googolplex

A googolplex is the number 10¹⁰¹⁰⁰ (or <math>{10}^\mbox{googol}</math>, or <math>{10}^\mbox{10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000}</math>), that is, 1 followed by a googol (10¹⁰⁰) zeroes. The term googol was coined by Milton Sirotta, nephew of mathematician Edward Kasner. Googolplex was coined by Kasner to define an especially large number by extension from his nephew's idea.

A googol is greater than the number of elementary particles in the known universe, which has been variously estimated from 10⁷² up to 10⁸⁷. Since this is less than the number of zeroes in a googolplex, it would not be possible to write down or store a googolplex in decimal notation, even if all the matter in the known universe were converted into paper and ink or disk drives.

Thinking of this another way, consider printing the digits of a googolplex in unreadable, 1-point font. TeX 1pt font is .3514598mm per digit, which means it would take about <math>3.5*10^{96} </math> meters to write in one point font. The known universe is estimated at <math> 7.4*10^{26} </math> meters in diameter, which means the distance to write the digits would be about <math>4.7*10^{69} </math> times the diameter of the known universe. The time it would take to write such a number also renders the task implausible: if a person can write two digits per second, it would take around <math>1.1*10^{82}</math> times the age of the universe to write down a googolplex.

Even then, the magnitude of the googolplex is not as large as some of the specially defined extraordinarily large numbers, such as those using Knuth's up-arrow notation or Steinhaus-Moser notation. Even more simply, one can name numbers larger than a googolplex with fewer symbols, for example,

<math>9^{9^{9^{9^{9^9}}}}

</math>, which is much larger.

Googolplex is often considered a cardinal number, which like any other number could represent quantity and not order.

In popular culture

• Googolplex is the name of a multiplex cinema in the fictional town of Springfield in the television series The Simpsons.

• Google refers to their headquarters as the "Googleplex".

• In Back to the Future Part III, googolplex was used by the "Doc" to describe his girlfriend, Clara Clayton:

Clara was one in a million. One in a billion. One in a googolplex!

See also

• Googol
• Standardized system of writing very large numbers
• Names of large numbers

External links

• Known prime factors of googolplex + n (0 <= n <= 999): http://www.alpertron.com.ar/GOOGOL.HTM
• Another Googolplex page: http://www.procrastinators.org/googolplex.html
• Includes C code to count to Googolplex http://www.fpx.de/fp/Fun/Googolplex/