Friday, June 11, 2004

How Many Atoms are there in a Dog?

I recently ran across the number 2^24036583 - 1. (No, that's not the answer to the above question.)

Looking at that number, I know that it's huge. There are about 3 decimal places for every 2^10 (2^10 = 1024), so I figure there are slightly more than 24036583/10 * 3 ~= 7.2 million digits in that number. 7.2 _million_. That's one huge number, many times larger than a googol!

Why anyone would want to use such a number is beyond me. Counting things, it's more than anything I could possibly comprehend, I'm sure. Supposedly there are about 10^50 (give or take a couple orders of magnitude) atoms in the earth. So this is much less than a googol, much much much (etc) less than 2^24036583 - 1 (which we'll call p from now on).

~10^60 atoms in the sun (and ~10^60 atoms in our solar system), there's still a lot of fudge room to have a googol atoms in our galaxy, much less p. According to people that know better than I, there are probably less than a googol atoms in the universe, much less than that in just our galaxy.

So what use are the other 7 million-ish digits in p? How can anyone possibly comprehend the /size/ of this number? How can anyone really /care/ about this number (even if everything should be loved, surely there are exceptions!) How can anyone hold enough of it in their mind to start thinking about it.

Why would anyone care to prove that p is prime?

Of course I then realize that while it's larger than tower(5), it's still less than tower(6), so life is again good.

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