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. \(\Sigma(5)\) is known to be at least \(4098\).
13 is associated with bad luck in Western superstition.
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 13√n, 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 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.