Skewes' number

Named after South African mathematician Stanley Skewes.

Skewes' number (plural Skewes' numbers)

1. (number theory) Any of several extremely large numbers used as upper bounds for the smallest natural number ${\displaystyle x}$ for which ${\displaystyle \pi (x)>\operatorname {li} (x)}$, where ${\displaystyle \pi }$ is the prime-counting function and ${\displaystyle li}$ is the logarithmic integral function. These bounds have since been improved by others.
   • 1976, Word Ways: The Journal of Recreational Linguistics, volumes 9-10, A. Ross Eckler, page 178:

     With this extension, the number system exceeds a number of previously-named giants, such as Archimedes' largest number, Kasner's googolplex, Skewes' number and Candelaria's googoltriplex.