Prime (mark) - Definition and Overview

This article is not about the symbol for the set of prime numbers, ℙ.

The prime (′, Unicode U+2032, ′) is a symbol with many mathematical uses:

• A complement in set theory: A′ is the complement of the set A
• A point related to another (e.g., by a transformation T): A′ is related to A
• A first derivative or derived function: f′(x) is the first derivative of f(x)
• An arcminute or minute of time: 42′ means 42 arcminutes or minutes
• A foot: 7′ means 7 feet

A double prime (″, Unicode U+2033, ″) is the equivalent of two prime characters, and is used for similar purposes:

• A second derivative: f″(x) is the second derivative of f(x)
• An arcsecond or second of time: 42″ means 42 arcseconds or seconds
• An inch: 7″ means 7 inches

As an extension of the above symbols, the triple prime (‴, Unicode U+2034) and quadruple prime (⁗, Unicode U+2057) are often used to indicate the third and fourth derivative of a function, respectively. (Not all Web browsers can display these symbols.)

To avoid counting the number of primes, the notation f⁽ⁿ⁾(x) can be used to mean the nth derivative of f(x) when n is large.

Non-mathematical uses

The prime can also be used in the transliteration of some languages, such as Russian, to denote palatalization.

Representations

The prime symbol should not be confused with the apostrophe (', Unicode U+0027) or acute accent (´, Unicode U+00B4); the double prime should not be confused with the quotation mark (", Unicode U+0022).

When the character set used does not include the prime or double prime character (e.g. ISO Latin-1 is commonly assumed on IRC), they are often respectively approximated by normal or italic apostrophes and quotation marks.