13 (number)
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13 is a natural number that comes after 12 and before 14. In base-10 notation it is written as 13, and in Roman numerals as XIII. It is a prime number, meaning it can be divided only by 1 and itself.
13 is the sixth prime number when counted in order: 2, 3, 5, 7, 11, 13. It is also an odd number and cannot be divided by two. The sum 12+1 makes it a number often referenced in cultural and commercial measurement practices.
Mathematical properties
13 is a member of the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13), where each number is the sum of the two preceding ones. It also appears in a well-known Pythagorean triple: 5² + 12² = 13². When squared, 13 yields 169.
In binary (base-2), 13 is written as 1101. It is also a prime number of the form 4k+1, and can therefore be expressed as the sum of two squares: 13 = 4 + 9 (that is, 2² + 3²).
Cultural use
In many European and North American cultures, 13 is regarded as an unlucky number. Because of this belief, some buildings and hotels have skipped the 13th floor, numbering directly from 12 to 14. This fear is called triskaidekaphobia in English. In other cultures, the number carries no such association.
In calendar history, the year contains 12 complete lunar months plus part of another; for this reason, some lunisolar calendar systems add a 13th month in certain years to align the calendar properly.