Upper Bound for Number of Grains of Sand to fill Universe

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Theorem

The number of grains of sand that would fill the Universe, to the extent it was believed to exist in the days of Archimedes, is bounded above by $10^{63}$.


Proof




Historical Note

As an exercise in his system of notation for denoting very large numbers, Archimedes determines an Upper Bound for Number of Grains of Sand to fill Universe in his book The Sand-Reckoner.

It needs to be emphasised that the actual size of the universe was little understood in those days.


Sources