The prime symbol ( ′ ), double prime symbol ( ″ ), triple prime symbol ( ‴ ) etc. are used to designate several different units, and for various other purposes in mathematics, the sciences and linguistics. The prime symbol should not be confused with the apostrophe, single quotation mark or acute accent; the double prime should not be confused with the double quotation mark.
In mathematics, the prime is generally used to generate more variable names for things which are similar, without resorting to subscripts—x′ generally means something related to x. For example, if a point is represented by the Cartesian coordinates (x, y), then that point rotated, translated or reflected might be represented as (x′, y′). The prime symbol is not related to prime numbers.
Usually, the meaning of x′ is defined when it is first used, but sometimes its meaning is assumed to be understood:
In physics, the prime is used to denote variables after an event. For example, vA′ would indicate the velocity of object A after an event. It is also commonly used in relativity: The event at (x, y, z, t) in frame S has coordinates (x′, y′, z′, t′) in frame S′.
In molecular biology, the prime is used to denote the positions of carbon on a ring of deoxyribose or ribose. The prime distinguishes places on these two chemicals, rather than places on other parts of DNA or RNA, like phosphate groups or nucleic acids. Thus, when indicating the direction of movement of an enzyme along a string of DNA, biologists will say that it moves from the 5′ end to the 3′ end, because these carbons are hanging from the ends of the molecule. Prime can also be used to indicate which position a molecule has attached to, such as “5′-monophosphate”.
The prime is also used in X-bar theory instead of a bar to indicate bar-levels in syntactic structures, because the bar is difficult to typeset. This is still read as "X bar", not "X prime".
Some X-bar notations use a double-prime (standing in for a double-bar) to indicate a phrasal level, indicated in most notations by "XP".
Unicode and HTML representations of the prime and related symbols are as follows.
|Prime ( ′ )||U+2032|
|Double prime ( ″ )||U+2033|
|Triple prime ( ‴ )||U+2034||–|
|Quadruple prime ( ⁗ )||U+2057||–|
|Modifier letter prime ( ʹ )||U+02B9||–|
|Modifier letter double prime ( ʺ )||U+02BA||–|
When the character set used does not include the prime or double prime character (e.g., ISO 8859-1 is commonly assumed on IRC), they are often respectively approximated by normal or italic apostrophes and quotation marks. In LaTeX math mode,
f' (f with an apostrophe) is rendered as . Furthermore, LaTeX provides an oversized prime symbol,
prime () for use in subscripts. For example,
f_prime^prime appears as .