I don't have the mathematic acuity displayed by some of posters here, but I thought I'd add my two cents anyway: A number is the concept of something finite(1 piece, 1 second, etc...), it has a beginning and an end(if you have 5 pieces of candy, you start with the first piece and end with the fifth). Infinity is the concept of something that has no end(the set of natural numbers) as well as something that has no beginning(the set of real numbers). To be a number is to have a specific beginning and a specific end. to have only one of those conditions is to be infinite.
A prime number is a number divisible only by 1 and itself.
The heart of this thread is this: Is the concept of infinity, when represented in the form and fashion of a number(the lemniscate or "lazy eight" symbol) divisible only by 1 and itself?
Because the concept of infinity is the concept of something without a definite number, it doesn't matter if you divide it up into one piece, 2 pieces, or 2 million pieces. Each piece is infinite. Therefore, because infinity can be divided by any number into equally infinite pieces, it is not a prime number.