13

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13 < 12 | 14 >
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13 (thirteen) is a positive integer following 12 and preceding 14. Its ordinal form is written "13th" or "thirteenth".

Properties

• 13 is an odd prime number.
• 13 is a permutable prime in base 10.
• 13 is the smallest emirp in base 10.
• 13 is the number for the French department of Bouches-du-Rhône.
• 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 \(4098\).
• Age 13 is the minimum age to collect personal information online under the Children's Online Privacy Protection Act of the Federal law of the United States, hence this, many websites which requires user registration and collects personal information disallow children under 13 from using their services.

(Un)lucky

• 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 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 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.

• DeepLineMadom calls this number zeroogolduplex and unoobol, and is equal to 10[0]10[0]10[0]100 in DeepLineMadom's Array Notation. He also calls it Hox, and it is the 1st number of Flenary of Ukrainian Town.