# 1013

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]

A free neutron decays with a half-life of about 1013 seconds into a proton, electron and antineutrino. [Hughes]

The average sea-level pressure on Earth is about 1013 millibars. [Webb]

2^{1013} + 3^{1013} + 5^{1013} + 7^{1013} is prime. [Opao]

The prime sum of p(i), where i takes the values of the 11 first Fibonacci numbers. [Gallardo]

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.

Virginia Intermont College (alma mater of one of the authors) was located at the triadic prime address 1013 Moore Street in Bristol, Virginia.

Government 1013: A course in the Department of Government, Harvard University. Taught in Spring 2012, by Patrick Moynihan. [Green]

The smallest 4-digit prime p whose the reversal of square is equal to the square of the reversal of p, i.e., 1013^2 = 1026169 and R(1013^2) = 9616201 = 3101^2. [Loungrides]

The smallest four-digit antipalindromic prime: prime with an even number of digits such that the digits in the first half of the prime differ from the corresponding digits of the second half. [Wesolowski]

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]

The smallest positive integer for which its number of prime anagrams equals its sum of digits. [Gaydos]

The smallest prime number of the form 24k+5 which does not have 2 as a primitive root. [Nie]