How am I?

Here is an exercise to help you appreciate how unique we are.

You have two parents.
Your 2 parents each have two parents.
Your 4 grandparents each have two parents.

This can be expressed mathematically like so:

Ancestors = 2 ^ G, read 2 to the power of G where G = generations

So, one generation is represented by 2 ^ 1, or 2
and two generations is represented by 2 ^ 2, or 4

Now, suppose we assume that 100 years approximates 3 generations and look in our ancestral rear-view mirror to see how many people it took to make me.

I remember singing "Columbus sailed the ocean blue in 1492" in grade-school. 1492 was 513 years ago, or approximately 15 generations (3 for every 100). Using the above ancestral formula, this means there were 32,768 people involved in my appearance (yours too).

Let's make a quick table with time-span on the left and ancestors on the right:

500 years ago I had 32,768 ancestors (G = 15)
1000 years ago I had 1,073,741,824 ancestors (G = 30)
1500 years ago I had 35,184,372,088,832 ancestors (G = 45)
2000 years ago I had 1,152,921,504,606,846,976 ancestors (G = 60)

I quickly exhausted the planet's population supply, yet my math appears to be irrefutable. Did I just prove that I can't possibly exist?

Is this an exercise in bad science or bad intentions?

Comments?