googol

Definition A googol equals to the number ${10}^{100}$, that is, a one followed by one hundred zeros. A googolplex is is 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 has a googol number of zeros in its decimal representation, 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 of a 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 an unimaginably large number and infinity. The name ’googol’ was supposedly coined by Kasner’s nine-year-old nephew Milton Sirotta in 1938 when asked to give a name for a huge number. The name googol was perhaps influenced by the comic strip character Barney Google [1, 3]. The name of the search engine google was inspired by the number googol [6].

Title	googol
Canonical name	Googol
Date of creation	2013-03-22 12:25:31
Last modified on	2013-03-22 12:25:31
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	19
Author	Mathprof (13753)
Entry type	Definition
Classification	msc 11-00
Related topic	Googolplex