I know a lot of us have already touched on the fact that prime numbers don't seem that interesting from the outside but if you look at the deeper meaning they can actually be more interesting. Like many other of my fellow classmates, I am going to be a math teacher for high school students and many times these students may not be so interested or excited to learn about a topic such as prime numbers. I went on a website to find why people find prime numbers and why they find it interesting and here is what I came up with. I found six pretty convincing reasons for finding primes:

1. Tradition: The quest for prime numbers started around 300 bc. Large primes were then studied by people such as Cataldi, Descartes, Fermat, Mersenne, Frenicle, Leibniz, Euler, Landry, Lucas, Catalan, Sylvester, Cunningham, Pepin, Putnam and Lehmer who are all big names in mathematics. "Much of elementary number theory was developed while deciding how to handle large numbers, how to characterize their factors and discover those which are prime. In short, the tradition of seeking large primes (especially the Mersennes) has been long and fruitful It is a tradition well worth continuing."

2. "For the by-products of the quest": The by-product I would find most useful as a teacher is how I could use the Mersenne search to involve my students in mathematical research, and perhaps to excite them into careers in science or engineering.

3. "People collect rare and beautiful items": "Mersenne primes, which are usually the largest known primes, are both rare and beautiful. Since Euclid initiated the search for and study of Mersennes approximately 300 BC, very few have been found. Less than fifty in all of human history—that is rare! But they are also beautiful. Mathematics, like all fields of study, has a definite notion of beauty. What qualities are perceived as beautiful in mathematics? We look for proofs that are short, concise, clear, and if possible that combine previous disparate concepts or teach you something new. Mersennes have one of the simplest possible forms for primes, 2n-1. The proof of their primality has an elegant simplicity. Mersennes are beautiful and have some surprising applications."

4. For the Glory: Just like athletes who have the desire to compete and be the best, those who search for giant primes are in essence doing the same thing. They are competing to find the largest prime number. "Their greatest contribution to mankind is not merely pragmatic, it is to the curiosity and spirit of man. If we lose the desire to do better, will we still be complete?"

5. To learn more about their distribution: "Though mathematics is not an experimental science, we often look for examples to test conjectures (which we hope to then prove). As the number of examples increase, so does (in a sense) our understanding of the distribution. The prime number theorem was discovered by looking at tables of primes. Simple calculations have found patterns, such as the prime number races, which have led to significant amounts of research."

6. For the money: There are a few who seek primes just for the money. There are prizes for the first ten-million digit prime ($100000), the first hundred-million digit prime ($150000), and the first billion digit prime ($250000)

When you first think of prime numbers I'm sure all these things don't come to mind. At least for me, a bunch of ugly looking numbers is all that shows up in my head and my brain wants to turn off. If you present these reasons to your students, they may not immediately be disinterested and may stop to think more about the reasoning and importance of prime numbers.