This number is a prime.
1013 Productions is the company owned and managed by Chris Carter, who created The X-Files. [Blanchette]
There are exactly 1013 ways ten people can line up so that only one person has a taller person in front of him. [Gudipati]
The average sea-level pressure on Earth is about 1013 millibars. [Webb]
In Marcus du Sautoy's book The Music of the Primes, while discussing Bertrand's postulate, he states that there are actually quite a lot of primes between 1009 and 2018, the first being 1013.
Government 1013: A course in the Department of Government, Harvard University. Taught in Spring 2012, by Patrick Moynihan. [Green]
1013 is the smallest 4-digit prime that starts a run of seven consecutive primes where between any two successive primes, exactly one digit changes (i.e., 1013, 1019, 1021, 1031, 1033, 1039, 1049). Can you find a run of more than seven consecutive primes where between any two successive primes exactly one digit changes? [Loungrides]
The five prime anagrams of 1013 all have squares that are anagrams of each other. [Gaydos]