime numbers are like the cool kids at school who don't hang out with anyone but themselves. They're only divisible by 1 and themselves, so they're like loners in the math world. Composite numbers, on the other hand, are like the social butterflies who can be divided by more than just 1 and themselves. In this case, prime numbers up to 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. The rest are all composite numbers, but who's counting, right?
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97 are prime. All others, from 4 upwards are composite.
24 is composite because it can factored or split up as 24 = 3 * 8 for example. Prime numbers, such as 23, can not be split into factors.
The odd numbers are 101, 103, 105, 107, 109, etc. - just add two at a time. To include only composite numbers, look up a table of prime numbers, and delete those from the list.
The first two prime numbers add up to another prime number.
Please note that there are infinitely many prime numbers. An Internet search for "list of prime numbers" will quickly give you a list of prime numbers up to a certain point, for example here: http://en.wikipedia.org/wiki/List_of_prime_numbers Any integer greater than 1 that is not in the list of prime numbers is a composite number. (1 is considered neither a prime number, nor a composite number.)
Prime numbers go on forever.