Ok, I'll be the first to admit that I don't have a clue as to why prime numbers are important. My daughter asked, "Why do we need them?" After doing some research on the Internet to try to answer her question, the best I can come up with is that they have something to do with computer encryption technology. Why they were important prior to the advent of computers is beyond me. Nonetheless, I do find them interesting.

During my Internet research I came across easy directions to generate prime numbers. This set of instructions is ideal for any age student who needs to study this topic.

Eratosthenes, a genius who lived about 200 years before Christ, formulated this "sieve," which is extremely easy to use. Follow these directions to discover how easy it is to find prime numbers:

First, write down a list of integers. Start with the number two and go as high as you like. The example below goes up to twenty:

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Not including two, mark all multiples of two:

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Moving up to the next unmarked number, which in this case is three, do not mark it, but mark all its multiples:

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Continue in this fashion, marking all multiples of the next unmarked number until there are no new unmarked numbers in your list. Draw a circle around all unmarked numbers that remain. If your list went up to 20, it should look like this:

2 3 5 7 11 13 17 19

For a more effective lesson, make the list longer. Up to 50 is a good choice for a younger student; up to 100 might be better for an older student.

To make this a "thematic" or "unit" study, do some research on Eratosthenes and incorporate what you find into the lesson. He's an interesting historical figure and is worth studying all on his own.

I still don't know why we need prime numbers, and I still don't know why I find them interesting. If I figure these things out, I'll let you know.