Prime (mark)

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

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The prime (′, Unicode 0x2032, ′) is not an apostrophe (', Unicode 0x0027) or an acute accent (´, Unicode 0x00B4). It has several uses:

• In set theory, A′ is the complement of the set A.
• A′ can mean a point related to A (e.g. by a transformation T).
• f′(x) is the first derivative (or derived function) of f(x).
• 42′ can mean 42 arcminutes (or sometimes, 42 minutes of time).
• 7′ can mean 7 feet.
• The prime can be used in the transliteration of some languages, such as Russian.

The double prime (″, Unicode 0x2033, ″) is not a quotation mark (", Unicode 0x0022), and is equivalent two prime characters. It is used for similar purposes:

• f″(x) is the second derivative of f(x).
• 42″ can mean 42 arcseconds (or sometimes, 42 seconds of time, e.g. on some digital cameras).
• 7″ can mean 7 inches.

The triple prime (‴, Unicode 0x2034) can mean the third derivative of a function. Similarly, the quadruple prime (⁗, Unicode 0x2057) can mean the fourth derivative of a function. 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.

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

References: Unicode NamesList (rather large)