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I was reading an Asimov book the other day and came across something called Skewes' number. At one time, Skewes' number was the largest number ever to appear in a mathematical proof.

^{1}It would be impossible to write Skewes' number out in the conventional way, but using exponents we can write it as

^{10101034}.

This is an exceedingly large number. It is vastly bigger than the number of grains of sand in the Earth. In fact, it's vastly bigger than the number of grains of sand in the solar system. In fact, it's vastly bigger than the number of atoms in the solar system. In fact, all of these physical quantities are extreme underestimates of Skewes' number.

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

**Note: It must be something physical like a molecule, atom, or grain of sand (i.e. not something abstract like a number appearing in a mathematical proof.)**

[1] It has since been replaced by other large numbers. For more info, see Graham's number and Moser's number.

Hi Aaron, that looks pretty huge. Are you looking for something combinatorial? (Ie. Number of ways of arranging the number of subsets of...) Otherwise I cant think of any dimensionful physical quantity that would be that big expressed in, say, units of Planck scale. Interesting question. Cheers.

ReplyDeleteYeah...it's almost indescribably huge. The answer could be something combinatorial as long as its physical (e.g. maybe the number of ways of arranging particles in the room if you discretized on the Planck scale.) I've had one interesting answer so far, but it did not use combinatorics.

DeleteI have a similar question to Kipton. Since this number seems to be very very large, are we to find something that comes close to that number and then work out the solution (i.e., if the answer that comes close is the grains of sand on the planet we are to find that number)?

ReplyDeleteYes, that's the basic idea. In some sense, it's a contest to come up with the largest possible physical number.

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