# Graham's number or...

• Sep 15th 2013, 08:56 AM
uperkurk
Graham's number or...
Hi all, this isn't a homework problem or anything just simply curious. Which is a larger number, Graham's number or the estimated number of atoms in the universe factorial?

So Graham's number or $\displaystyle (10^{80})!$
• Sep 15th 2013, 12:46 PM
Shakarri
Re: Graham's number or...
Since this is in math puzzles I've hidden my solution
Spoiler:
$\displaystyle 10^{80}!<10^{80}\cdot10^{80}\cdot10^{80}\cdot...$
$\displaystyle 10^{80}\cdot10^{80}\cdot10^{80}\cdot...=10^{80^{10 ^{80}}}$

Graham's number is said to be too large to express in the form $\displaystyle a^{b^{c^{...}}}$ with any reasonable number of indices. I have shown that the estimated number of atoms in the universe factorial is smaller than a number which can be expressed in multiple indices so it must be lower than Graham's number
• Sep 15th 2013, 02:19 PM
uperkurk
Re: Graham's number or...
I posted it in here not as a challenge to others but really as an answer to something I was just wondering. I was recently told to think of the largest possible number that still has some kind of meaning. I decided that the total number of atoms in the observable universe factorial is the largest number that still has any relevant meaning... I can't believe that even g1 is larger... considering graham's number is g64. Graham's number must really be the largest number that has any meaning.