*Diary of Numbers*history has been made. For the first time, we have a tied contest. Congratulations to our winners. They'll both receive a free signed copy of

*How Many Licks?*

In this contest, we considered Skewes' number. At one time, Skewes' number was the largest number ever to appear in a mathematical proof. It can be written as

^{10101034}.

**What physical quantity comes closest to Skewes' number?**

The Universe. Vastly smaller than Skewes' number. |

This is a

__large number. As mentioned in the contest post, it's vastly bigger than the number of atoms in the solar system. To even come close, we're going to have to think on the scale of the universe. There have been about 10__*very*^{18}seconds since the big bang. Since the fastest rate at which information can travel is the speed of light, there's only a finite region of the universe that's observable. Anything outside this region is so far away that even light left over from the beginning of time hasn't had time to reach us yet. This distance will be equal to the speed of light times the age of the universe, roughly 10^{26}m. The total volume of the observable universe will be this cubed, or roughly 10^{78}m^{3}. Notice our exponent is only 78. We need it to be 10^{1034}. We're not even close yet!What if we measured using a smaller unit than meters? What is the smallest unit we could measure with? We could use the Planck length ~10

^{-35}, which is the length scale at which our conceptions of space start to break down. If we measure the size of the observable universe in Planck lengths, it would be about 10^{183}Planck lengths. That's still only an exponent of 183. We've barely scratched the surface.What if we considered space-time rather than just space? Einstein's theory of relativity treats time as just another dimension. Just like space, there is a Planck time (10

^{-44}s) at which our concept of time begins to break down. The universe is about 10^{62}Planck times old. This means there are about 10^{245}observable points in space-time. Again, we're still only scratching the surface of Skewes' number.Perhaps we should think about combinatorics. If we only consider universes that are the same size as our own, how many different possible universes can there be? According to particle physics, there are on the order of 10 fundamental particles (e.g., photons, electrons, quarks, etc.) If I consider only one point in space time, it has roughly 10 possible states corresponding to the different particles (or absence of particles) that can be found at that point. If there were only 2 points in space-time, there would be roughly 10

^{2}=100 possible universes. For 10^{245}points in space time, there are roughly 10^{10245}= 10^{10102.4}possible universes. The third exponent 2.4 is still much smaller than the 34 that appears is Skewes' number. Even if we counted every*possible*universe, we'd still be very far away from Skewes' number!