On Talking About Prime Numbers With a Math Teacher (When I Am Just a Lowly High School English Teacher)

I am an English teacher (and thus not a Math teacher). I was mussing with the in-house math guru today at work, helping him make a powerpoint using a "fly-in" effect and we discussed "what is a prime number?"
And How I Failed Miserably to Explain Prime
    I took a stab at a cursory definition and 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 of how they appear on the number line. Mathematicians are hard at work, though.
    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? The questions never cease!

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