Comments by "David Terr" (@dcterr1) on "Why is this number everywhere?" video.

  1. According to Sheldon on an episode of the Big Bang Theory, 73 is the most interesting number in the world. I won't cite his reasons for this claim, but note that 73 is just 37 with its digits reversed. Also note that 10001 = 73 * 137, and 1/137 is the approximate value of the fine structure constant, a very important dimensionless physical constant which appears a lot in atomic theory as well as quantum electrodynamics (QED).
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  2. Wow, these are some amazing facts about 37! My favorite is the secretary problem, marriage problem, or whatever you like to call it. I think this problem is also closely related to the fact that after the mean lifetime of a radioactive particle, it has roughly a 37% chance (1/e precisely) of not having decayed yet, a fact I learned way back when I was a physics undergrad student.
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  3. Here's one of my favorite properties of 37 - it's a prime divisor of the third repunit, namely 111, which is equal to 3 times 37, which also implies that 10^3 - 1 = 999 is divisible by 37, whence 10^6 - 1, 10^9 - 1, etc., and in general, 10^(3n) - 1 is as well for every positive integer n. This is most likely the reason the 37-obsessed guy's number trick works. (I'm a number theorist, by the way, with a PhD from UC Berkeley in algebraic number theory.)
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