googol

DefinitionA googol equals to the number ${10}^{100}$, that is, a one followed byone hundred zeros.A googolplex isis ten raised to the power of a googol, i.e., ${10}^{({10}^{100})}$.

This is already a huge number. For instance,it is more than the number of atoms in the known universe.A googoplex is even larger. In fact, since a googolplex hasa googol number of zeros in its decimalrepresentation,a googoplex has more digits than there are atoms in our universe.Thus, even if all matter in the universe were at disposal,it would not be possible to write down the decimal representation ofa googolplex [1].

Properties

1. A googol is approximately the factorial of $70$.The only prime factors in a googol and a googolplex are $2$ and $5$ [1].

2. Using Stirling’s formula we can approximate the factorial of a googol to obtain

   $${10}^{100}!\approx {10}^{9.95\cdot {10}^{101}}.$$

3. A googoplex plus one is not a prime. One factor is 316912650057057350374175801344000001 [5].

History and etymology

The googol was created by the American mathematician Edward Kasner (1878-1955) [4]in [2] to illustrate the difference between anunimaginably large number and infinity.The name ’googol’ was supposedly coined by Kasner’snine-year-old nephew Milton Sirotta in 1938 when asked to give a name for a huge number.The name googol was perhaps influenced bythe comic strip character Barney Google [1, 3].The name of the search engine google was inspired by the numbergoogol [6].