Prime Numbers

I was mussing with the in-house math guru today, helping him make a power point using a "fly-in" effect and we discussed "what is a prime number?" I said, " it's a number divisible by itself and two!" My colleague chuckled, "Remain an English teacher, Greig. Your definition could be any number! A prime is an integer greater than 1 whose factor is only itself and 1"

Albeit, I can't remember a sufficient definition for a prime number, but I find it fascinating that (1. There are an infinite set of 'em and 2.) There is no way as of yet to determine the pattern to how they appear on the number line.

Four primes exist between 1-9. But, how many between 1,000,000 and 3,000,000? Is there a pattern? And why so many primes between 1-9 but so few between larger sets of integers, like 600,000 - 700,000?

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