Googology Wiki
Googology Wiki

13 (thirteen) is a positive integer following 12 and preceding 14. Its ordinal form is written "13th" or "thirteenth".[1]


  • 13 is an odd prime number.
  • 13 is a permutable prime in base 10.
  • 13 is the smallest emirp in base 10.
  • A set of 13 objects is sometimes called a baker's dozen.
  • 13 is the fourth busy beaver number \(\Sigma(4) = 13\), the largest known value of the function. It is also called ebony elephant. \(\Sigma(5)\) is known to be at least \(4098\).


  • 13 is associated with bad luck in Western superstition.
  • However, in Italy, it is considered good luck.
  • Also, it is the 5th lucky number (in the mathematical sense).

Partition number-related use

  • It is the first prime, which is not a partition number.
  • It is also the first prime p, for which there is a congruence of the partition function modulo p, but not for all indices with a certain remainder modulo p.
  • Furthermore, the partition function grows roughly like 13n, since e√(2/3)π is almost equal to 13. The emphasis is on “almost”, since e√(2/3)π is a transcendental number.

In googology

  • In Greek-based naming systems, 13 is associated with prefix "trideka-", and with prefix "tredeci-" in Latin systems.
  • 13 is the current lower bound for the mathematical problem where Graham's number arose.