It's Time For...

...another frightening look inside my head.

As an engineer I occasionally have to deal with numbers.

Yesterday, I somehow spent my thinking time while I ate my lunch pondering prime numbers.

Just go with me here, OK?

I'll just ask y'all; can one type of infinity be less infinite than another type of infinity?

This is the conundrum that has me asking this.

A) There are an infinite number of integers.
B) Some integers are what we call even numbers, all perfectly divisible by the number 2 (no remainder).
C) Some integers are what we call prime numbers and can only be divided evenly by themselves and the number 1.

With me so far?

Every other integer is an even number; 2, 4, 6, 8, ..., 2200, 2202, 2204, ...

But prime numbers happen less often; 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, ...

So, again my question, rephrased: If there are an infinite number of even integers, and an infinite number of prime integers, and if prime integers "happen" less often than even integers, are there fewer prime integers than there are even integers, despite the fact that they both continue on to infinity?

In short, are prime integers "less infinite" in number than "even integers" are?

I was just wondering.

Then I finished my lunch and had to go back to work.

I needed a work break to get away from my lunch break.