What are prime numbers good for?

They can help you to factor out expressions and find a prime factorizations. For example: if you have a number: 200, and you are asked to find out how many factors it has, you find the prime factorization-- that is the expression of the product of all primes which are factors of 200:

200=2*100=2*2*50=2*2*2*25=2*2*2*5*5=(2^3) * (5^2)

so 200 has (3+1)(2+1)= 12 factors: but only 2 are prime:

primes can also help you figure out how many numbers aren't prime. These are the composite numbers, although not sure why to use them a lot...

sometimes primes can help you with powers of other primes, or to find out if a number is divisible by another number or not.

Prime numbers are good for many things. If you take a look at RSA cryptography, the basic scheme of it is based on the difficulty of factoring large numbers into two primes. Imagine factoring a really, really large number into its only two factors, those factors being primes. It would be extremely time consuming. Primes are good for security, but they also possess very interesting properties (and you might say that they have special properties) that make computations easier; for example, take a look at Fermat's Little Theorem.

Try balancing your checkbook without using any.